https://hal.archives-ouvertes.fr/hal-02398953
Tip revision: c33910a29d53f4e137c225b21a8d59e43327cbf9 authored by Software Heritage on 08 December 2019, 12:26:32 UTC
hal: Deposit 351 in collection hal
hal: Deposit 351 in collection hal
Tip revision: c33910a
res_m7-13%42_save
Testing group m7-13%42
arg(t3)/2pi=13/6
arg(t3)/2pi num: 1
arg(t3)/2pi den: 6
tau^3 as rootof: (1+i*sqrt(3))/2
zeta=rootof([1,0],[1,1,1,1,1,1,1])
Computed taugen, d=42
p=7
t=13/42
zeta interval=[0.623489801858733530523..0.623489801858733530528]+[0.781831482468029808705..0.781831482468029808711]*i
zeta=rootof([1,0],[1,1,1,1,1,1,1])
Checked, not -1 nor 1
min pol of zeta: z^6+z^5+z^4+z^3+z^2+z+1
zeta in field: 56532/97567*x^11+402066/97567*x^10+3215919/195134*x^9+8708161/195134*x^8+17482141/195134*x^7+26623177/195134*x^6+15284969/97567*x^5+24394027/195134*x^4+9303385/195134*x^3-2372447/195134*x^2-1686277/195134*x+367635/195134
arg_t3/2pi: 1/6
t3ro=rootof([1,0],[1,-1,1])
t3 int: [0.499999999999999999999999999999999997..0.500000000000000000000000000000000003]+[0.866025403784438646763723170752936181..0.866025403784438646763723170752936186]*i
pol_t3ro=z^2-z+1
t3 in field: -56532/97567*x^11-402066/97567*x^10-3215919/195134*x^9-8708161/195134*x^8-17482141/195134*x^7-26623177/195134*x^6-15284969/97567*x^5-24394027/195134*x^4-9303385/195134*x^3+2372447/195134*x^2+1881411/195134*x-172501/195134
t3c in field: (113064*x^11+804132*x^10+3215919*x^9+8708161*x^8+17482141*x^7+26623177*x^6+30569938*x^5+24394027*x^4+9303385*x^3-2372447*x^2-1881411*x+367635)/195134
Defining taugen of group: rootof([1,0],[1,1,0,-1,-1,0,1,0,-1,-1,0,1,1])
(0.988830826225+0.149042266176*i)
x is a root of x^12+8*x^11+35*x^10+104*x^9+230*x^8+392*x^7+519*x^6+518*x^5+349*x^4+118*x^3-6*x+1
R1 has order 7
H=[[(30909*x^11+225267*x^10+935532*x^9+2643893*x^8+5589215*x^7+9064230*x^6+11337923*x^5+10416068*x^4+5977758*x^3+1198262*x^2-569912*x+216722)/195134,(-143973*x^11-1029399*x^10-4151451*x^9-11352054*x^8-23071356*x^7-35687407*x^6-41907861*x^5-34810095*x^4-15281143*x^3+1174185*x^2+2256189*x-389223)/195134,(235449*x^11+1691736*x^10+6837057*x^9+18750595*x^8+38232150*x^7+59437303*x^6+70337857*x^5+59359461*x^4+27466384*x^3-116258*x^2-2939338*x+316474)/195134],[(113064*x^11+804132*x^10+3215919*x^9+8708161*x^8+17482141*x^7+26623177*x^6+30569938*x^5+24394027*x^4+9303385*x^3-2372447*x^2-1686277*x+172501)/195134,(30909*x^11+225267*x^10+935532*x^9+2643893*x^8+5589215*x^7+9064230*x^6+11337923*x^5+10416068*x^4+5977758*x^3+1198262*x^2-569912*x+216722)/195134,(-143973*x^11-1029399*x^10-4151451*x^9-11352054*x^8-23071356*x^7-35687407*x^6-41907861*x^5-34810095*x^4-15281143*x^3+1174185*x^2+2256189*x-389223)/195134],[(-213444*x^11-1545453*x^10-6266414*x^9-17230740*x^8-35180052*x^7-54733455*x^6-64743063*x^5-54549978*x^4-25017384*x^3+491036*x^2+2732296*x-480699)/195134,(113064*x^11+804132*x^10+3215919*x^9+8708161*x^8+17482141*x^7+26623177*x^6+30569938*x^5+24394027*x^4+9303385*x^3-2372447*x^2-1686277*x+172501)/195134,(30909*x^11+225267*x^10+935532*x^9+2643893*x^8+5589215*x^7+9064230*x^6+11337923*x^5+10416068*x^4+5977758*x^3+1198262*x^2-569912*x+216722)/195134]]
R1=[[(113064*x^11+804132*x^10+3215919*x^9+8708161*x^8+17482141*x^7+26623177*x^6+30569938*x^5+24394027*x^4+9303385*x^3-2372447*x^2-1686277*x+367635)/195134,1,(-113064*x^11-804132*x^10-3215919*x^9-8708161*x^8-17482141*x^7-26623177*x^6-30569938*x^5-24394027*x^4-9303385*x^3+2372447*x^2+1881411*x-367635)/195134],[0,1,0],[0,0,1]]
J=[[0,0,(-122385*x^11-887604*x^10-3621138*x^9-10042434*x^8-20750009*x^7-32814126*x^6-39767919*x^5-34965434*x^4-18162999*x^3-2256189*x^2+1057927*x+51161)/195134],[1,0,0],[0,1,0]]
R1, R2 braid with order 3
P has order 6
K.genasrootof=rootof([1,0],poly1[1,8,35,104,230,392,519,518,349,118,0,-6,1])
Sto j with rootof([1,0],poly1[1,8,35,104,230,392,519,518,349,118,0,-6,1])
Computations will take place in a number field of degree 12
R1*J = P has order 6
hopefully this is an integer (or at least rational): 1
P^2 has a repeated eigenvalue
Other eigenvector is positive, this is a reflection in a complex line
p0=[1,(113064*x^11+804132*x^10+3215919*x^9+8708161*x^8+17482141*x^7+26623177*x^6+30569938*x^5+24394027*x^4+9303385*x^3-2372447*x^2-1881411*x+367635)/195134,(113064*x^11+804132*x^10+3215919*x^9+8708161*x^8+17482141*x^7+26623177*x^6+30569938*x^5+24394027*x^4+9303385*x^3-2372447*x^2-1881411*x+172501)/195134]
<p0,p0>=-2*s^5+20*s^4-68*s^3+86*s^2-26*s+4 ([-1.9553233049005141802789715317360344526219..-1.9553233049005141802789715317360344519059]
Check p0 fixed by P? OK
Power 2 of P is a complex reflection (or parabolic)
Creating braid relation for Vector [1] and Vector [2]
1 and 2 braid with order 3
Creating braid relation for Vector [1] and Vector [2,3,-2]
1 and 2,3,-2 braid with order 3
Creating braid relation for Vector [1] and Vector [-3,2,3]
1 and -3,2,3 braid with order 3
Creating braid relation for Vector [1] and Vector [2,3,2,-3,-2]
1 and 2,3,2,-3,-2 braid with order 3
Relations:
1,2,1,-2,-1,-2
2,1,2,-1,-2,-1
2,3,2,-3,-2,-3
3,2,3,-2,-3,-2
3,1,3,-1,-3,-1
1,3,1,-3,-1,-3
1,2,3,-2,1,2,-3,-2,-1,2,-3,-2
2,3,-2,1,2,3,-2,-1,2,-3,-2,-1
2,3,1,-3,2,3,-1,-3,-2,3,-1,-3
3,1,-3,2,3,1,-3,-2,3,-1,-3,-2
3,1,2,-1,3,1,-2,-1,-3,1,-2,-1
1,2,-1,3,1,2,-1,-3,1,-2,-1,-3
1,-3,2,3,1,-3,-2,3,-1,-3,-2,3
-3,2,3,1,-3,2,3,-1,-3,-2,3,-1
2,-1,3,1,2,-1,-3,1,-2,-1,-3,1
-1,3,1,2,-1,3,1,-2,-1,-3,1,-2
3,-2,1,2,3,-2,-1,2,-3,-2,-1,2
-2,1,2,3,-2,1,2,-3,-2,-1,2,-3
1,2,3,2,-3,-2,1,2,3,-2,-3,-2,-1,2,3,-2,-3,-2
2,3,2,-3,-2,1,2,3,2,-3,-2,-1,2,3,-2,-3,-2,-1
2,3,1,3,-1,-3,2,3,1,-3,-1,-3,-2,3,1,-3,-1,-3
3,1,3,-1,-3,2,3,1,3,-1,-3,-2,3,1,-3,-1,-3,-2
3,1,2,1,-2,-1,3,1,2,-1,-2,-1,-3,1,2,-1,-2,-1
1,2,1,-2,-1,3,1,2,1,-2,-1,-3,1,2,-1,-2,-1,-3
Creating initial prism...
Will now compute vertices for [3] 1 | 2; 3; 2,3,-2
Product of order 42
Braid length 3
Adding [3] 1 | 2; 3; 2,3,-2
Adding [3] 1,2,-1 | 1,3,-1; 1; 3
Adding [3] 1,2,3,-2,-1 | 2; 1,2,-1; 1
Adding [3] 1,2,3,1,-3,-2,-1 | 1,3,-1; 1,2,3,-2,-1; 1,2,-1
Adding [3] -3,2,3 | 2; -3,-2,1,2,3; 1,-3,2,3,-1
Adding [3] 3 | -3,1,3; -3,2,3; -3,1,2,-1,3
Expanding family of prisms...
There are now 6 faces.
Will now compute vertices for [3] 1 | 1,2,3,-2,-1; 1,2,-1; 1,2,3,2,-3,-2,-1
Product of order 42
Braid length 3
Adding [3] 1 | 1,2,3,-2,-1; 1,2,-1; 1,3,-1
Adding [3] 1,2,-1 | 1,2,3,1,-3,-2,-1; 1,2,3,-2,-1; 2
Adding [3] 1,2,3,-2,-1 | 1,2,3,1,2,-1,-3,-2,-1; 1,2,3,1,-3,-2,-1; 1,3,-1
Adding [3] 1,2,3,1,-3,-2,-1 | 1,2,3,1,2,3,-2,-1,-3,-2,-1; 1,2,3,1,2,-1,-3,-2,-1; 2
Adding [3] -3,2,3 | 1; 3; -3,1,3
Adding [3] 3 | 1,2,-1; 1; 2
Will now compute vertices for [3] 2 | 1; 2,3,-2; 1,2,3,-2,-1
Product of order 42
Braid length 3
Adding [3] 2 | 1; 2,3,-2; 1,2,3,-2,-1
Adding [3] 1,3,-1 | 1,2,-1; 3; 1,2,3,1,-3,-2,-1
There are now 14 faces.
Will now compute vertices for [3] 1,3,-1 | 1,2,3,-2,-1; 1; 1,2,3,-2,1,2,-3,-2,-1
Product of order 42
Braid length 3
Adding [3] 1,3,-1 | 1,2,3,-2,-1; 1; 2,3,-2
Adding [3] 2 | 1,2,3,1,-3,-2,-1; 1,2,-1; 3
There are now 16 faces.
The polytope has no free ridge!
0,1,2,3,4,5
6,7,8,9,10,11
12,13
14,15
Done exporting face data
#0: [3] 1 | 2; 3; 2,3,-2
paired with [3] 1 | 1,2,3,-2,-1; 1,2,-1; 1,3,-1
#1: [3] 1,2,-1 | 1,3,-1; 1; 3
paired with [3] 1,2,-1 | 1,2,3,1,-3,-2,-1; 1,2,3,-2,-1; 2
#2: [3] 1,2,3,-2,-1 | 2; 1,2,-1; 1
paired with [3] 1,2,3,-2,-1 | 1,2,3,1,2,-1,-3,-2,-1; 1,2,3,1,-3,-2,-1; 1,3,-1
#3: [3] 1,2,3,1,-3,-2,-1 | 1,3,-1; 1,2,3,-2,-1; 1,2,-1
paired with [3] 1,2,3,1,-3,-2,-1 | 1,2,3,1,2,3,-2,-1,-3,-2,-1; 1,2,3,1,2,-1,-3,-2,-1; 2
#4: [3] -3,2,3 | 2; -3,-2,1,2,3; 1,-3,2,3,-1
paired with [3] -3,2,3 | 1; 3; -3,1,3
#5: [3] 3 | -3,1,3; -3,2,3; -3,1,2,-1,3
paired with [3] 3 | 1,2,-1; 1; 2
#6: [3] 1 | 1,2,3,-2,-1; 1,2,-1; 1,3,-1
[inverse] paired with [3] 1 | 2; 3; 2,3,-2
#7: [3] 1,2,-1 | 1,2,3,1,-3,-2,-1; 1,2,3,-2,-1; 2
[inverse] paired with [3] 1,2,-1 | 1,3,-1; 1; 3
#8: [3] 1,2,3,-2,-1 | 1,2,3,1,2,-1,-3,-2,-1; 1,2,3,1,-3,-2,-1; 1,3,-1
[inverse] paired with [3] 1,2,3,-2,-1 | 2; 1,2,-1; 1
#9: [3] 1,2,3,1,-3,-2,-1 | 1,2,3,1,2,3,-2,-1,-3,-2,-1; 1,2,3,1,2,-1,-3,-2,-1; 2
[inverse] paired with [3] 1,2,3,1,-3,-2,-1 | 1,3,-1; 1,2,3,-2,-1; 1,2,-1
#10: [3] -3,2,3 | 1; 3; -3,1,3
[inverse] paired with [3] -3,2,3 | 2; -3,-2,1,2,3; 1,-3,2,3,-1
#11: [3] 3 | 1,2,-1; 1; 2
[inverse] paired with [3] 3 | -3,1,3; -3,2,3; -3,1,2,-1,3
#12: [3] 2 | 1; 2,3,-2; 1,2,3,-2,-1
[inverse] paired with [3] 2 | 1,2,3,1,-3,-2,-1; 1,2,-1; 3
#13: [3] 1,3,-1 | 1,2,-1; 3; 1,2,3,1,-3,-2,-1
[inverse] paired with [3] 1,3,-1 | 1,2,3,-2,-1; 1; 2,3,-2
#14: [3] 1,3,-1 | 1,2,3,-2,-1; 1; 2,3,-2
paired with [3] 1,3,-1 | 1,2,-1; 3; 1,2,3,1,-3,-2,-1
#15: [3] 2 | 1,2,3,1,-3,-2,-1; 1,2,-1; 3
paired with [3] 2 | 1; 2,3,-2; 1,2,3,-2,-1
List of pairings:
Face #0 --> 6
Face #1 --> 7
Face #2 --> 8
Face #3 --> 9
Face #4 --> 10
Face #5 --> 11
Face #6 --> 0
Face #7 --> 1
Face #8 --> 2
Face #9 --> 3
Face #10 --> 4
Face #11 --> 5
Face #12 --> 15
Face #13 --> 14
Face #14 --> 13
Face #15 --> 12
Collected 24 vertices...
The vertices come in 4 P-orbits.
Orbit #0: Vector [0,1,2,3,4,5]
Vert #0 is on 0,2,6,10,12,14
and on following mirrors:
Vector [1]
Vector [1,2,3,-2,1,2,3,-2,1,2,3,-2]
Orbit #1: Vector [6,7,8,9,10,11]
Vert #6 is on 0,1,2,6,11,12
and on following mirrors:
Vector [1]
Vector [1,2,1,2,1,2]
Orbit #2: Vector [12,13,14,15,16,17]
Vert #12 is on 0,1,6,10,11,14
and on following mirrors:
Vector [1]
Vector [1,3,1,3,1,3]
Orbit #3: Vector [18,19,20,21,22,23]
Vert #18 is on 0,4,9,11,12,15
and on following mirrors:
Vector [2,3,2,3,2,3]
Vector [2]
vertex #0 is on: Vector [0,2,6,10,12,14]
Applying pairing for face #0
image by pairing is vertex #0, which is on: Vector [0,2,6,10,12,14]
v#0 --(0)--> v#0
v#0 --(6)--> v#0
v#1 --(1)--> v#1
v#1 --(7)--> v#1
v#2 --(2)--> v#2
v#2 --(8)--> v#2
v#3 --(3)--> v#3
v#3 --(9)--> v#3
v#4 --(4)--> v#4
v#4 --(10)--> v#4
v#5 --(5)--> v#5
v#5 --(11)--> v#5
(image is in orbit #0)
Applying pairing for face #2
image by pairing is vertex #4, which is on: Vector [4,0,10,8,12,14]
v#0 --(2)--> v#4
v#4 --(8)--> v#0
v#1 --(3)--> v#5
v#5 --(9)--> v#1
v#2 --(4)--> v#0
v#0 --(10)--> v#2
v#3 --(5)--> v#1
v#1 --(11)--> v#3
v#4 --(0)--> v#2
v#2 --(6)--> v#4
v#5 --(1)--> v#3
v#3 --(7)--> v#5
(image is in orbit #0)
Applying pairing for face #6
image by pairing is vertex #0, which is on: Vector [0,2,6,10,12,14]
v#0 --(6)--> v#0
v#0 --(0)--> v#0
v#1 --(7)--> v#1
v#1 --(1)--> v#1
v#2 --(8)--> v#2
v#2 --(2)--> v#2
v#3 --(9)--> v#3
v#3 --(3)--> v#3
v#4 --(10)--> v#4
v#4 --(4)--> v#4
v#5 --(11)--> v#5
v#5 --(5)--> v#5
(image is in orbit #0)
Applying pairing for face #10
image by pairing is vertex #2, which is on: Vector [2,4,8,6,12,14]
v#0 --(10)--> v#2
v#2 --(4)--> v#0
v#1 --(11)--> v#3
v#3 --(5)--> v#1
v#2 --(6)--> v#4
v#4 --(0)--> v#2
v#3 --(7)--> v#5
v#5 --(1)--> v#3
v#4 --(8)--> v#0
v#0 --(2)--> v#4
v#5 --(9)--> v#1
v#1 --(3)--> v#5
(image is in orbit #0)
Applying pairing for face #12
image by pairing is vertex #1, which is on: Vector [1,3,7,11,13,15]
v#0 --(12)--> v#1
v#1 --(15)--> v#0
Interesting, a vertex has smaller P-orbit than the face..
v#1 --(13)--> v#2
v#2 --(14)--> v#1
v#2 --(12)--> v#3
v#3 --(15)--> v#2
v#3 --(13)--> v#4
v#4 --(14)--> v#3
v#4 --(12)--> v#5
v#5 --(15)--> v#4
v#5 --(13)--> v#0
v#0 --(14)--> v#5
(image is in orbit #0)
Applying pairing for face #14
image by pairing is vertex #5, which is on: Vector [5,1,11,9,13,15]
v#0 --(14)--> v#5
v#5 --(13)--> v#0
Interesting, a vertex has smaller P-orbit than the face..
v#1 --(15)--> v#0
v#0 --(12)--> v#1
v#2 --(14)--> v#1
v#1 --(13)--> v#2
v#3 --(15)--> v#2
v#2 --(12)--> v#3
v#4 --(14)--> v#3
v#3 --(13)--> v#4
v#5 --(15)--> v#4
v#4 --(12)--> v#5
(image is in orbit #0)
vertex #6 is on: Vector [0,1,2,6,11,12]
Applying pairing for face #0
image by pairing is vertex #6, which is on: Vector [0,1,2,6,11,12]
v#6 --(0)--> v#6
v#6 --(6)--> v#6
v#7 --(1)--> v#7
v#7 --(7)--> v#7
v#8 --(2)--> v#8
v#8 --(8)--> v#8
v#9 --(3)--> v#9
v#9 --(9)--> v#9
v#10 --(4)--> v#10
v#10 --(10)--> v#10
v#11 --(5)--> v#11
v#11 --(11)--> v#11
(image is in orbit #1)
Applying pairing for face #1
image by pairing is vertex #20, which is on: Vector [2,0,11,7,12,15]
v#6 --(1)--> v#20
v#20 --(7)--> v#6
v#7 --(2)--> v#21
v#21 --(8)--> v#7
v#8 --(3)--> v#22
v#22 --(9)--> v#8
v#9 --(4)--> v#23
v#23 --(10)--> v#9
v#10 --(5)--> v#18
v#18 --(11)--> v#10
v#11 --(0)--> v#19
v#19 --(6)--> v#11
(image is in orbit #3)
Applying pairing for face #2
image by pairing is vertex #16, which is on: Vector [4,5,10,8,9,14]
v#6 --(2)--> v#16
v#16 --(8)--> v#6
v#7 --(3)--> v#17
v#17 --(9)--> v#7
v#8 --(4)--> v#12
v#12 --(10)--> v#8
v#9 --(5)--> v#13
v#13 --(11)--> v#9
v#10 --(0)--> v#14
v#14 --(6)--> v#10
v#11 --(1)--> v#15
v#15 --(7)--> v#11
(image is in orbit #2)
Applying pairing for face #6
image by pairing is vertex #6, which is on: Vector [0,1,2,6,11,12]
v#6 --(6)--> v#6
v#6 --(0)--> v#6
v#7 --(7)--> v#7
v#7 --(1)--> v#7
v#8 --(8)--> v#8
v#8 --(2)--> v#8
v#9 --(9)--> v#9
v#9 --(3)--> v#9
v#10 --(10)--> v#10
v#10 --(4)--> v#10
v#11 --(11)--> v#11
v#11 --(5)--> v#11
(image is in orbit #1)
Applying pairing for face #11
image by pairing is vertex #23, which is on: Vector [5,3,8,10,13,14]
v#6 --(11)--> v#23
v#23 --(5)--> v#6
v#7 --(6)--> v#18
v#18 --(0)--> v#7
v#8 --(7)--> v#19
v#19 --(1)--> v#8
v#9 --(8)--> v#20
v#20 --(2)--> v#9
v#10 --(9)--> v#21
v#21 --(3)--> v#10
v#11 --(10)--> v#22
v#22 --(4)--> v#11
(image is in orbit #3)
Applying pairing for face #12
image by pairing is vertex #13, which is on: Vector [1,2,7,11,6,15]
v#6 --(12)--> v#13
v#13 --(15)--> v#6
Interesting, a vertex has smaller P-orbit than the face..
v#7 --(13)--> v#14
v#14 --(14)--> v#7
v#8 --(12)--> v#15
v#15 --(15)--> v#8
v#9 --(13)--> v#16
v#16 --(14)--> v#9
v#10 --(12)--> v#17
v#17 --(15)--> v#10
v#11 --(13)--> v#12
v#12 --(14)--> v#11
(image is in orbit #2)
vertex #12 is on: Vector [0,1,6,10,11,14]
Applying pairing for face #0
image by pairing is vertex #12, which is on: Vector [0,1,6,10,11,14]
v#12 --(0)--> v#12
v#12 --(6)--> v#12
v#13 --(1)--> v#13
v#13 --(7)--> v#13
v#14 --(2)--> v#14
v#14 --(8)--> v#14
v#15 --(3)--> v#15
v#15 --(9)--> v#15
v#16 --(4)--> v#16
v#16 --(10)--> v#16
v#17 --(5)--> v#17
v#17 --(11)--> v#17
(image is in orbit #2)
Applying pairing for face #1
image by pairing is vertex #22, which is on: Vector [4,2,7,9,12,15]
v#12 --(1)--> v#22
v#22 --(7)--> v#12
v#13 --(2)--> v#23
v#23 --(8)--> v#13
v#14 --(3)--> v#18
v#18 --(9)--> v#14
v#15 --(4)--> v#19
v#19 --(10)--> v#15
v#16 --(5)--> v#20
v#20 --(11)--> v#16
v#17 --(0)--> v#21
v#21 --(6)--> v#17
(image is in orbit #3)
Applying pairing for face #6
image by pairing is vertex #12, which is on: Vector [0,1,6,10,11,14]
v#12 --(6)--> v#12
v#12 --(0)--> v#12
v#13 --(7)--> v#13
v#13 --(1)--> v#13
v#14 --(8)--> v#14
v#14 --(2)--> v#14
v#15 --(9)--> v#15
v#15 --(3)--> v#15
v#16 --(10)--> v#16
v#16 --(4)--> v#16
v#17 --(11)--> v#17
v#17 --(5)--> v#17
(image is in orbit #2)
Applying pairing for face #10
image by pairing is vertex #8, which is on: Vector [2,3,4,8,7,12]
v#12 --(10)--> v#8
v#8 --(4)--> v#12
v#13 --(11)--> v#9
v#9 --(5)--> v#13
v#14 --(6)--> v#10
v#10 --(0)--> v#14
v#15 --(7)--> v#11
v#11 --(1)--> v#15
v#16 --(8)--> v#6
v#6 --(2)--> v#16
v#17 --(9)--> v#7
v#7 --(3)--> v#17
(image is in orbit #1)
Applying pairing for face #11
image by pairing is vertex #19, which is on: Vector [1,5,10,6,13,14]
v#12 --(11)--> v#19
v#19 --(5)--> v#12
v#13 --(6)--> v#20
v#20 --(0)--> v#13
v#14 --(7)--> v#21
v#21 --(1)--> v#14
v#15 --(8)--> v#22
v#22 --(2)--> v#15
v#16 --(9)--> v#23
v#23 --(3)--> v#16
v#17 --(10)--> v#18
v#18 --(4)--> v#17
(image is in orbit #3)
Applying pairing for face #14
image by pairing is vertex #11, which is on: Vector [5,0,1,11,10,13]
v#12 --(14)--> v#11
v#11 --(13)--> v#12
Interesting, a vertex has smaller P-orbit than the face..
v#13 --(15)--> v#6
v#6 --(12)--> v#13
v#14 --(14)--> v#7
v#7 --(13)--> v#14
v#15 --(15)--> v#8
v#8 --(12)--> v#15
v#16 --(14)--> v#9
v#9 --(13)--> v#16
v#17 --(15)--> v#10
v#10 --(12)--> v#17
(image is in orbit #1)
vertex #18 is on: Vector [0,4,9,11,12,15]
Applying pairing for face #0
image by pairing is vertex #7, which is on: Vector [1,2,3,7,6,13]
v#18 --(0)--> v#7
v#7 --(6)--> v#18
v#19 --(1)--> v#8
v#8 --(7)--> v#19
v#20 --(2)--> v#9
v#9 --(8)--> v#20
v#21 --(3)--> v#10
v#10 --(9)--> v#21
v#22 --(4)--> v#11
v#11 --(10)--> v#22
v#23 --(5)--> v#6
v#6 --(11)--> v#23
(image is in orbit #1)
Applying pairing for face #4
image by pairing is vertex #17, which is on: Vector [5,0,11,9,10,15]
v#18 --(4)--> v#17
v#17 --(10)--> v#18
v#19 --(5)--> v#12
v#12 --(11)--> v#19
v#20 --(0)--> v#13
v#13 --(6)--> v#20
v#21 --(1)--> v#14
v#14 --(7)--> v#21
v#22 --(2)--> v#15
v#15 --(8)--> v#22
v#23 --(3)--> v#16
v#16 --(9)--> v#23
(image is in orbit #2)
Applying pairing for face #9
image by pairing is vertex #14, which is on: Vector [2,3,8,6,7,14]
v#18 --(9)--> v#14
v#14 --(3)--> v#18
v#19 --(10)--> v#15
v#15 --(4)--> v#19
v#20 --(11)--> v#16
v#16 --(5)--> v#20
v#21 --(6)--> v#17
v#17 --(0)--> v#21
v#22 --(7)--> v#12
v#12 --(1)--> v#22
v#23 --(8)--> v#13
v#13 --(2)--> v#23
(image is in orbit #2)
Applying pairing for face #11
image by pairing is vertex #10, which is on: Vector [4,5,0,10,9,12]
v#18 --(11)--> v#10
v#10 --(5)--> v#18
v#19 --(6)--> v#11
v#11 --(0)--> v#19
v#20 --(7)--> v#6
v#6 --(1)--> v#20
v#21 --(8)--> v#7
v#7 --(2)--> v#21
v#22 --(9)--> v#8
v#8 --(3)--> v#22
v#23 --(10)--> v#9
v#9 --(4)--> v#23
(image is in orbit #1)
Applying pairing for face #12
image by pairing is vertex #18, which is on: Vector [0,4,9,11,12,15]
v#18 --(12)--> v#18
v#18 --(15)--> v#18
Interesting, a vertex has smaller P-orbit than the face..
v#19 --(13)--> v#19
v#19 --(14)--> v#19
v#20 --(12)--> v#20
v#20 --(15)--> v#20
v#21 --(13)--> v#21
v#21 --(14)--> v#21
v#22 --(12)--> v#22
v#22 --(15)--> v#22
v#23 --(13)--> v#23
v#23 --(14)--> v#23
(image is in orbit #3)
Applying pairing for face #15
image by pairing is vertex #18, which is on: Vector [0,4,9,11,12,15]
v#18 --(15)--> v#18
v#18 --(12)--> v#18
Interesting, a vertex has smaller P-orbit than the face..
v#19 --(14)--> v#19
v#19 --(13)--> v#19
v#20 --(15)--> v#20
v#20 --(12)--> v#20
v#21 --(14)--> v#21
v#21 --(13)--> v#21
v#22 --(15)--> v#22
v#22 --(12)--> v#22
v#23 --(14)--> v#23
v#23 --(13)--> v#23
(image is in orbit #3)
Vertex #0 is on 0,2,6,10,12,14
Vertex #1 is on 1,3,7,11,13,15
Vertex #2 is on 2,4,8,6,12,14
Vertex #3 is on 3,5,9,7,13,15
Vertex #4 is on 4,0,10,8,12,14
Vertex #5 is on 5,1,11,9,13,15
Vertex #6 is on 0,1,2,6,11,12
Vertex #7 is on 1,2,3,7,6,13
Vertex #8 is on 2,3,4,8,7,12
Vertex #9 is on 3,4,5,9,8,13
Vertex #10 is on 4,5,0,10,9,12
Vertex #11 is on 5,0,1,11,10,13
Vertex #12 is on 0,1,6,10,11,14
Vertex #13 is on 1,2,7,11,6,15
Vertex #14 is on 2,3,8,6,7,14
Vertex #15 is on 3,4,9,7,8,15
Vertex #16 is on 4,5,10,8,9,14
Vertex #17 is on 5,0,11,9,10,15
Vertex #18 is on 0,4,9,11,12,15
Vertex #19 is on 1,5,10,6,13,14
Vertex #20 is on 2,0,11,7,12,15
Vertex #21 is on 3,1,6,8,13,14
Vertex #22 is on 4,2,7,9,12,15
Vertex #23 is on 5,3,8,10,13,14
Will now construct edges...
Face #0
Adding edge... v#10,18 (which is on faces 4,0,9,12)
Adding edge... v#11,19 (which is on faces 5,1,10,13)
Adding edge... v#6,20 (which is on faces 0,2,11,12)
Adding edge... v#7,21 (which is on faces 1,3,6,13)
Adding edge... v#8,22 (which is on faces 2,4,7,12)
Adding edge... v#9,23 (which is on faces 3,5,8,13)
Adding edge... v#18,17 (which is on faces 0,9,11,15)
Adding edge... v#19,12 (which is on faces 1,10,6,14)
Adding edge... v#20,13 (which is on faces 2,11,7,15)
Adding edge... v#21,14 (which is on faces 3,6,8,14)
Adding edge... v#22,15 (which is on faces 4,7,9,15)
Adding edge... v#23,16 (which is on faces 5,8,10,14)
Adding edge... v#17,10 (which is on faces 5,0,9,10)
Adding edge... v#12,11 (which is on faces 0,1,10,11)
Adding edge... v#13,6 (which is on faces 1,2,11,6)
Adding edge... v#14,7 (which is on faces 2,3,6,7)
Adding edge... v#15,8 (which is on faces 3,4,7,8)
Adding edge... v#16,9 (which is on faces 4,5,8,9)
Adding edge... v#0,6 (which is on faces 0,2,6,12)
Adding edge... v#1,7 (which is on faces 1,3,7,13)
Adding edge... v#2,8 (which is on faces 2,4,8,12)
Adding edge... v#3,9 (which is on faces 3,5,9,13)
Adding edge... v#4,10 (which is on faces 4,0,10,12)
Adding edge... v#5,11 (which is on faces 5,1,11,13)
Adding edge... v#6,12 (which is on faces 0,1,6,11)
Adding edge... v#7,13 (which is on faces 1,2,7,6)
Adding edge... v#8,14 (which is on faces 2,3,8,7)
Adding edge... v#9,15 (which is on faces 3,4,9,8)
Adding edge... v#10,16 (which is on faces 4,5,10,9)
Adding edge... v#11,17 (which is on faces 5,0,11,10)
Adding edge... v#12,0 (which is on faces 0,6,10,14)
Adding edge... v#13,1 (which is on faces 1,7,11,15)
Adding edge... v#14,2 (which is on faces 2,8,6,14)
Adding edge... v#15,3 (which is on faces 3,9,7,15)
Adding edge... v#16,4 (which is on faces 4,10,8,14)
Adding edge... v#17,5 (which is on faces 5,11,9,15)
Adding edge... v#0,4 (which is on faces 0,10,12,14)
Adding edge... v#1,5 (which is on faces 1,11,13,15)
Adding edge... v#2,0 (which is on faces 2,6,12,14)
Adding edge... v#3,1 (which is on faces 3,7,13,15)
Adding edge... v#4,2 (which is on faces 4,8,12,14)
Adding edge... v#5,3 (which is on faces 5,9,13,15)
Adding edge... v#20,18 (which is on faces 0,11,12,15)
Adding edge... v#21,19 (which is on faces 1,6,13,14)
Adding edge... v#22,20 (which is on faces 2,7,12,15)
Adding edge... v#23,21 (which is on faces 3,8,13,14)
Adding edge... v#18,22 (which is on faces 4,9,12,15)
Adding edge... v#19,23 (which is on faces 5,10,13,14)
Face #6
Face #12
Face #14
Created 48 edges...
Will now construct ridges...
Face #0
vertex #18: Vector [0,4,9,11,12,15]
vertex #10: Vector [4,5,0,10,9,12]
vertex #4: Vector [4,0,10,8,12,14]
vertex #0: Vector [0,2,6,10,12,14]
vertex #6: Vector [0,1,2,6,11,12]
vertex #20: Vector [2,0,11,7,12,15]
Adding ridge w/ vertices 18,10,4,0,6,20 (which is on faces 0,12)
Adding ridge w/ vertices 19,11,5,1,7,21 (which is on faces 1,13)
Adding ridge w/ vertices 20,6,0,2,8,22 (which is on faces 2,12)
Adding ridge w/ vertices 21,7,1,3,9,23 (which is on faces 3,13)
Adding ridge w/ vertices 22,8,2,4,10,18 (which is on faces 4,12)
Adding ridge w/ vertices 23,9,3,5,11,19 (which is on faces 5,13)
vertex #17: Vector [5,0,11,9,10,15]
vertex #18: Vector [0,4,9,11,12,15]
vertex #20: Vector [2,0,11,7,12,15]
vertex #6: Vector [0,1,2,6,11,12]
vertex #12: Vector [0,1,6,10,11,14]
vertex #11: Vector [5,0,1,11,10,13]
Adding ridge w/ vertices 17,18,20,6,12,11 (which is on faces 0,11)
Adding ridge w/ vertices 12,19,21,7,13,6 (which is on faces 1,6)
Adding ridge w/ vertices 13,20,22,8,14,7 (which is on faces 2,7)
Adding ridge w/ vertices 14,21,23,9,15,8 (which is on faces 3,8)
Adding ridge w/ vertices 15,22,18,10,16,9 (which is on faces 4,9)
Adding ridge w/ vertices 16,23,19,11,17,10 (which is on faces 5,10)
vertex #10: Vector [4,5,0,10,9,12]
vertex #17: Vector [5,0,11,9,10,15]
vertex #11: Vector [5,0,1,11,10,13]
vertex #12: Vector [0,1,6,10,11,14]
vertex #0: Vector [0,2,6,10,12,14]
vertex #4: Vector [4,0,10,8,12,14]
Adding ridge w/ vertices 10,17,11,12,0,4 (which is on faces 0,10)
Adding ridge w/ vertices 11,12,6,13,1,5 (which is on faces 1,11)
Adding ridge w/ vertices 6,13,7,14,2,0 (which is on faces 2,6)
Adding ridge w/ vertices 7,14,8,15,3,1 (which is on faces 3,7)
Adding ridge w/ vertices 8,15,9,16,4,2 (which is on faces 4,8)
Adding ridge w/ vertices 9,16,10,17,5,3 (which is on faces 5,9)
vertex #0: Vector [0,2,6,10,12,14]
vertex #6: Vector [0,1,2,6,11,12]
vertex #12: Vector [0,1,6,10,11,14]
Adding ridge w/ vertices 0,6,12 (which is on faces 0,6)
Adding ridge w/ vertices 1,7,13 (which is on faces 1,7)
Adding ridge w/ vertices 2,8,14 (which is on faces 2,8)
Adding ridge w/ vertices 3,9,15 (which is on faces 3,9)
Adding ridge w/ vertices 4,10,16 (which is on faces 4,10)
Adding ridge w/ vertices 5,11,17 (which is on faces 5,11)
vertex #10: Vector [4,5,0,10,9,12]
vertex #18: Vector [0,4,9,11,12,15]
vertex #17: Vector [5,0,11,9,10,15]
Adding ridge w/ vertices 10,18,17 (which is on faces 0,9)
Adding ridge w/ vertices 11,19,12 (which is on faces 1,10)
Adding ridge w/ vertices 6,20,13 (which is on faces 2,11)
Adding ridge w/ vertices 7,21,14 (which is on faces 3,6)
Adding ridge w/ vertices 8,22,15 (which is on faces 4,7)
Adding ridge w/ vertices 9,23,16 (which is on faces 5,8)
Face #6
vertex #14: Vector [2,3,8,6,7,14]
vertex #21: Vector [3,1,6,8,13,14]
vertex #19: Vector [1,5,10,6,13,14]
vertex #12: Vector [0,1,6,10,11,14]
vertex #0: Vector [0,2,6,10,12,14]
vertex #2: Vector [2,4,8,6,12,14]
Adding ridge w/ vertices 14,21,19,12,0,2 (which is on faces 6,14)
Adding ridge w/ vertices 15,22,20,13,1,3 (which is on faces 7,15)
Adding ridge w/ vertices 16,23,21,14,2,4 (which is on faces 8,14)
Adding ridge w/ vertices 17,18,22,15,3,5 (which is on faces 9,15)
Adding ridge w/ vertices 12,19,23,16,4,0 (which is on faces 10,14)
Adding ridge w/ vertices 13,20,18,17,5,1 (which is on faces 11,15)
Face #12
vertex #22: Vector [4,2,7,9,12,15]
vertex #20: Vector [2,0,11,7,12,15]
vertex #18: Vector [0,4,9,11,12,15]
Adding ridge w/ vertices 22,20,18 (which is on faces 12,15)
Adding ridge w/ vertices 23,21,19 (which is on faces 13,14)
vertex #2: Vector [2,4,8,6,12,14]
vertex #0: Vector [0,2,6,10,12,14]
vertex #4: Vector [4,0,10,8,12,14]
Adding ridge w/ vertices 2,0,4 (which is on faces 12,14)
Adding ridge w/ vertices 3,1,5 (which is on faces 13,15)
Face #14
Created 40 ridges...
Will now check that the 1-skeleton is embedded (there are 8 orbits of edges)
Studying edge #0, whose endpoints are vertices of: 4,0,9,12... check!
Studying edge #6, whose endpoints are vertices of: 0,9,11,15... check!
Studying edge #12, whose endpoints are vertices of: 5,0,9,10... check!
Studying edge #18, whose endpoints are vertices of: 0,2,6,12... check!
Studying edge #24, whose endpoints are vertices of: 0,1,6,11... check!
Studying edge #30, whose endpoints are vertices of: 0,6,10,14... check!
Studying edge #36, whose endpoints are vertices of: 0,10,12,14... check!
Studying edge #42, whose endpoints are vertices of: 0,11,12,15... check!
If you read this, the 1-skeleton is embedded!
Will now check that G-polygons defining ridges are embedded
be patient, there are 8 P-orbits of ridges...
Ridge P-orbit #0...
Checking ridge on faces #0 and 12
Real spines don't intersect
Will construct third bisector (Giraud)
Eq #0 is 0...
For eq#1, found 2 critical point(s)..
outside (t1<t1min)
outside (t1<t1min)
For eq#2, found 3 critical point(s)..
outside (t1<t1min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t2<t2min)
For eq#3, found 1 critical point(s)..
outside (t2<t2min)
For eq#4, found 3 critical point(s)..
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t1<t1min)
outside (t2<t2min)
For eq#5, found 1 critical point(s)..
outside (t1<t1min)
For eq#6, found 0 critical point(s)..
For eq#7, found 2 critical point(s)..
outside (t1<t1min)
outside (t2<t2min)
For eq#8, found 1 critical point(s)..
outside (t2<t2min)
For eq#9, found 1 critical point(s)..
outside (t1<t1min)
For eq#10, found 3 critical point(s)..
outside (t1<t1min)
outside (t1<t1min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
For eq#11, found 3 critical point(s)..
outside (t1<t1min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t1<t1min)
Eq #12 is 0...
For eq#13, found 1 critical point(s)..
outside (t1<t1min)
For eq#14, found 1 critical point(s)..
outside (t1<t1min)
For eq#15, found 0 critical point(s)..
Ridge P-orbit #1...
Checking ridge on faces #0 and 11
Real spines don't intersect
Will construct third bisector (Giraud)
Eq #0 is 0...
For eq#1, found 3 critical point(s)..
outside (t2<t2min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t1<t1min)
For eq#2, found 1 critical point(s)..
outside (t1<t1min)
For eq#3, found 1 critical point(s)..
outside (t2<t2min)
For eq#4, found 1 critical point(s)..
outside (t1<t1min)
For eq#5, found 0 critical point(s)..
For eq#6, found 0 critical point(s)..
For eq#7, found 1 critical point(s)..
outside (t2<t2min)
For eq#8, found 1 critical point(s)..
outside (t1<t1min)
For eq#9, found 1 critical point(s)..
outside (t1<t1min)
For eq#10, found 3 critical point(s)..
outside (t1<t1min)
outside (t1<t1min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
Eq #11 is 0...
For eq#12, found 3 critical point(s)..
outside (t1<t1min)
outside (t1<t1min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
For eq#13, found 2 critical point(s)..
outside (t1<t1min)
outside (t2<t2min)
For eq#14, found 2 critical point(s)..
outside (t1<t1min)
outside (t1<t1min)
For eq#15, found 3 critical point(s)..
outside (t1<t1min)
outside (t2<t2min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
Ridge P-orbit #2...
Checking ridge on faces #0 and 10
Real spines don't intersect
Will construct third bisector (Giraud)
Eq #0 is 0...
For eq#1, found 1 critical point(s)..
outside (t1<t1min)
For eq#2, found 2 critical point(s)..
outside (t1<t1min)
outside (t1<t1min)
For eq#3, found 1 critical point(s)..
outside (t2<t2min)
For eq#4, found 0 critical point(s)..
For eq#5, found 3 critical point(s)..
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t2<t2min)
outside (t1<t1min)
For eq#6, found 0 critical point(s)..
For eq#7, found 1 critical point(s)..
outside (t1<t1min)
For eq#8, found 2 critical point(s)..
outside (t1<t1min)
outside (t2<t2min)
For eq#9, found 1 critical point(s)..
outside (t1<t1min)
Eq #10 is 0...
For eq#11, found 3 critical point(s)..
outside (t1<t1min)
outside (t1<t1min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
For eq#12, found 3 critical point(s)..
outside (t1<t1min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t1<t1min)
For eq#13, found 1 critical point(s)..
outside (t2<t2min)
For eq#14, found 3 critical point(s)..
outside (t1<t1min)
outside (t2<t2min)
CRITICAL POINT IS INSIDE, but the equation is negative there!
For eq#15, found 1 critical point(s)..
outside (t1<t1min)
Ridge P-orbit #3...
Checking ridge on faces #0 and 6
Same mirror, this gives the common slice
For this ridge there is nothing to do, it is enough to check the 1-skeleton!
Ridge P-orbit #4...
Checking ridge on faces #0 and 9
Top of face#9 is same as top face of #0
this gives the common slice
For this ridge there is nothing to do, it is enough to check the 1-skeleton!
Ridge P-orbit #5...
Checking ridge on faces #6 and 14
Real spines don't intersect
Will construct third bisector (Giraud)
For eq#0, found 0 critical point(s)..
For eq#1, found 3 critical point(s)..
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t1<t1min)
outside (t1<t1min)
For eq#2, found 3 critical point(s)..
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t1<t1min)
outside (t1<t1min)
For eq#3, found 1 critical point(s)..
outside (t1<t1min)
For eq#4, found 1 critical point(s)..
outside (t2<t2min)
For eq#5, found 2 critical point(s)..
outside (t1<t1min)
outside (t2<t2min)
Eq #6 is 0...
For eq#7, found 1 critical point(s)..
outside (t1<t1min)
For eq#8, found 3 critical point(s)..
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t1<t1min)
outside (t2<t2min)
For eq#9, found 1 critical point(s)..
outside (t2<t2min)
For eq#10, found 3 critical point(s)..
CRITICAL POINT IS INSIDE, but the equation is negative there!
outside (t2<t2min)
outside (t1<t1min)
For eq#11, found 2 critical point(s)..
outside (t1<t1min)
outside (t1<t1min)
For eq#12, found 1 critical point(s)..
outside (t1<t1min)
For eq#13, found 0 critical point(s)..
Eq #14 is 0...
For eq#15, found 1 critical point(s)..
outside (t1<t1min)
Ridge P-orbit #6...
Checking ridge on faces #12 and 15
Same mirror, this gives the common slice
For this ridge there is nothing to do, it is enough to check the 1-skeleton!
Ridge P-orbit #7...
Checking ridge on faces #12 and 14
Top of face#14 is same as top face of #12
this gives the common slice
For this ridge there is nothing to do, it is enough to check the 1-skeleton!
* *
\_/
If you read this, the program checked that the polytope for m7-13%42 is embedded!
Used at most 30 digits to perform the computations.
Computing cycle for ridge on faces 0,12
0, 12
2, 6
8, 14
3, 13
Got back to the same ridge, word so far is 4,4,4,1,3,2,3,-2
Power 1 brings p0 back
Corresponding power is in <P>
(4,4,4,1,3,2,3,-2)^1=id on the ridge
(4,4,4,1,3,2,3,-2)^1=id
Check matrix OK
Computing cycle for ridge on faces 0,11
0, 11
1, 6
Got back to the same ridge, word so far is -4,1
Power 3 brings p0 back
Corresponding power is in <P>
(-4,1)^3=id on the ridge
(-4,1)^3=id (need to check angles)
Check matrix OK
Computing cycle for ridge on faces 0,6
Should compute angles!
0, 6
0, 6
Got back to the same ridge, word so far is 1
Power 7 brings p0 back
Corresponding power is in <P>
(1)^1=id on the ridge
(1)^7=id (need to check angles)
Rotation by 2*pi/7 (for complex refl)
Check matrix OK
Computing cycle for ridge on faces 0,9
Should compute angles!
0, 9
3, 6
Got back to the same ridge, word so far is 4,4,4,1
Power 42 brings p0 back
Corresponding power is in <P>
(4,4,4,1)^3=id on the ridge
(4,4,4,1)^42=id (need to check angles)
Angles: -14/42, -1/42
Longitudinal angle 2*pi*(-1/3)
Transversal angle 2*pi*(-1/42)
Integrality condition holds on this ridge!
Check matrix OK
Computing cycle for ridge on faces 12,15
Should compute angles!
12, 15
12, 15
Got back to the same ridge, word so far is -2
Power 7 brings p0 back
Corresponding power is in <P>
(-2)^1=id on the ridge
(-2)^7=id (need to check angles)
Rotation by 2*pi/-7 (for complex refl)
Check matrix OK
Ridge is invariant by P^2
Adding commutation relation with power of P: P^2*R2^-1*P^-2*R2
Computing cycle for ridge on faces 12,14
Should compute angles!
12, 14
13, 15
Got back to the same ridge, word so far is -4,-2
Power 42 brings p0 back
Corresponding power is in <P>
(-4,-2)^1=id on the ridge
(-4,-2)^42=id (need to check angles)
Rotation by 2*pi/42 (for complex refl)
Check matrix OK
Ridge is invariant by P^2
Adding commutation relation with power of P: P^2*P^-1*R2^-1*P^-2*R2*P
Wrote the presentation in GAP style in the file: pres/presm7-13%42.g
Will now compute e0
0 -> 0
via 1
0 -> 0
via 4,4,1,2,3,-2,-1
0 -> 0
via -1
0 -> 0
via -4,-4,-3,-2,3
0 -> 0
via -4,-2
0 -> 0
via 4,1,3,-1
1 -> 1
via 1
1 -> 3
via -4,-4,1,2,-1
1 -> 2
via 4,4,1,2,3,-2,-1
1 -> 1
via -1
1 -> 3
via 4,-3
1 -> 2
via -4,-2
2 -> 2
via 1
2 -> 3
via 4,4,1,2,-1
2 -> 2
via -1
2 -> 1
via -4,-4,-3,-2,3
2 -> 3
via -4,-3
2 -> 1
via 4,1,3,-1
3 -> 1
via -4,1
3 -> 2
via 4,-3,2,3
3 -> 2
via -4,-4,1,2,3,-1,-3,-2,-1
3 -> 1
via 4,4,-3
3 -> 3
via -2
3 -> 3
via 2
Vertex orbits (under side pairings, * denotes an ideal vertex):
[0], [1,3,2],
There are 2 orbits of vertices
Still need to compute the order of stabilizer (only when finite vertex!)
Computing stabilizer of vertex P-Orbit #0
On mirror of [3] 1 | 2; 3; 2,3,-2
On mirror of [3] 1 | 1,2,3,-2,-1; 1,2,-1; 1,3,-1
On top face of [3] 2 | 1; 2,3,-2; 1,2,3,-2,-1
(1,2,3,-2)^3 (refl of order 14)
On top face of [3] 1,3,-1 | 1,2,3,-2,-1; 1; 2,3,-2
(1,2,3,-2)^3 (refl of order 14)
Generators of stab:
1
(order 7)
(reflection in line)
Check!
4,4,1,2,3,-2,-1
(order 42)
(distinct eigenvalues)
Check!
-1
(order 7)
(reflection in line)
Check!
-4,-4,-3,-2,3
(order 42)
(distinct eigenvalues)
Check!
-4,-2
(order 42)
(reflection in line)
Check!
4,1,3,-1
(order 42)
(reflection in line)
Check!
Found 4 reflections
Orders: Vector [7,7,42,42]
Multipliers, exp(2*pi*i*...): [1/7,-1/7,1/42,-1/42]
There are some non-reflection generators...
Found two reflections of order 7, 42, that commute
Found a subgroup generated by two reflections, of order 294
center of order 294
The stabilizer is a 2-generator reflection group, computation is easy
(it has order 294)
Computing stabilizer of vertex P-Orbit #1
On mirror of [3] 1 | 2; 3; 2,3,-2
On top face of [3] 1,2,3,-2,-1 | 2; 1,2,-1; 1
(2,1,2,-1)^3 (refl of order 14)
On mirror of [3] 1 | 1,2,3,-2,-1; 1,2,-1; 1,3,-1
On top face of [3] 3 | 1,2,-1; 1; 2
(1,2)^3 (refl of order 14)
Generators of stab:
-1
(order 7)
(reflection in line)
Check!
1,-2,-1,4,4,4,-3
(order 7)
(reflection in line)
Check!
1,2,-3,-2,-1,-4,-4,-4,-2
(order 7)
(reflection in line)
Check!
1,2,-3,-2,-1,-4,-4,1,4,4,1,2,3,-2,-1
(order 7)
(reflection in line)
Check!
1,-2,-1,4,4,4,4,1,2,-1,4,4,1,2,3,-2,-1
(order 14)
(distinct eigenvalues)
Check!
1,2,-3,-2,-1,-4,-4,-1,4,4,1,2,3,-2,-1
(order 7)
(reflection in line)
Check!
-4,-4,-3,-2,3,4,4,1,2,3,-2,-1
(order 1)
-4,-4,-3,-2,3,4,4,1,2,3,-2,-1 is identity
1,-2,-1,4,-3,4,4,1,2,3,-2,-1
(order 14)
(distinct eigenvalues)
Check!
4,1,3,-1,4,4,1,2,3,-2,-1
(order 7)
(reflection in line)
Check!
-4,1,-4,-4,1,2,-1
(order 7)
(reflection in line)
Check!
1,2,-3,-2,-1,-4,-3,2,3,-4,-4,1,2,-1
(order 14)
(distinct eigenvalues)
Check!
1,2,-3,-2,-1,-4,-4,-4,-4,1,2,3,-1,-3,-2,-1,-4,-4,1,2,-1
(order 14)
(distinct eigenvalues)
Check!
4,4,-3,-4,-4,1,2,-1
(order 1)
4,4,-3,-4,-4,1,2,-1 is identity
1,-2,-1,4,4,-2,-4,-4,1,2,-1
(order 7)
(reflection in line)
Check!
1,-2,-1,4,4,2,-4,-4,1,2,-1
(order 7)
(reflection in line)
Check!
1
(order 7)
(reflection in line)
Check!
Found 2 reflections
Orders: Vector [7,7]
Multipliers, exp(2*pi*i*...): [-1/7,1/7]
There are some non-reflection generators...
Did not find any coherent pair of reflections
The stabilizer is a NOT 2-generator reflection group
I'm not quite sure how to get the order of stabilizer, will use brute force (this may take some time!)
Current nb of elements: 19
Current nb of elements: 57
Current nb of elements: 98
Current nb of elements: 98
Found a group with 98 elements
There are 19 reflections in this group
Current nb of elements: 98
Current nb of elements: 98
Found a group with 98 elements
Subgroup generated by reflections has order 98
The stabilizer is generated by reflections!
Will now compute e1
jo=10
je=17
Pairing for face #4 maps edge #0 to edge #12
This gives a map from P-orbit #0 to P-orbit #2, at index 0
Map: -3,2,3
jo=14
je=7
Pairing for face #0 maps edge #0 to edge #15
This gives a map from P-orbit #0 to P-orbit #2, at index 3
Map: -4,-4,-4,1
jo=21
je=14
Pairing for face #9 maps edge #0 to edge #9
This gives a map from P-orbit #0 to P-orbit #1, at index 3
Map: -4,-4,-4,1,2,3,-1,-3,-2,-1
jo=17
je=18
Pairing for face #12 maps edge #0 to edge #6
This gives a map from P-orbit #0 to P-orbit #1, at index 0
Map: -2
jo=7
je=21
Pairing for face #0 maps edge #6 to edge #3
This gives a map from P-orbit #1 to P-orbit #0, at index 3
Map: -4,-4,-4,1
jo=14
je=7
Pairing for face #9 maps edge #6 to edge #15
This gives a map from P-orbit #1 to P-orbit #2, at index 3
Map: -4,-4,-4,1,2,3,-1,-3,-2,-1
jo=10
je=17
Pairing for face #11 maps edge #6 to edge #12
This gives a map from P-orbit #1 to P-orbit #2, at index 0
Map: -3
jo=18
je=10
Pairing for face #15 maps edge #6 to edge #0
This gives a map from P-orbit #1 to P-orbit #0, at index 0
Map: 2
jo=17
je=18
Pairing for face #5 maps edge #12 to edge #6
This gives a map from P-orbit #2 to P-orbit #1, at index 0
Map: 3
jo=21
je=14
Pairing for face #0 maps edge #12 to edge #9
This gives a map from P-orbit #2 to P-orbit #1, at index 3
Map: -4,-4,-4,1
jo=7
je=21
Pairing for face #9 maps edge #12 to edge #3
This gives a map from P-orbit #2 to P-orbit #0, at index 3
Map: -4,-4,-4,1,2,3,-1,-3,-2,-1
jo=18
je=10
Pairing for face #10 maps edge #12 to edge #0
This gives a map from P-orbit #2 to P-orbit #0, at index 0
Map: -3,-2,3
jo=0
je=6
Pairing for face #0 maps edge #18 to edge #18
This gives a map from P-orbit #3 to P-orbit #3, at index 0
Map: 1
jo=4
je=16
Pairing for face #2 maps edge #18 to edge #34
This gives a map from P-orbit #3 to P-orbit #5, at index 4
Map: 4,4,1,2,3,-2,-1
jo=0
je=6
Pairing for face #6 maps edge #18 to edge #18
This gives a map from P-orbit #3 to P-orbit #3, at index 0
Map: -1
jo=1
je=13
Pairing for face #12 maps edge #18 to edge #31
This gives a map from P-orbit #3 to P-orbit #5, at index 1
Map: -4,-2
jo=6
je=12
Pairing for face #0 maps edge #24 to edge #24
This gives a map from P-orbit #4 to P-orbit #4, at index 0
Map: 1
jo=20
je=22
Pairing for face #1 maps edge #24 to edge #44
This gives a map from P-orbit #4 to P-orbit #7, at index 2
Map: -4,-4,1,2,-1
jo=6
je=12
Pairing for face #6 maps edge #24 to edge #24
This gives a map from P-orbit #4 to P-orbit #4, at index 0
Map: -1
jo=23
je=19
Pairing for face #11 maps edge #24 to edge #47
This gives a map from P-orbit #4 to P-orbit #7, at index 5
Map: 4,-3
jo=12
je=0
Pairing for face #0 maps edge #30 to edge #30
This gives a map from P-orbit #5 to P-orbit #5, at index 0
Map: 1
jo=12
je=0
Pairing for face #6 maps edge #30 to edge #30
This gives a map from P-orbit #5 to P-orbit #5, at index 0
Map: -1
jo=8
je=2
Pairing for face #10 maps edge #30 to edge #20
This gives a map from P-orbit #5 to P-orbit #3, at index 2
Map: -4,-4,-3,-2,3
jo=11
je=5
Pairing for face #14 maps edge #30 to edge #23
This gives a map from P-orbit #5 to P-orbit #3, at index 5
Map: 4,1,3,-1
jo=0
je=2
Pairing for face #0 maps edge #36 to edge #38
This gives a map from P-orbit #6 to P-orbit #6, at index 2
Map: -4,-4,1
jo=2
je=4
Pairing for face #10 maps edge #36 to edge #40
This gives a map from P-orbit #6 to P-orbit #6, at index 4
Map: 4,4,-3,-2,3
jo=1
je=5
Pairing for face #12 maps edge #36 to edge #37
This gives a map from P-orbit #6 to P-orbit #6, at index 1
Map: -4,-2
jo=5
je=3
Pairing for face #14 maps edge #36 to edge #41
This gives a map from P-orbit #6 to P-orbit #6, at index 5
Map: 4,1,3,-1
jo=13
je=7
Pairing for face #0 maps edge #42 to edge #25
This gives a map from P-orbit #7 to P-orbit #4, at index 1
Map: -4,1
jo=16
je=10
Pairing for face #11 maps edge #42 to edge #28
This gives a map from P-orbit #7 to P-orbit #4, at index 4
Map: 4,4,-3
jo=20
je=18
Pairing for face #12 maps edge #42 to edge #42
This gives a map from P-orbit #7 to P-orbit #7, at index 0
Map: -2
jo=20
je=18
Pairing for face #15 maps edge #42 to edge #42
This gives a map from P-orbit #7 to P-orbit #7, at index 0
Map: 2
Edge orbits (under side pairings):
[0,2,1], [3,5], [4,7], [6],
There are 4 orbits of edges
Still need to compute the order of stabilizer...
No element in this orbit is on mirror of power of P!
Computing stabilizer of edge P-Orbit #0
-3,-2,3,-4,-4,-4,1
1,2,3,1,-3,-2,-1,4,4,4,-2
-4,-4,-4,1,-4,-4,-4,1,2,3,-1,-3,-2,-1
-3,-2,3,-4,-4,-4,1,2,3,-1,-3,-2,-1,-4,-4,-4,1,2,3,-1,-3,-2,-1
-3,-2,-4,-4,-4,1,2,3,-1,-3,-2,-1
2,-4,-4,-4,1,2,3,-1,-3,-2,-1
1,2,3,1,-3,-2,-1,4,4,4,2,3
1,2,3,1,-3,-2,-3,2,3
-4,-4,-4,1,2,3,-1,-3,-2,-1,-3,2,3
Trivial elt!
Done computing stab
Generators of stab: (there are 10)
-3,-2,3,-4,-4,-4,1
(order 28) (distinct eigenvalues)
Check (edge is flipped)
1,2,3,1,-3,-2,-1,4,4,4,-2
(order 28) (distinct eigenvalues)
Check (edge is flipped)
-4,-4,-4,1,-4,-4,-4,1,2,3,-1,-3,-2,-1
(order 1)
-3,-2,3,-4,-4,-4,1,2,3,-1,-3,-2,-1,-4,-4,-4,1,2,3,-1,-3,-2,-1
(order 28) (distinct eigenvalues)
Check (edge is flipped)
-3,-2,-4,-4,-4,1,2,3,-1,-3,-2,-1
(order 1)
2,-4,-4,-4,1,2,3,-1,-3,-2,-1
(order 28) (distinct eigenvalues)
Check (edge is flipped)
1,2,3,1,-3,-2,-1,4,4,4,2,3
(order 1)
1,2,3,1,-3,-2,-3,2,3
(order 28) (distinct eigenvalues)
Check (edge is flipped)
-4,-4,-4,1,2,3,-1,-3,-2,-1,-3,2,3
(order 28) (distinct eigenvalues)
Check (edge is flipped)
Current nb of elements: 5
Current nb of elements: 9
Current nb of elements: 17
Current nb of elements: 28
Current nb of elements: 28
Found a group with 28 elements
Stab has order 28
There are 13 reflections in this group
Current nb of elements: 14
Found a group with 14 elements
Subgroup generated by reflections has order 14
The stabilizer is NOT generated by reflections, this will give a singular point of the quotient
No element in this orbit is on mirror of power of P!
Computing stabilizer of edge P-Orbit #3
-1
1,2,-3,-2,-1,-4,-4,-4,-2
1,2,-3,-2,-1,-4,-4,1,4,4,1,2,3,-2,-1
1,2,-3,-2,-1,-4,-4,-1,4,4,1,2,3,-2,-1
-4,-4,-3,-2,3,4,4,1,2,3,-2,-1
4,1,3,-1,4,4,1,2,3,-2,-1
1
Done computing stab
Generators of stab: (there are 7)
-1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
1,2,-3,-2,-1,-4,-4,-4,-2
(order 7) (reflection in line)
Check (edge is fixed pointwise)
1,2,-3,-2,-1,-4,-4,1,4,4,1,2,3,-2,-1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
1,2,-3,-2,-1,-4,-4,-1,4,4,1,2,3,-2,-1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
-4,-4,-3,-2,3,4,4,1,2,3,-2,-1
(order 1)
4,1,3,-1,4,4,1,2,3,-2,-1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
Current nb of elements: 5
Current nb of elements: 7
Current nb of elements: 7
Found a group with 7 elements
Stab has order 7
There are 6 reflections in this group
Current nb of elements: 7
Found a group with 7 elements
Subgroup generated by reflections has order 7
The stabilizer is generated by reflections!
Edge is orthogonal to mirror of P^2
No element in this orbit is on mirror of power of P!
Computing stabilizer of edge P-Orbit #4
-1
1,-2,-1,4,4,4,-3
-4,1,-4,-4,1,2,-1
4,4,-3,-4,-4,1,2,-1
1,-2,-1,4,4,-2,-4,-4,1,2,-1
1,-2,-1,4,4,2,-4,-4,1,2,-1
1
Done computing stab
Generators of stab: (there are 7)
-1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
1,-2,-1,4,4,4,-3
(order 7) (reflection in line)
Check (edge is fixed pointwise)
-4,1,-4,-4,1,2,-1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
4,4,-3,-4,-4,1,2,-1
(order 1)
1,-2,-1,4,4,-2,-4,-4,1,2,-1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
1,-2,-1,4,4,2,-4,-4,1,2,-1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
1
(order 7) (reflection in line)
Check (edge is fixed pointwise)
Current nb of elements: 5
Current nb of elements: 7
Current nb of elements: 7
Found a group with 7 elements
Stab has order 7
There are 6 reflections in this group
Current nb of elements: 7
Found a group with 7 elements
Subgroup generated by reflections has order 7
The stabilizer is generated by reflections!
Edge is orthogonal to mirror of P^2
No element in this orbit is on mirror of power of P!
Computing stabilizer of edge P-Orbit #6
Done computing stab
Generators of stab: (there are 4)
-4,-4,1
(order 84) (distinct eigenvalues)
Check (edge is flipped)
4,4,-3,-2,3
(order 84) (distinct eigenvalues)
Check (edge is flipped)
-4,-2
(order 42) (reflection in line)
Check (edge is fixed pointwise)
4,1,3,-1
(order 42) (reflection in line)
Check (edge is fixed pointwise)
Current nb of elements: 9
Current nb of elements: 17
Current nb of elements: 33
Current nb of elements: 65
Current nb of elements: 84
Current nb of elements: 84
Found a group with 84 elements
Stab has order 84
There are 41 reflections in this group
Current nb of elements: 42
Found a group with 42 elements
Subgroup generated by reflections has order 42
The stabilizer is NOT generated by reflections, this will give a singular point of the quotient
Will now compute e2
Ridge orbits to check: 0,1,2,3,4,5,6,7
Studying orbit Vector [0,1,2,3,4,5]
Computing cycle for ridge on faces 0,12
Ridge #0 is NOT invariant by P^2 (image is #2)
Ridge #2 is NOT invariant by P^2 (image is #16)
Ridge #14 is NOT invariant by P^2 (image is #34)
1->
1,2,3,-2,-1->
1,3,-1->
P^(-3)
Found a ridge with stabilizer of order 1
Ridge orbits to check: 1,3,4,6,7
Studying orbit Vector [6,7,8,9,10,11]
Computing cycle for ridge on faces 0,11
Ridge #0 is NOT invariant by P^2 (image is #8)
1->
P^(-1)
Found a ridge with stabilizer of order 3
Cyclic group generated by regular elliptic
this gives a singular point in the quotient
Ridge orbits to check: 3,4,6,7
Studying orbit Vector [18,19,20,21,22,23]
Computing cycle for ridge on faces 0,6
Ridge #0 is NOT invariant by P^2 (image is #20)
1->
P^(-0)
Found a ridge with stabilizer of order 7
(reflection in line)
Ridge orbits to check: 4,6,7
Studying orbit Vector [24,25,26,27,28,29]
Computing cycle for ridge on faces 0,9
Ridge #0 is NOT invariant by P^2 (image is #26)
1->
P^(-3)
Found a ridge with stabilizer of order 42
Cyclic group generated by regular elliptic
this gives a singular point in the quotient
Ridge orbits to check: 6,7
Studying orbit Vector [36,37]
Computing cycle for ridge on faces 12,15
Ridge #36 is invariant by P^2
Element in ridge orbit is stabilized by P^2.
Found ridge in orbit stabilized by P power!
Will start with orbit of 12,15, because it is fixed py power of P
-2->
P^(-0)
Elements in stab:
-2 (order 7) (reflection in line)
P^2 (this is a complex reflection)
Generators are reflections with orthogonal mirrors
Order is simply the product of the orders (21)
Ridge orbits to check: 7
Studying orbit Vector [38,39]
Computing cycle for ridge on faces 12,14
Ridge #38 is invariant by P^2
Element in ridge orbit is stabilized by P^2.
Found ridge in orbit stabilized by P power!
Will start with orbit of 12,14, because it is fixed py power of P
-2->
P^(-1)
Elements in stab:
-4,-2 (order 42) (reflection in line)
P^2 (this is a complex reflection)
Generators are reflections with orthogonal mirrors
Order is simply the product of the orders (126)
Will now compute e3
Will now compute e4
Euler 0-dim contribution: 2
Euler 1-dim contribution: 2
Euler 2-dim contribution: 6
Euler 3-dim contribution: 2
Euler 4-dim contribution: 1
Topological Euler characteristic: 5
Orbifold Euler 0-dim contribution: 2/147
Orbifold Euler 1-dim contribution: 1/3
Orbifold Euler 2-dim contribution: 14/9
Orbifold Euler 3-dim contribution: 4/3
Orbifold Euler 4-dim contribution: 1/6
Orbifold Euler characteristic: 61/882
Studying link for vertex #0
Ignoring digon, irrelevant for orientation check
Ignoring digon, irrelevant for orientation check
Studying link for vertex #6
Ignoring digon, irrelevant for orientation check
Ignoring digon, irrelevant for orientation check
Studying link for vertex #12
Ignoring digon, irrelevant for orientation check
Ignoring digon, irrelevant for orientation check
Studying link for vertex #18
Ignoring digon, irrelevant for orientation check
Ignoring digon, irrelevant for orientation check
Great! Vertex links are spheres!
The boundary of the polytope is a manifold.
1-skeleton has 24 vertices, 48 edges
Found 25 gens for pi_1 of 1-skeleton
Will write the presentation of the pi_1 of the boundary of the polytope in GAP style in the file: sphere/spherePresm7-13%42.g
(you should check that that group is trivial by simplifying it with GAP)
sigma=rootof([1,0],[1,1,0,-1,-1,0,1,0,-1,-1,0,1,1])
(0.988830826225+0.1490422661761744469293547152772175569096694389982224957595504011185284844321936038013265059043708919183312979919149129155019160677467165859084008790377335744671011154626245492723733297914137274494982092049690535805855747117546550239786656769541002452620778060364757727121428370796458371331456631740989359632*i)
Will now compute an upper bound for the degree of adjoint trace field..
tau^3=rootof([1,0],[1,1,0,-1,-1,0,1,0,-1,-1,0,1,1])
pm=poly1[1,1,0,-1,-1,0,1,0,-1,-1,0,1,1]
sigminpol x^12+x^11-x^9-x^8+x^6-x^4-x^3+x+1
Minimal polynomial of exp(2*pi*i/p): z^6+z^5+z^4+z^3+z^2+z+1
Degree of adjoint trace field is at most 6
K.minpol: x^12+8*x^11+35*x^10+104*x^9+230*x^8+392*x^7+519*x^6+518*x^5+349*x^4+118*x^3-6*x+1
K.realminpol: s^6-13*s^5+64*s^4-146*s^3+148*s^2-48*s+1
K.realgen: (22005*x^11+146283*x^10+570643*x^9+1519855*x^8+3052098*x^7+4703848*x^6+5594794*x^5+4809483*x^4+2449000*x^3+374778*x^2-207042*x+30909)/195134
K.realgenasrootof: rootof([[22005,146283,570643,1519855,3052098,4703848,5594794,4809483,2449000,374778,-207042,30909],[1,8,35,104,230,392,519,518,349,118,0,-6,1]])/195134
Values of |tr|^2 found
1: 2*s^5-20*s^4+68*s^3-86*s^2+24*s+7
1,1: -2*s^5+20*s^4-70*s^3+98*s^2-42*s+5
2,1: s^5-10*s^4+34*s^3-43*s^2+12*s+3
-2,1: 3*s^5-30*s^4+101*s^3-123*s^2+27*s+10
1,1,1: 2*s^3-12*s^2+18*s+1
-2,1,1: 2*s^5-20*s^4+66*s^3-74*s^2+6*s+10
-3,2,1: 5*s^5-50*s^4+169*s^3-210*s^2+57*s+8
4,2,1: 2*s^5-20*s^4+68*s^3-86*s^2+26*s+3
-3,-2,1: 2*s^5-20*s^4+67*s^3-80*s^2+15*s+8
4,-2,1: s
good traces: [5*s^5-50*s^4+169*s^3-210*s^2+57*s+8,2*s^5-20*s^4+68*s^3-86*s^2+26*s+3,s]
The adjoint trace field is equal to the upper bound, it has degree 6
It is generated by s
gentf as rootof: rootof([[22005,146283,570643,1519855,3052098,4703848,5594794,4809483,2449000,374778,-207042,30909],[1,8,35,104,230,392,519,518,349,118,0,-6,1]])/195134
min pol of gentf: a^6-13*a^5+64*a^4-146*a^3+148*a^2-48*a+1
Done computing 4 Galois conjugates of trace field generator
Other roots: [b^2-4*b+4,b^5-10*b^4+35*b^3-50*b^2+25*b,-b^5+10*b^4-34*b^3+43*b^2-13*b+3,-b^4+7*b^3-14*b^2+7*b+2]
Original signature ++-
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Non-arithmeticity index: 2
The group is NOT arithmetic, NA index 2
Done studying group m7-13%42
If you read this message, all requested checks were successful:
1-skeleton is embedded
2-skeleton is embedded
The boundary of the polytope should be a sphere
(to be completely sure, you should simplify the presentation using GAP)
Hypotheses of the Poincaré polyhedron theorem hold
I computed the Euler characteristic, it is 61/882
The group is cocompact
The group is non-arithmetic!
I will now draw pictures of the polyhedron, in projections onto the axes of P, one for each axis
The pictures will be stored in in the pics directory, they need to be compiled with asymptote.
Done drawing pics
Total time elapsed : 25m8s
