import graph3;
import three;
size(7.5cm,0);
pen p=black+1;
draw(unithemisphere,white+opacity(0.1));
currentprojection=orthographic((-8.71743084494e-15,-1.0,0.3));
draw(Arc((2.35883422863e-14,0.866025403784,0.707106781187),(0.25,0.433012701892,0.707106781187),(-0.25,0.433012701892,0.707106781187),(0,0,1),false),p);
draw(Arc((-0.75,0.433012701892,0.707106781187),(-0.25,0.433012701892,0.707106781187),(-0.5,0,0.707106781187),(0,0,1),false),p);
draw(Arc((-0.75,-0.433012701892,0.707106781187),(-0.5,0,0.707106781187),(-0.25,-0.433012701892,0.707106781187),(0,0,1),false),p);
draw(Arc((-2.05116019881e-14,-0.866025403784,0.707106781187),(-0.25,-0.433012701892,0.707106781187),(0.25,-0.433012701892,0.707106781187),(0,0,1),false),p);
draw(Arc((0.75,-0.433012701892,0.707106781187),(0.25,-0.433012701892,0.707106781187),(0.5,0,0.707106781187),(0,0,1),false),p);
draw(Arc((0.75,0.433012701892,0.707106781187),(0.5,0,0.707106781187),(0.25,0.433012701892,0.707106781187),(0,0,1),false),p);
draw(Arc((2.66650825845e-14,1.15470053838,-5.02429586779e-14),(0.5,0.866025403784,-5.02429586779e-14),(-0.5,0.866025403784,-5.02429586779e-14),(0,0,1),false),p);
label("$13\bar1$",(8.86205420349e-15,0.57735026919,-5.02429586779e-14));
draw(Arc((-1.0,0.57735026919,-5.02429586779e-14),(-0.5,0.866025403784,-5.02429586779e-14),(-1.0,0,-5.02429586779e-14),(0,0,1),false),p);
label("$13\bar1$",(-0.5,0.288675134595,-5.02429586779e-14));
draw(Arc((-1.0,-0.57735026919,-5.02429586779e-14),(-1.0,0,-5.02429586779e-14),(-0.5,-0.866025403784,-5.02429586779e-14),(0,0,1),false),p);
label("$13\bar1$",(-0.5,-0.288675134595,-5.02429586779e-14));
draw(Arc((-2.05116019881e-15,-1.15470053838,-5.02429586779e-14),(-0.5,-0.866025403784,-5.02429586779e-14),(0.5,-0.866025403784,-5.02429586779e-14),(0,0,1),false),p);
label("$13\bar1$",(7.38023071701e-15,-0.57735026919,-5.02429586779e-14));
draw(Arc((1.0,-0.57735026919,-5.02429586779e-14),(0.5,-0.866025403784,-5.02429586779e-14),(1.0,0,-5.02429586779e-14),(0,0,1),false),p);
label("$13\bar1$",(0.5,-0.288675134595,-5.02429586779e-14));
draw(Arc((1.0,0.57735026919,-5.02429586779e-14),(1.0,0,-5.02429586779e-14),(0.5,0.866025403784,-5.02429586779e-14),(0,0,1),false),p);
label("$13\bar1$",(0.5,0.288675134595,-5.02429586779e-14));
draw((0.25,0.433012701892,0.707106781187)--(0.5,0.866025403784,-5.02429586779e-14),p);
draw((-0.25,0.433012701892,0.707106781187)--(-0.5,0.866025403784,-3.01457752067e-14),p);
label("$123\bar212\bar3\bar2\bar1$",(-0.375,0.649519052838,0.353553390593),align=right);
draw((-0.5,0,0.707106781187)--(-1.0,0,-1.72484715322e-14),p);
label("$123\bar2\bar1$",(-0.75,0,0.353553390593),align=right);
draw((-0.25,-0.433012701892,0.707106781187)--(-0.5,-0.866025403784,-3.14018491737e-15),p);
label("$1$",(-0.375,-0.649519052838,0.353553390593),align=right);
draw((0.25,-0.433012701892,0.707106781187)--(0.5,-0.866025403784,-7.53644380168e-15),p);
label("$23\bar2$",(0.375,-0.649519052838,0.353553390593),align=right);
draw((0.5,0,0.707106781187)--(1.0,0,-4.11798947492e-14),p);
label("$2\bar3\bar2123\bar2$",(0.75,0,0.353553390593),align=right);
pen dp = blue+4;
pen dpi = red+4;
dot((0.25,0.433012701892,0.707106781187),dp);
dot((-0.25,0.433012701892,0.707106781187),dp);
dot((-0.5,0,0.707106781187),dp);
dot((-0.25,-0.433012701892,0.707106781187),dp);
dot((0.25,-0.433012701892,0.707106781187),dp);
dot((0.5,0,0.707106781187),dp);
dot((0.5,0.866025403784,-5.02429586779e-14),dpi);
dot((-0.5,0.866025403784,-3.01457752067e-14),dpi);
dot((-1.0,0,-1.72484715322e-14),dpi);
dot((-0.5,-0.866025403784,-3.14018491737e-15),dpi);
dot((0.5,-0.866025403784,-7.53644380168e-15),dpi);
dot((1.0,0,-4.11798947492e-14),dpi);
draw((0,0,0)--(0,0,0.707106781187),black+dashed);
draw((-0.25,-0.433012701892,0.707106781187)--(0,0,0.707106781187),black+dashed);
draw((0.25,-0.433012701892,0.707106781187)--(0,0,0.707106781187),black+dashed);
draw((-0.5,-0.866025403784,-3.14018491737e-15)--(0,0,0),black+dashed);
draw((0.5,-0.866025403784,-7.53644380168e-15)--(0,0,0),black+dashed);