Polytope of Type {5,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6}*120c
if this polytope has a name.
Group : SmallGroup(120,35)
Rank : 3
Schlafli Type : {5,6}
Number of vertices, edges, etc : 10, 30, 12
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,6,2} of size 240
   {5,6,4} of size 480
   {5,6,6} of size 720
   {5,6,8} of size 960
   {5,6,10} of size 1200
   {5,6,12} of size 1440
   {5,6,14} of size 1680
   {5,6,16} of size 1920
Vertex Figure Of :
   {2,5,6} of size 240
   {3,5,6} of size 1320
   {4,5,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,6}*240b, {10,6}*240c, {10,6}*240d
   4-fold covers : {10,12}*480c, {10,12}*480d, {5,12}*480, {10,6}*480c
   6-fold covers : {10,6}*720b, {15,6}*720c, {15,6}*720d
   8-fold covers : {10,24}*960c, {10,24}*960d, {10,12}*960c, {20,6}*960c, {10,12}*960d, {20,6}*960d, {10,6}*960b
   10-fold covers : {5,6}*1200b, {5,30}*1200b, {10,30}*1200b
   12-fold covers : {10,12}*1440e, {10,12}*1440f, {15,12}*1440a, {15,12}*1440b, {10,6}*1440f, {30,6}*1440e, {30,6}*1440f
   14-fold covers : {10,42}*1680b, {35,6}*1680c
   16-fold covers : {10,48}*1920c, {10,48}*1920d, {20,12}*1920g, {10,24}*1920d, {40,6}*1920f, {10,12}*1920c, {20,6}*1920d, {20,12}*1920k, {20,12}*1920l, {20,12}*1920m, {10,24}*1920f, {40,6}*1920h, {5,6}*1920b
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);;
s1 := ( 1, 4)( 2, 7)( 3,11)( 5,10)( 6, 9)( 8,12);;
s2 := ( 1, 3)( 2, 6)( 8, 9)(10,11);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);
s1 := Sym(12)!( 1, 4)( 2, 7)( 3,11)( 5,10)( 6, 9)( 8,12);
s2 := Sym(12)!( 1, 3)( 2, 6)( 8, 9)(10,11);
poly := sub<Sym(12)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0 >;

References : None.
to this polytope