Polytope of Type {12,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,10}*480
if this polytope has a name.
Group : SmallGroup(480,1087)
Rank : 4
Schlafli Type : {12,2,10}
Number of vertices, edges, etc : 12, 12, 10, 10
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2,10,2} of size 960
   {12,2,10,4} of size 1920
Vertex Figure Of :
   {2,12,2,10} of size 960
   {4,12,2,10} of size 1920
   {4,12,2,10} of size 1920
   {4,12,2,10} of size 1920
   {3,12,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,2,5}*240, {6,2,10}*240
   3-fold quotients : {4,2,10}*160
   4-fold quotients : {3,2,10}*120, {6,2,5}*120
   5-fold quotients : {12,2,2}*96
   6-fold quotients : {4,2,5}*80, {2,2,10}*80
   8-fold quotients : {3,2,5}*60
   10-fold quotients : {6,2,2}*48
   12-fold quotients : {2,2,5}*40
   15-fold quotients : {4,2,2}*32
   20-fold quotients : {3,2,2}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,20}*960, {12,4,10}*960, {24,2,10}*960
   3-fold covers : {36,2,10}*1440, {12,6,10}*1440a, {12,6,10}*1440b, {12,2,30}*1440
   4-fold covers : {12,4,20}*1920, {12,8,10}*1920a, {24,4,10}*1920a, {12,8,10}*1920b, {24,4,10}*1920b, {12,4,10}*1920a, {12,2,40}*1920, {24,2,20}*1920, {48,2,10}*1920, {12,4,10}*1920b
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (15,16)(17,18)(19,20)(21,22);;
s3 := (13,17)(14,15)(16,21)(18,19)(20,22);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(22)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(22)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(22)!(15,16)(17,18)(19,20)(21,22);
s3 := Sym(22)!(13,17)(14,15)(16,21)(18,19)(20,22);
poly := sub<Sym(22)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope