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Polytope of Type {2,12,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,2,10}*960
if this polytope has a name.
Group : SmallGroup(960,11208)
Rank : 5
Schlafli Type : {2,12,2,10}
Number of vertices, edges, etc : 2, 12, 12, 10, 10
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,2,10,2} of size 1920
Vertex Figure Of :
   {2,2,12,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,2,5}*480, {2,6,2,10}*480
   3-fold quotients : {2,4,2,10}*320
   4-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
   5-fold quotients : {2,12,2,2}*192
   6-fold quotients : {2,4,2,5}*160, {2,2,2,10}*160
   8-fold quotients : {2,3,2,5}*120
   10-fold quotients : {2,6,2,2}*96
   12-fold quotients : {2,2,2,5}*80
   15-fold quotients : {2,4,2,2}*64
   20-fold quotients : {2,3,2,2}*48
   30-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,4,10}*1920, {4,12,2,10}*1920a, {2,12,2,20}*1920, {2,24,2,10}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14);;
s2 := ( 3, 9)( 4, 6)( 5,13)( 7,10)( 8,11)(12,14);;
s3 := (17,18)(19,20)(21,22)(23,24);;
s4 := (15,19)(16,17)(18,23)(20,21)(22,24);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(24)!(1,2);
s1 := Sym(24)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14);
s2 := Sym(24)!( 3, 9)( 4, 6)( 5,13)( 7,10)( 8,11)(12,14);
s3 := Sym(24)!(17,18)(19,20)(21,22)(23,24);
s4 := Sym(24)!(15,19)(16,17)(18,23)(20,21)(22,24);
poly := sub<Sym(24)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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