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Polytope of Type {10,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,24}*960
if this polytope has a name.
Group : SmallGroup(960,8150)
Rank : 4
Schlafli Type : {10,2,24}
Number of vertices, edges, etc : 10, 10, 24, 24
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,2,24,2} of size 1920
Vertex Figure Of :
   {2,10,2,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,24}*480, {10,2,12}*480
   3-fold quotients : {10,2,8}*320
   4-fold quotients : {5,2,12}*240, {10,2,6}*240
   5-fold quotients : {2,2,24}*192
   6-fold quotients : {5,2,8}*160, {10,2,4}*160
   8-fold quotients : {5,2,6}*120, {10,2,3}*120
   10-fold quotients : {2,2,12}*96
   12-fold quotients : {5,2,4}*80, {10,2,2}*80
   15-fold quotients : {2,2,8}*64
   16-fold quotients : {5,2,3}*60
   20-fold quotients : {2,2,6}*48
   24-fold quotients : {5,2,2}*40
   30-fold quotients : {2,2,4}*32
   40-fold quotients : {2,2,3}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,4,24}*1920a, {20,2,24}*1920, {10,2,48}*1920
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (12,13)(14,15)(16,19)(17,21)(18,20)(22,25)(23,27)(24,26)(29,32)(30,31)
(33,34);;
s3 := (11,17)(12,14)(13,23)(15,18)(16,20)(19,29)(21,24)(22,26)(25,33)(27,30)
(28,31)(32,34);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(34)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(34)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(34)!(12,13)(14,15)(16,19)(17,21)(18,20)(22,25)(23,27)(24,26)(29,32)
(30,31)(33,34);
s3 := Sym(34)!(11,17)(12,14)(13,23)(15,18)(16,20)(19,29)(21,24)(22,26)(25,33)
(27,30)(28,31)(32,34);
poly := sub<Sym(34)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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