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Polytope of Type {10,2,24,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,24,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235347)
Rank : 5
Schlafli Type : {10,2,24,2}
Number of vertices, edges, etc : 10, 10, 24, 24, 2
Order of s0s1s2s3s4 : 120
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,24,2}*960, {10,2,12,2}*960
   3-fold quotients : {10,2,8,2}*640
   4-fold quotients : {5,2,12,2}*480, {10,2,6,2}*480
   5-fold quotients : {2,2,24,2}*384
   6-fold quotients : {5,2,8,2}*320, {10,2,4,2}*320
   8-fold quotients : {5,2,6,2}*240, {10,2,3,2}*240
   10-fold quotients : {2,2,12,2}*192
   12-fold quotients : {5,2,4,2}*160, {10,2,2,2}*160
   15-fold quotients : {2,2,8,2}*128
   16-fold quotients : {5,2,3,2}*120
   20-fold quotients : {2,2,6,2}*96
   24-fold quotients : {5,2,2,2}*80
   30-fold quotients : {2,2,4,2}*64
   40-fold quotients : {2,2,3,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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);;
s4 := (35,36);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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(36)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(36)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(36)!(12,13)(14,15)(16,19)(17,21)(18,20)(22,25)(23,27)(24,26)(29,32)
(30,31)(33,34);
s3 := Sym(36)!(11,17)(12,14)(13,23)(15,18)(16,20)(19,29)(21,24)(22,26)(25,33)
(27,30)(28,31)(32,34);
s4 := Sym(36)!(35,36);
poly := sub<Sym(36)|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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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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