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Polytope of Type {3,2,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,10}*480
if this polytope has a name.
Group : SmallGroup(480,1097)
Rank : 5
Schlafli Type : {3,2,4,10}
Number of vertices, edges, etc : 3, 3, 4, 20, 10
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,4,10,2} of size 960
   {3,2,4,10,4} of size 1920
Vertex Figure Of :
   {2,3,2,4,10} of size 960
   {3,3,2,4,10} of size 1920
   {4,3,2,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,10}*240
   4-fold quotients : {3,2,2,5}*120
   5-fold quotients : {3,2,4,2}*96
   10-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,20}*960, {3,2,8,10}*960, {6,2,4,10}*960
   3-fold covers : {9,2,4,10}*1440, {3,2,12,10}*1440, {3,6,4,10}*1440, {3,2,4,30}*1440a
   4-fold covers : {3,2,8,20}*1920a, {3,2,4,40}*1920a, {3,2,8,20}*1920b, {3,2,4,40}*1920b, {3,2,4,20}*1920, {3,2,16,10}*1920, {6,4,4,10}*1920, {6,2,4,20}*1920, {12,2,4,10}*1920, {6,2,8,10}*1920, {3,4,4,10}*1920b
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 9,14)(10,15)(16,20)(17,21);;
s3 := ( 4, 5)( 6,10)( 7, 9)( 8,13)(11,17)(12,16)(14,19)(15,18)(20,23)(21,22);;
s4 := ( 4, 6)( 5, 9)( 7,11)( 8,14)(10,16)(13,18)(15,20)(19,22);;
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, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(23)!(2,3);
s1 := Sym(23)!(1,2);
s2 := Sym(23)!( 5, 8)( 9,14)(10,15)(16,20)(17,21);
s3 := Sym(23)!( 4, 5)( 6,10)( 7, 9)( 8,13)(11,17)(12,16)(14,19)(15,18)(20,23)
(21,22);
s4 := Sym(23)!( 4, 6)( 5, 9)( 7,11)( 8,14)(10,16)(13,18)(15,20)(19,22);
poly := sub<Sym(23)|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, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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