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Polytope of Type {6,4,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,2,5}*480a
if this polytope has a name.
Group : SmallGroup(480,1097)
Rank : 5
Schlafli Type : {6,4,2,5}
Number of vertices, edges, etc : 6, 12, 4, 5, 5
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,4,2,5,2} of size 960
Vertex Figure Of :
   {2,6,4,2,5} of size 960
   {3,6,4,2,5} of size 1440
   {4,6,4,2,5} of size 1920
   {3,6,4,2,5} of size 1920
   {4,6,4,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,2,5}*240
   3-fold quotients : {2,4,2,5}*160
   4-fold quotients : {3,2,2,5}*120
   6-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4,2,5}*960a, {6,8,2,5}*960, {6,4,2,10}*960a
   3-fold covers : {18,4,2,5}*1440a, {6,12,2,5}*1440a, {6,12,2,5}*1440c, {6,4,2,15}*1440a
   4-fold covers : {12,8,2,5}*1920a, {24,4,2,5}*1920a, {12,8,2,5}*1920b, {24,4,2,5}*1920b, {12,4,2,5}*1920a, {6,16,2,5}*1920, {6,4,4,10}*1920, {12,4,2,10}*1920a, {6,4,2,20}*1920a, {6,8,2,10}*1920, {6,4,2,5}*1920b
Permutation Representation (GAP) :
s0 := ( 3, 4)( 6, 7)( 9,10)(11,12);;
s1 := ( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,11);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,11)(10,12);;
s3 := (14,15)(16,17);;
s4 := (13,14)(15,16);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(17)!( 3, 4)( 6, 7)( 9,10)(11,12);
s1 := Sym(17)!( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,11);
s2 := Sym(17)!( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,11)(10,12);
s3 := Sym(17)!(14,15)(16,17);
s4 := Sym(17)!(13,14)(15,16);
poly := sub<Sym(17)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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