Polytope of Type {4,2,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,10,6}*960
if this polytope has a name.
Group : SmallGroup(960,11219)
Rank : 5
Schlafli Type : {4,2,10,6}
Number of vertices, edges, etc : 4, 4, 10, 30, 6
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,10,6,2} of size 1920
Vertex Figure Of :
   {2,4,2,10,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,10,6}*480
   3-fold quotients : {4,2,10,2}*320
   5-fold quotients : {4,2,2,6}*192
   6-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
   10-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   12-fold quotients : {2,2,5,2}*80
   15-fold quotients : {4,2,2,2}*64
   20-fold quotients : {2,2,2,3}*48
   30-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,10,6}*1920, {4,2,10,12}*1920, {4,2,20,6}*1920a, {8,2,10,6}*1920
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 9,10)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)
(31,32)(33,34);;
s3 := ( 5, 9)( 6,13)( 7,17)( 8,15)(10,19)(11,23)(12,21)(14,25)(16,29)(18,27)
(22,33)(24,31)(28,30)(32,34);;
s4 := ( 5,11)( 6, 7)( 8,12)( 9,21)(10,22)(13,15)(14,16)(17,23)(18,24)(19,31)
(20,32)(25,27)(26,28)(29,33)(30,34);;
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*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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)!(2,3);
s1 := Sym(34)!(1,2)(3,4);
s2 := Sym(34)!( 9,10)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30)(31,32)(33,34);
s3 := Sym(34)!( 5, 9)( 6,13)( 7,17)( 8,15)(10,19)(11,23)(12,21)(14,25)(16,29)
(18,27)(22,33)(24,31)(28,30)(32,34);
s4 := Sym(34)!( 5,11)( 6, 7)( 8,12)( 9,21)(10,22)(13,15)(14,16)(17,23)(18,24)
(19,31)(20,32)(25,27)(26,28)(29,33)(30,34);
poly := sub<Sym(34)|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*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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