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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,10,2}*960
if this polytope has a name.
Group : SmallGroup(960,11219)
Rank : 6
Schlafli Type : {3,2,4,10,2}
Number of vertices, edges, etc : 3, 3, 4, 20, 10, 2
Order of s₀s₁s₂s₃s₄s₅ : 60
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,4,10,2,2} of size 1920
Vertex Figure Of :
   {2,3,2,4,10,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,10,2}*480
   4-fold quotients : {3,2,2,5,2}*240
   5-fold quotients : {3,2,4,2,2}*192
   10-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,20,2}*1920, {3,2,4,10,4}*1920, {3,2,8,10,2}*1920, {6,2,4,10,2}*1920
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);;
s5 := (24,25);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
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(25)!(2,3);
s1 := Sym(25)!(1,2);
s2 := Sym(25)!( 5, 8)( 9,14)(10,15)(16,20)(17,21);
s3 := Sym(25)!( 4, 5)( 6,10)( 7, 9)( 8,13)(11,17)(12,16)(14,19)(15,18)(20,23)
(21,22);
s4 := Sym(25)!( 4, 6)( 5, 9)( 7,11)( 8,14)(10,16)(13,18)(15,20)(19,22);
s5 := Sym(25)!(24,25);
poly := sub<Sym(25)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, 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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