Polytope of Type {12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,10}*480a
if this polytope has a name.
Group : SmallGroup(480,951)
Rank : 3
Schlafli Type : {12,10}
Number of vertices, edges, etc : 24, 120, 20
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,10,2} of size 960
Vertex Figure Of :
   {2,12,10} of size 960
   {4,12,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,10}*240b
   4-fold quotients : {6,5}*120a
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,10}*960a, {24,10}*960b, {12,10}*960b
   3-fold covers : {12,10}*1440c
   4-fold covers : {48,10}*1920a, {48,10}*1920b, {12,20}*1920f, {24,10}*1920c, {12,10}*1920b, {12,20}*1920h, {24,10}*1920e
Permutation Representation (GAP) :

s0 := (3,4)(7,9);;
s1 := (1,3)(2,4)(5,6)(8,9);;
s2 := (6,8)(7,9);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(9)!(3,4)(7,9);
s1 := Sym(9)!(1,3)(2,4)(5,6)(8,9);
s2 := Sym(9)!(6,8)(7,9);
poly := sub<Sym(9)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2 >;

References : None.
to this polytope