Polytope of Type {10,12}

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

s0 := (6,7)(8,9);;
s1 := (1,3)(2,4)(5,6)(7,8);;
s2 := (3,4)(8,9);;
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, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope