Polytope of Type {6,20}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20}*480b
if this polytope has a name.
Group : SmallGroup(480,956)
Rank : 3
Schlafli Type : {6,20}
Number of vertices, edges, etc : 12, 120, 40
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,20,2} of size 960
   {6,20,4} of size 1920
Vertex Figure Of :
   {2,6,20} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,10}*240c
   4-fold quotients : {3,10}*120b, {6,5}*120c
   8-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,20}*960c
   3-fold covers : {6,60}*1440b
   4-fold covers : {12,20}*1920g, {6,40}*1920f, {6,20}*1920d, {12,20}*1920k, {6,40}*1920h
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,20}

Twisty Puzzle