Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*120
if this polytope has a name.
Group : SmallGroup(120,34)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 10, 30, 10
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 5
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Dual
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 240
   {6,6,4} of size 1920
   {6,6,4} of size 1920
Vertex Figure Of :
   {2,6,6} of size 240
   {4,6,6} of size 1920
   {4,6,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,6}*240a, {6,6}*240b, {6,6}*240c
   4-fold covers : {6,12}*480a, {6,12}*480b, {12,6}*480a, {12,6}*480b, {6,6}*480
   6-fold covers : {6,6}*720b, {6,6}*720c, {6,6}*720d
   8-fold covers : {6,24}*960a, {6,24}*960b, {24,6}*960a, {24,6}*960b, {6,24}*960c, {6,24}*960d, {24,6}*960c, {24,6}*960d, {6,6}*960, {6,12}*960a, {12,6}*960a, {6,12}*960b, {12,6}*960b
   10-fold covers : {6,30}*1200, {30,6}*1200
   12-fold covers : {6,12}*1440a, {6,12}*1440b, {12,6}*1440a, {12,6}*1440b, {6,6}*1440d, {6,6}*1440e, {6,6}*1440f
   14-fold covers : {6,42}*1680, {42,6}*1680
   16-fold covers : {6,48}*1920a, {6,48}*1920b, {48,6}*1920a, {48,6}*1920b, {12,12}*1920a, {6,24}*1920a, {24,6}*1920a, {6,48}*1920c, {6,48}*1920d, {48,6}*1920c, {48,6}*1920d, {6,12}*1920a, {12,6}*1920a, {12,12}*1920b, {12,12}*1920c, {12,12}*1920d, {6,24}*1920b, {24,6}*1920b, {6,6}*1920, {6,12}*1920b, {12,6}*1920b, {12,12}*1920e
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope