Polytope of Type {6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*120
if this polytope has a name.
Group : SmallGroup(120,34)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 15, 30, 10
Order of s₀s₁s₂ : 5
Order of s₀s₁s₂s₁ : 3
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {6,4,2} of size 240
   {6,4,3} of size 1920
   {6,4,4} of size 1920
Vertex Figure Of :
   {2,6,4} of size 240
   {3,6,4} of size 720
   {4,6,4} of size 720
   {4,6,4} of size 1440
   {6,6,4} of size 1440
   {4,6,4} of size 1920
   {4,6,4} of size 1920
   {6,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,4}*240a, {6,4}*240b, {6,4}*240c
   4-fold covers : {6,8}*480a, {6,8}*480b, {12,4}*480a, {12,4}*480b, {6,4}*480
   6-fold covers : {6,4}*720, {6,12}*720a, {6,12}*720b
   8-fold covers : {24,4}*960a, {24,4}*960b, {6,8}*960a, {6,4}*960, {12,4}*960a, {6,8}*960b, {12,4}*960b
   10-fold covers : {6,20}*1200c, {30,4}*1200a
   12-fold covers : {12,12}*1440c, {12,12}*1440d, {6,8}*1440a, {6,8}*1440b, {6,24}*1440a, {6,24}*1440b, {6,4}*1440b, {6,12}*1440c, {6,12}*1440d
   14-fold covers : {6,28}*1680, {42,4}*1680
   16-fold covers : {12,4}*1920a, {6,8}*1920a, {24,4}*1920a, {24,4}*1920b, {12,8}*1920a, {12,8}*1920b, {24,4}*1920c, {24,4}*1920d, {12,8}*1920c, {6,8}*1920b, {12,8}*1920d, {12,4}*1920b, {6,4}*1920, {6,8}*1920c, {12,4}*1920c, {12,8}*1920e
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope