Polytope of Type {6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*240c
Also Known As : {6,4}5. if this polytope has another name.
Group : SmallGroup(240,189)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 30, 60, 20
Order of s0s1s2 : 5
Order of s0s1s2s1 : 6
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 480
Vertex Figure Of :
{2,6,4} of size 480
{3,6,4} of size 1440
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,4}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,8}*480a, {6,8}*480b, {6,4}*480
3-fold covers : {6,4}*720, {6,12}*720a
4-fold covers : {6,8}*960a, {6,4}*960, {12,4}*960a, {6,8}*960b, {12,4}*960b
5-fold covers : {6,20}*1200c, {30,4}*1200a
6-fold covers : {6,8}*1440a, {6,8}*1440b, {6,24}*1440a, {6,24}*1440b, {6,4}*1440b, {6,12}*1440c, {6,12}*1440d
7-fold covers : {6,28}*1680, {42,4}*1680
8-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
Permutation Representation (GAP) :
s0 := (4,5);;
s1 := (1,2)(3,4)(6,7);;
s2 := (2,3)(6,7);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(7)!(4,5);
s1 := Sym(7)!(1,2)(3,4)(6,7);
s2 := Sym(7)!(2,3)(6,7);
poly := sub<Sym(7)|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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 >;
References : None.
to this polytope