# Polytope of Type {6,10}

Atlas Canonical Name : {6,10}*240a
if this polytope has a name.
Group : SmallGroup(240,189)
Rank : 3
Schlafli Type : {6,10}
Number of vertices, edges, etc : 12, 60, 20
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 :
{6,10,2} of size 480
{6,10,4} of size 960
{6,10,6} of size 1440
{6,10,8} of size 1920
Vertex Figure Of :
{2,6,10} of size 480
{4,6,10} of size 960
{6,6,10} of size 1440
{8,6,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,5}*120a
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,10}*480b
4-fold covers : {6,10}*960a, {12,10}*960a, {6,20}*960a, {6,20}*960b, {12,10}*960b
6-fold covers : {6,10}*1440e, {6,30}*1440c, {6,30}*1440d
8-fold covers : {12,20}*1920f, {24,10}*1920c, {6,40}*1920e, {12,10}*1920b, {12,20}*1920h, {24,10}*1920e, {12,20}*1920i, {12,20}*1920j, {6,20}*1920c, {6,40}*1920g
Permutation Representation (GAP) :
s0 := (4,5);;
s1 := (1,2)(3,4);;
s2 := (2,3)(4,5)(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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(7)!(4,5);
s1 := Sym(7)!(1,2)(3,4);
s2 := Sym(7)!(2,3)(4,5)(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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1 >;

References : None.
to this polytope