Polytope of Type {5,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6}*120a
if this polytope has a name.
Group : SmallGroup(120,34)
Rank : 3
Schlafli Type : {5,6}
Number of vertices, edges, etc : 10, 30, 12
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 :
   {5,6,2} of size 240
   {5,6,4} of size 480
   {5,6,6} of size 720
   {5,6,8} of size 960
   {5,6,10} of size 1200
   {5,6,12} of size 1440
   {5,6,14} of size 1680
   {5,6,16} of size 1920
Vertex Figure Of :
   {2,5,6} of size 240
   {4,5,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,6}*240a, {10,6}*240a, {10,6}*240b
   4-fold covers : {5,6}*480, {10,6}*480a, {10,12}*480a, {10,12}*480b, {10,6}*480b
   6-fold covers : {10,6}*720a, {15,6}*720a, {15,6}*720b
   8-fold covers : {10,24}*960a, {10,24}*960b, {10,6}*960a, {10,12}*960a, {20,6}*960a, {20,6}*960b, {10,12}*960b
   10-fold covers : {5,6}*1200a, {5,30}*1200a, {10,30}*1200a
   12-fold covers : {10,12}*1440a, {10,12}*1440c, {15,6}*1440a, {15,6}*1440b, {30,6}*1440a, {30,6}*1440b, {10,6}*1440e, {30,6}*1440c, {30,6}*1440d
   14-fold covers : {10,42}*1680a, {35,6}*1680b
   16-fold covers : {10,48}*1920a, {10,48}*1920b, {20,12}*1920f, {10,24}*1920c, {40,6}*1920e, {10,12}*1920b, {20,12}*1920h, {10,24}*1920e, {20,12}*1920i, {20,12}*1920j, {20,6}*1920c, {40,6}*1920g, {5,6}*1920a, {5,12}*1920a, {5,12}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope