Polytope of Type {5,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6,2}*240a
if this polytope has a name.
Group : SmallGroup(240,189)
Rank : 4
Schlafli Type : {5,6,2}
Number of vertices, edges, etc : 10, 30, 12, 2
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,6,2,2} of size 480
   {5,6,2,3} of size 720
   {5,6,2,4} of size 960
   {5,6,2,5} of size 1200
   {5,6,2,6} of size 1440
   {5,6,2,7} of size 1680
   {5,6,2,8} of size 1920
Vertex Figure Of :
   {2,5,6,2} of size 480
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,6,4}*480a, {5,6,2}*480a, {10,6,2}*480a, {10,6,2}*480b
   3-fold covers : {5,6,6}*720a
   4-fold covers : {5,6,8}*960a, {5,6,2}*960, {10,6,2}*960a, {5,6,4}*960a, {10,6,4}*960a, {10,6,4}*960b, {10,12,2}*960a, {10,12,2}*960b, {10,6,2}*960b
   5-fold covers : {5,6,10}*1200a
   6-fold covers : {5,6,12}*1440a, {5,6,6}*1440a, {10,6,6}*1440a, {10,6,6}*1440b, {10,6,2}*1440a, {15,6,2}*1440a, {15,6,2}*1440b
   7-fold covers : {5,6,14}*1680a
   8-fold covers : {5,6,16}*1920a, {10,12,4}*1920d, {10,12,4}*1920e, {5,6,8}*1920a, {10,6,8}*1920c, {10,6,8}*1920d, {10,24,2}*1920a, {10,24,2}*1920b, {10,6,4}*1920c, {10,12,2}*1920b, {20,6,2}*1920b, {5,6,4}*1920, {10,6,4}*1920e, {10,6,2}*1920a, {10,12,2}*1920d, {20,6,2}*1920d
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (4,5);;
s3 := (6,7);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
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(7)!(2,3)(4,5);
s1 := Sym(7)!(1,2)(3,4);
s2 := Sym(7)!(4,5);
s3 := Sym(7)!(6,7);
poly := sub<Sym(7)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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 >;

to this polytope