Polytope of Type {2,5,6}

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

s0 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4)(5,6);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(7)!(1,2);
s1 := Sym(7)!(4,5)(6,7);
s2 := Sym(7)!(3,4)(5,6);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s3 >;

to this polytope