Polytope of Type {3,3,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,3,3,2}*240
if this polytope has a name.
Group : SmallGroup(240,189)
Rank : 5
Schlafli Type : {3,3,3,2}
Number of vertices, edges, etc : 5, 10, 10, 5, 2
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Projective
   Locally Projective
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,3,3,2,2} of size 480
   {3,3,3,2,3} of size 720
   {3,3,3,2,4} of size 960
   {3,3,3,2,5} of size 1200
   {3,3,3,2,6} of size 1440
   {3,3,3,2,7} of size 1680
   {3,3,3,2,8} of size 1920
Vertex Figure Of :
   {2,3,3,3,2} of size 480
   {3,3,3,3,2} of size 1440
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,3,6,2}*480, {3,6,3,2}*480, {6,3,3,2}*480
   4-fold covers : {3,12,3,2}*960, {3,3,6,4}*960, {3,6,6,2}*960, {6,3,6,2}*960, {6,6,3,2}*960
   6-fold covers : {3,3,6,6}*1440, {3,3,6,2}*1440, {3,6,3,2}*1440a, {3,6,3,2}*1440b, {6,3,3,2}*1440
   8-fold covers : {3,3,6,8}*1920, {3,6,6,4}*1920, {6,3,6,4}*1920, {3,6,12,2}*1920, {12,6,3,2}*1920, {6,6,6,2}*1920, {3,12,6,2}*1920, {6,12,3,2}*1920
Permutation Representation (GAP) :

s0 := (4,5);;
s1 := (3,4);;
s2 := (2,3);;
s3 := (1,2);;
s4 := (6,7);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(7)!(4,5);
s1 := Sym(7)!(3,4);
s2 := Sym(7)!(2,3);
s3 := Sym(7)!(1,2);
s4 := Sym(7)!(6,7);
poly := sub<Sym(7)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3 >;

to this polytope