Polytope of Type {3,2,3,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,3,4}*288
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 5
Schlafli Type : {3,2,3,4}
Number of vertices, edges, etc : 3, 3, 6, 12, 8
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,3,4,2} of size 576
   {3,2,3,4,4} of size 1152
   {3,2,3,4,6} of size 1728
Vertex Figure Of :
   {2,3,2,3,4} of size 576
   {3,3,2,3,4} of size 1152
   {4,3,2,3,4} of size 1152
   {6,3,2,3,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,3,4}*144
   4-fold quotients : {3,2,3,2}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,3,8}*576, {3,2,6,4}*576, {6,2,3,4}*576
   3-fold covers : {9,2,3,4}*864, {3,2,9,4}*864, {3,6,3,4}*864, {3,2,3,12}*864
   4-fold covers : {3,2,3,8}*1152, {3,2,12,4}*1152b, {12,2,3,4}*1152, {3,2,6,4}*1152b, {3,2,12,4}*1152c, {3,2,6,8}*1152b, {6,2,3,8}*1152, {3,2,6,8}*1152c, {6,2,6,4}*1152
   5-fold covers : {3,2,15,4}*1440, {15,2,3,4}*1440
   6-fold covers : {9,2,3,8}*1728, {3,2,9,8}*1728, {3,6,3,8}*1728, {9,2,6,4}*1728, {18,2,3,4}*1728, {3,2,18,4}*1728, {6,2,9,4}*1728, {3,6,6,4}*1728a, {6,6,3,4}*1728a, {3,2,3,24}*1728, {3,6,6,4}*1728b, {6,6,3,4}*1728b, {3,2,6,12}*1728a, {3,2,6,12}*1728b, {6,2,3,12}*1728
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,7)(5,9);;
s3 := (6,7)(8,9);;
s4 := (6,8);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(9)!(2,3);
s1 := Sym(9)!(1,2);
s2 := Sym(9)!(4,7)(5,9);
s3 := Sym(9)!(6,7)(8,9);
s4 := Sym(9)!(6,8);
poly := sub<Sym(9)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope