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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,3,2}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 5
Schlafli Type : {2,3,3,2}
Number of vertices, edges, etc : 2, 4, 6, 4, 2
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Locally Projective
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,3,2,2} of size 192
   {2,3,3,2,3} of size 288
   {2,3,3,2,4} of size 384
   {2,3,3,2,5} of size 480
   {2,3,3,2,6} of size 576
   {2,3,3,2,7} of size 672
   {2,3,3,2,8} of size 768
   {2,3,3,2,9} of size 864
   {2,3,3,2,10} of size 960
   {2,3,3,2,11} of size 1056
   {2,3,3,2,12} of size 1152
   {2,3,3,2,13} of size 1248
   {2,3,3,2,14} of size 1344
   {2,3,3,2,15} of size 1440
   {2,3,3,2,17} of size 1632
   {2,3,3,2,18} of size 1728
   {2,3,3,2,19} of size 1824
   {2,3,3,2,20} of size 1920
Vertex Figure Of :
   {2,2,3,3,2} of size 192
   {3,2,3,3,2} of size 288
   {4,2,3,3,2} of size 384
   {5,2,3,3,2} of size 480
   {6,2,3,3,2} of size 576
   {7,2,3,3,2} of size 672
   {8,2,3,3,2} of size 768
   {9,2,3,3,2} of size 864
   {10,2,3,3,2} of size 960
   {11,2,3,3,2} of size 1056
   {12,2,3,3,2} of size 1152
   {13,2,3,3,2} of size 1248
   {14,2,3,3,2} of size 1344
   {15,2,3,3,2} of size 1440
   {17,2,3,3,2} of size 1632
   {18,2,3,3,2} of size 1728
   {19,2,3,3,2} of size 1824
   {20,2,3,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,6,2}*192, {2,6,3,2}*192
   4-fold covers : {2,3,3,4}*384, {4,3,3,2}*384, {2,3,6,4}*384, {4,6,3,2}*384, {2,3,12,2}*384, {2,12,3,2}*384, {2,6,6,2}*384
   6-fold covers : {2,3,6,2}*576, {2,3,6,6}*576, {2,6,3,2}*576, {6,6,3,2}*576
   8-fold covers : {2,3,3,4}*768, {2,3,6,4}*768a, {2,6,3,4}*768a, {4,3,3,2}*768, {4,3,6,2}*768a, {4,6,3,2}*768a, {2,3,6,2}*768, {2,6,3,2}*768, {2,3,6,4}*768b, {2,6,3,4}*768b, {2,6,6,2}*768a, {4,3,6,2}*768b, {4,6,3,2}*768b, {2,3,12,4}*768, {4,12,3,2}*768, {2,3,6,8}*768, {8,6,3,2}*768, {2,6,6,4}*768, {2,6,12,2}*768a, {2,12,6,2}*768a, {4,6,6,2}*768, {2,6,12,2}*768b, {2,12,6,2}*768b, {2,6,6,2}*768b
   10-fold covers : {2,3,6,10}*960, {2,6,15,2}*960, {2,15,6,2}*960, {10,6,3,2}*960
   12-fold covers : {2,3,6,12}*1152, {12,6,3,2}*1152, {2,3,12,2}*1152, {2,12,3,2}*1152, {2,3,12,6}*1152, {6,12,3,2}*1152, {2,3,6,4}*1152a, {4,6,3,2}*1152a, {2,6,6,2}*1152a, {2,6,6,2}*1152b, {2,6,6,6}*1152b, {6,6,6,2}*1152a
   14-fold covers : {2,3,6,14}*1344, {2,6,21,2}*1344, {2,21,6,2}*1344, {14,6,3,2}*1344
   18-fold covers : {2,3,6,18}*1728, {2,6,9,2}*1728, {2,9,6,2}*1728, {18,6,3,2}*1728, {2,3,6,2}*1728, {2,6,3,2}*1728, {2,3,6,6}*1728, {2,6,3,6}*1728b, {6,3,6,2}*1728a, {6,6,3,2}*1728
   20-fold covers : {2,3,6,20}*1920, {20,6,3,2}*1920, {2,12,15,2}*1920, {2,15,12,2}*1920, {2,3,12,10}*1920, {10,12,3,2}*1920, {2,15,6,4}*1920, {4,6,15,2}*1920, {2,6,6,10}*1920, {2,6,30,2}*1920, {2,30,6,2}*1920, {10,6,6,2}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope