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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,4,2}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 5
Schlafli Type : {2,3,4,2}
Number of vertices, edges, etc : 2, 3, 6, 4, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,4,2,2} of size 192
   {2,3,4,2,3} of size 288
   {2,3,4,2,4} of size 384
   {2,3,4,2,5} of size 480
   {2,3,4,2,6} of size 576
   {2,3,4,2,7} of size 672
   {2,3,4,2,8} of size 768
   {2,3,4,2,9} of size 864
   {2,3,4,2,10} of size 960
   {2,3,4,2,11} of size 1056
   {2,3,4,2,12} of size 1152
   {2,3,4,2,13} of size 1248
   {2,3,4,2,14} of size 1344
   {2,3,4,2,15} of size 1440
   {2,3,4,2,17} of size 1632
   {2,3,4,2,18} of size 1728
   {2,3,4,2,19} of size 1824
   {2,3,4,2,20} of size 1920
Vertex Figure Of :
   {2,2,3,4,2} of size 192
   {3,2,3,4,2} of size 288
   {4,2,3,4,2} of size 384
   {5,2,3,4,2} of size 480
   {6,2,3,4,2} of size 576
   {7,2,3,4,2} of size 672
   {8,2,3,4,2} of size 768
   {9,2,3,4,2} of size 864
   {10,2,3,4,2} of size 960
   {11,2,3,4,2} of size 1056
   {12,2,3,4,2} of size 1152
   {13,2,3,4,2} of size 1248
   {14,2,3,4,2} of size 1344
   {15,2,3,4,2} of size 1440
   {17,2,3,4,2} of size 1632
   {18,2,3,4,2} of size 1728
   {19,2,3,4,2} of size 1824
   {20,2,3,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,4,2}*192, {2,6,4,2}*192b, {2,6,4,2}*192c
   3-fold covers : {2,9,4,2}*288, {6,3,4,2}*288
   4-fold covers : {2,3,4,4}*384a, {2,12,4,2}*384b, {2,12,4,2}*384c, {2,3,4,4}*384b, {4,6,4,2}*384b, {2,3,8,2}*384, {2,6,4,2}*384, {4,3,4,2}*384b
   5-fold covers : {2,15,4,2}*480
   6-fold covers : {2,9,4,2}*576, {2,18,4,2}*576b, {2,18,4,2}*576c, {2,3,4,6}*576, {2,3,12,2}*576, {2,6,12,2}*576d, {6,3,4,2}*576, {6,6,4,2}*576d, {6,6,4,2}*576e, {6,6,4,2}*576f
   7-fold covers : {2,21,4,2}*672
   8-fold covers : {2,3,4,4}*768a, {4,12,4,2}*768b, {4,12,4,2}*768c, {2,3,8,2}*768, {2,6,8,2}*768a, {2,3,4,4}*768b, {2,6,4,2}*768a, {2,6,4,4}*768b, {2,6,4,4}*768c, {2,24,4,2}*768c, {2,24,4,2}*768d, {2,3,8,4}*768, {2,3,4,8}*768, {8,6,4,2}*768b, {2,12,4,2}*768b, {2,6,4,2}*768b, {2,6,4,4}*768d, {2,12,4,2}*768c, {4,6,4,2}*768a, {2,6,8,2}*768b, {2,6,8,2}*768c, {8,3,4,2}*768, {4,3,4,2}*768, {4,6,4,2}*768d, {4,6,4,2}*768e
   9-fold covers : {2,27,4,2}*864, {6,9,4,2}*864, {6,3,4,2}*864
   10-fold covers : {2,3,4,10}*960, {2,6,20,2}*960b, {10,6,4,2}*960b, {2,15,4,2}*960, {2,30,4,2}*960b, {2,30,4,2}*960c
   11-fold covers : {2,33,4,2}*1056
   12-fold covers : {2,9,4,4}*1152a, {2,36,4,2}*1152b, {2,36,4,2}*1152c, {2,9,4,4}*1152b, {4,18,4,2}*1152b, {2,9,8,2}*1152, {6,3,4,4}*1152a, {2,18,4,2}*1152, {4,9,4,2}*1152b, {6,12,4,2}*1152d, {6,12,4,2}*1152e, {6,12,4,2}*1152f, {6,12,4,2}*1152g, {2,3,4,12}*1152, {12,6,4,2}*1152d, {6,3,4,4}*1152b, {2,3,24,2}*1152, {2,3,8,6}*1152, {6,3,8,2}*1152, {2,3,12,4}*1152, {12,6,4,2}*1152e, {6,3,4,2}*1152, {2,6,4,6}*1152b, {2,6,12,2}*1152a, {2,6,12,2}*1152b, {6,6,4,2}*1152a, {6,6,4,2}*1152b, {12,3,4,2}*1152
   13-fold covers : {2,39,4,2}*1248
   14-fold covers : {2,3,4,14}*1344, {2,6,28,2}*1344b, {14,6,4,2}*1344b, {2,21,4,2}*1344, {2,42,4,2}*1344b, {2,42,4,2}*1344c
   15-fold covers : {2,45,4,2}*1440, {6,15,4,2}*1440
   17-fold covers : {2,51,4,2}*1632
   18-fold covers : {2,27,4,2}*1728, {2,54,4,2}*1728b, {2,54,4,2}*1728c, {2,3,4,18}*1728, {2,6,36,2}*1728c, {18,6,4,2}*1728c, {2,9,4,6}*1728, {2,9,12,2}*1728, {2,18,12,2}*1728c, {6,9,4,2}*1728, {6,18,4,2}*1728c, {6,18,4,2}*1728d, {6,18,4,2}*1728e, {2,3,12,2}*1728, {2,3,12,6}*1728a, {2,6,12,2}*1728d, {6,3,4,2}*1728, {6,6,4,2}*1728e, {6,6,4,2}*1728f, {6,6,4,2}*1728g, {6,3,4,6}*1728, {2,3,12,6}*1728b, {2,6,12,6}*1728i, {6,3,12,2}*1728, {6,6,4,2}*1728i, {6,6,12,2}*1728h
   19-fold covers : {2,57,4,2}*1824
   20-fold covers : {2,15,4,4}*1920a, {10,12,4,2}*1920b, {10,12,4,2}*1920c, {2,3,4,20}*1920, {20,6,4,2}*1920b, {2,3,8,10}*1920, {2,60,4,2}*1920b, {2,60,4,2}*1920c, {2,15,4,4}*1920b, {4,30,4,2}*1920b, {2,15,8,2}*1920, {2,6,4,10}*1920, {2,6,20,2}*1920a, {10,6,4,2}*1920a, {2,30,4,2}*1920, {4,15,4,2}*1920b
Permutation Representation (GAP) :

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

to this polytope