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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,3,4}*192
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 5
Schlafli Type : {4,2,3,4}
Number of vertices, edges, etc : 4, 4, 3, 6, 4
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,3,4,2} of size 384
Vertex Figure Of :
   {2,4,2,3,4} of size 384
   {3,4,2,3,4} of size 576
   {4,4,2,3,4} of size 768
   {6,4,2,3,4} of size 1152
   {3,4,2,3,4} of size 1152
   {6,4,2,3,4} of size 1152
   {6,4,2,3,4} of size 1152
   {9,4,2,3,4} of size 1728
   {4,4,2,3,4} of size 1728
   {6,4,2,3,4} of size 1728
   {10,4,2,3,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,3,4}*384, {4,2,3,4}*384, {4,2,6,4}*384b, {4,2,6,4}*384c
   3-fold covers : {4,2,9,4}*576, {12,2,3,4}*576, {4,6,3,4}*576
   4-fold covers : {16,2,3,4}*768, {4,4,6,4}*768b, {4,2,12,4}*768b, {4,2,12,4}*768c, {8,2,3,4}*768, {8,2,6,4}*768b, {8,2,6,4}*768c, {4,2,3,8}*768, {4,2,6,4}*768, {4,4,3,4}*768b
   5-fold covers : {20,2,3,4}*960, {4,2,15,4}*960
   6-fold covers : {8,2,9,4}*1152, {4,2,9,4}*1152, {4,2,18,4}*1152b, {4,2,18,4}*1152c, {24,2,3,4}*1152, {8,6,3,4}*1152, {12,2,3,4}*1152, {12,2,6,4}*1152b, {12,2,6,4}*1152c, {4,6,6,4}*1152d, {4,2,3,12}*1152, {4,2,6,12}*1152d, {4,6,3,4}*1152, {4,6,6,4}*1152g, {4,6,6,4}*1152h
   7-fold covers : {28,2,3,4}*1344, {4,2,21,4}*1344
   9-fold covers : {4,2,27,4}*1728, {36,2,3,4}*1728, {12,2,9,4}*1728, {12,6,3,4}*1728a, {4,6,9,4}*1728, {4,6,3,4}*1728a, {12,6,3,4}*1728b, {4,6,3,4}*1728b
   10-fold covers : {40,2,3,4}*1920, {8,2,15,4}*1920, {20,2,3,4}*1920, {20,2,6,4}*1920b, {20,2,6,4}*1920c, {4,10,6,4}*1920b, {4,2,6,20}*1920b, {4,2,15,4}*1920, {4,2,30,4}*1920b, {4,2,30,4}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope