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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,3,2}*192
if this polytope has a name.
Group : SmallGroup(192,1537)
Rank : 5
Schlafli Type : {2,4,3,2}
Number of vertices, edges, etc : 2, 8, 12, 6, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,3,2,2} of size 384
   {2,4,3,2,3} of size 576
   {2,4,3,2,4} of size 768
   {2,4,3,2,5} of size 960
   {2,4,3,2,6} of size 1152
   {2,4,3,2,7} of size 1344
   {2,4,3,2,9} of size 1728
   {2,4,3,2,10} of size 1920
Vertex Figure Of :
   {2,2,4,3,2} of size 384
   {3,2,4,3,2} of size 576
   {4,2,4,3,2} of size 768
   {5,2,4,3,2} of size 960
   {6,2,4,3,2} of size 1152
   {7,2,4,3,2} of size 1344
   {9,2,4,3,2} of size 1728
   {10,2,4,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,3,2}*96
   4-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,3,2}*384b, {2,8,3,2}*384, {2,4,6,2}*384
   3-fold covers : {2,4,9,2}*576, {2,4,3,6}*576, {2,12,3,2}*576, {6,4,3,2}*576
   4-fold covers : {2,8,3,2}*768, {4,4,3,2}*768b, {4,8,3,2}*768, {8,4,3,2}*768, {2,4,12,2}*768b, {2,4,6,2}*768b, {2,4,6,4}*768b, {2,4,12,2}*768c, {4,4,6,2}*768d, {2,8,6,2}*768b, {2,8,6,2}*768c, {2,4,3,4}*768
   5-fold covers : {10,4,3,2}*960, {2,4,15,2}*960
   6-fold covers : {4,4,9,2}*1152b, {2,8,9,2}*1152, {2,4,18,2}*1152, {12,4,3,2}*1152, {4,4,3,6}*1152b, {2,24,3,2}*1152, {2,8,3,6}*1152, {6,8,3,2}*1152, {4,12,3,2}*1152, {2,4,6,6}*1152a, {2,4,6,6}*1152b, {2,12,6,2}*1152a, {2,12,6,2}*1152b, {6,4,6,2}*1152a
   7-fold covers : {14,4,3,2}*1344, {2,4,21,2}*1344
   9-fold covers : {2,4,27,2}*1728, {18,4,3,2}*1728, {2,4,9,6}*1728, {2,12,9,2}*1728, {6,4,9,2}*1728, {2,4,3,6}*1728, {2,12,3,2}*1728, {6,12,3,2}*1728a, {6,4,3,6}*1728, {2,12,3,6}*1728, {6,12,3,2}*1728b
   10-fold covers : {20,4,3,2}*1920, {10,8,3,2}*1920, {4,4,15,2}*1920b, {2,8,15,2}*1920, {2,4,6,10}*1920a, {2,20,6,2}*1920a, {10,4,6,2}*1920, {2,4,30,2}*1920
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (6,8);;
s2 := (5,6)(7,8);;
s3 := (3,5)(4,7);;
s4 := ( 9,10);;
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, s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(1,2);
s1 := Sym(10)!(6,8);
s2 := Sym(10)!(5,6)(7,8);
s3 := Sym(10)!(3,5)(4,7);
s4 := Sym(10)!( 9,10);
poly := sub<Sym(10)|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, 
s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope