Polytope of Type {8,2,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,3,2}*192
if this polytope has a name.
Group : SmallGroup(192,1313)
Rank : 5
Schlafli Type : {8,2,3,2}
Number of vertices, edges, etc : 8, 8, 3, 3, 2
Order of s₀s₁s₂s₃s₄ : 24
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,3,2,2} of size 384
   {8,2,3,2,3} of size 576
   {8,2,3,2,4} of size 768
   {8,2,3,2,5} of size 960
   {8,2,3,2,6} of size 1152
   {8,2,3,2,7} of size 1344
   {8,2,3,2,9} of size 1728
   {8,2,3,2,10} of size 1920
Vertex Figure Of :
   {2,8,2,3,2} of size 384
   {4,8,2,3,2} of size 768
   {4,8,2,3,2} of size 768
   {6,8,2,3,2} of size 1152
   {3,8,2,3,2} of size 1152
   {10,8,2,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,3,2}*96
   4-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,2,3,2}*384, {8,2,6,2}*384
   3-fold covers : {8,2,9,2}*576, {24,2,3,2}*576, {8,2,3,6}*576, {8,6,3,2}*576
   4-fold covers : {32,2,3,2}*768, {8,4,6,2}*768a, {8,2,6,4}*768a, {8,2,12,2}*768, {16,2,6,2}*768, {8,2,3,4}*768, {8,4,3,2}*768
   5-fold covers : {40,2,3,2}*960, {8,2,15,2}*960
   6-fold covers : {16,2,9,2}*1152, {16,2,3,6}*1152, {16,6,3,2}*1152, {48,2,3,2}*1152, {8,2,18,2}*1152, {8,2,6,6}*1152a, {8,2,6,6}*1152c, {8,6,6,2}*1152a, {8,6,6,2}*1152c, {24,2,6,2}*1152
   7-fold covers : {56,2,3,2}*1344, {8,2,21,2}*1344
   9-fold covers : {8,2,27,2}*1728, {72,2,3,2}*1728, {24,2,9,2}*1728, {24,6,3,2}*1728a, {8,2,9,6}*1728, {8,2,3,6}*1728, {8,6,9,2}*1728, {8,6,3,2}*1728a, {24,2,3,6}*1728, {24,6,3,2}*1728b, {8,6,3,6}*1728, {8,6,3,2}*1728b
   10-fold covers : {16,2,15,2}*1920, {80,2,3,2}*1920, {8,2,30,2}*1920, {8,2,6,10}*1920, {8,10,6,2}*1920, {40,2,6,2}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11);;
s3 := ( 9,10);;
s4 := (12,13);;
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, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(13)!(2,3)(4,5)(6,7);
s1 := Sym(13)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(13)!(10,11);
s3 := Sym(13)!( 9,10);
s4 := Sym(13)!(12,13);
poly := sub<Sym(13)|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, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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