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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2,3}*192
if this polytope has a name.
Group : SmallGroup(192,1147)
Rank : 5
Schlafli Type : {4,4,2,3}
Number of vertices, edges, etc : 4, 8, 4, 3, 3
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,2,3,2} of size 384
   {4,4,2,3,3} of size 768
   {4,4,2,3,4} of size 768
   {4,4,2,3,6} of size 1152
   {4,4,2,3,5} of size 1920
Vertex Figure Of :
   {2,4,4,2,3} of size 384
   {4,4,4,2,3} of size 768
   {6,4,4,2,3} of size 1152
   {3,4,4,2,3} of size 1152
   {6,4,4,2,3} of size 1728
   {10,4,4,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96
   4-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,8,2,3}*384a, {8,4,2,3}*384a, {4,8,2,3}*384b, {8,4,2,3}*384b, {4,4,2,3}*384, {4,4,2,6}*384
   3-fold covers : {4,4,2,9}*576, {4,12,2,3}*576a, {12,4,2,3}*576a, {4,4,6,3}*576
   4-fold covers : {4,8,2,3}*768a, {8,4,2,3}*768a, {8,8,2,3}*768a, {8,8,2,3}*768b, {8,8,2,3}*768c, {8,8,2,3}*768d, {4,16,2,3}*768a, {16,4,2,3}*768a, {4,16,2,3}*768b, {16,4,2,3}*768b, {4,4,2,3}*768, {4,8,2,3}*768b, {8,4,2,3}*768b, {4,4,4,6}*768, {4,4,2,12}*768, {4,8,2,6}*768a, {8,4,2,6}*768a, {4,8,2,6}*768b, {8,4,2,6}*768b, {4,4,2,6}*768, {4,4,4,3}*768b
   5-fold covers : {4,20,2,3}*960, {20,4,2,3}*960, {4,4,2,15}*960
   6-fold covers : {4,8,2,9}*1152a, {8,4,2,9}*1152a, {8,4,6,3}*1152a, {8,12,2,3}*1152a, {12,8,2,3}*1152a, {4,8,6,3}*1152a, {4,24,2,3}*1152a, {24,4,2,3}*1152a, {4,8,2,9}*1152b, {8,4,2,9}*1152b, {8,4,6,3}*1152b, {8,12,2,3}*1152b, {12,8,2,3}*1152b, {4,8,6,3}*1152b, {4,24,2,3}*1152b, {24,4,2,3}*1152b, {4,4,2,9}*1152, {4,4,6,3}*1152, {4,12,2,3}*1152a, {12,4,2,3}*1152a, {4,4,2,18}*1152, {4,4,6,6}*1152a, {4,4,6,6}*1152c, {4,12,2,6}*1152a, {12,4,2,6}*1152a
   7-fold covers : {4,28,2,3}*1344, {28,4,2,3}*1344, {4,4,2,21}*1344
   9-fold covers : {4,4,2,27}*1728, {4,12,2,9}*1728a, {12,4,2,9}*1728a, {4,36,2,3}*1728a, {36,4,2,3}*1728a, {4,12,6,3}*1728a, {4,4,6,9}*1728, {4,4,6,3}*1728a, {12,12,2,3}*1728a, {12,12,2,3}*1728b, {12,12,2,3}*1728c, {12,4,6,3}*1728, {4,12,6,3}*1728d, {4,4,6,3}*1728b, {4,4,2,3}*1728, {4,12,2,3}*1728, {12,4,2,3}*1728
   10-fold covers : {4,8,2,15}*1920a, {8,4,2,15}*1920a, {8,20,2,3}*1920a, {20,8,2,3}*1920a, {4,40,2,3}*1920a, {40,4,2,3}*1920a, {4,8,2,15}*1920b, {8,4,2,15}*1920b, {8,20,2,3}*1920b, {20,8,2,3}*1920b, {4,40,2,3}*1920b, {40,4,2,3}*1920b, {4,4,2,15}*1920, {4,20,2,3}*1920, {20,4,2,3}*1920, {4,4,2,30}*1920, {4,4,10,6}*1920, {4,20,2,6}*1920, {20,4,2,6}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope