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

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

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

Permutation Representation (Magma) :

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

to this polytope