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Polytope of Type {4,3,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,3}*192
Also Known As : hemi-4-cube, {4,3,3}4if this polytope has another name.
Group : SmallGroup(192,955)
Rank : 4
Schlafli Type : {4,3,3}
Number of vertices, edges, etc : 8, 16, 12, 4
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 4
Special Properties :
   Projective
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,3,3,2} of size 384
Vertex Figure Of :
   {2,4,3,3} of size 384
   {4,4,3,3} of size 768
   {6,4,3,3} of size 1152
   {10,4,3,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,3,3}*384, {4,3,6}*384a, {4,6,3}*384a, {4,3,6}*384b, {4,6,3}*384b
   4-fold covers : {8,3,3}*768a, {8,3,3}*768b, {4,3,12}*768a, {4,12,3}*768a, {4,12,3}*768b, {4,6,3}*768a, {4,3,6}*768, {4,6,3}*768c, {4,6,6}*768a, {4,6,6}*768b, {4,6,6}*768c, {4,6,3}*768d, {4,12,3}*768c, {4,3,12}*768b, {4,12,3}*768d, {4,6,6}*768d
   6-fold covers : {4,3,6}*1152a, {4,6,3}*1152a, {12,6,3}*1152
   10-fold covers : {4,6,15}*1920, {4,15,6}*1920, {20,6,3}*1920
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)(11,12);;
s1 := ( 5,11)( 6,12)( 7, 9)( 8,10);;
s2 := (1,5)(2,6)(3,7)(4,8);;
s3 := ( 5, 9)( 6,10)( 7,11)( 8,12);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s2*s1*s0*s1*s2*s3*s1*s2*s0*s1*s0*s2*s1*s2*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(12)!( 3, 4)( 7, 8)(11,12);
s1 := Sym(12)!( 5,11)( 6,12)( 7, 9)( 8,10);
s2 := Sym(12)!(1,5)(2,6)(3,7)(4,8);
s3 := Sym(12)!( 5, 9)( 6,10)( 7,11)( 8,12);
poly := sub<Sym(12)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s3*s2*s1*s0*s1*s2*s3*s1*s2*s0*s1*s0*s2*s1*s2*s0 >; 
 
References : None.
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