Polytope of Type {3,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,4}*192
Also Known As : {{3,6}₄,{6,4|2}}. if this polytope has another name.
Group : SmallGroup(192,1472)
Rank : 4
Schlafli Type : {3,6,4}
Number of vertices, edges, etc : 4, 12, 16, 4
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,4,2} of size 384
   {3,6,4,4} of size 768
   {3,6,4,6} of size 1152
   {3,6,4,3} of size 1152
   {3,6,4,6} of size 1728
   {3,6,4,10} of size 1920
Vertex Figure Of :
   {2,3,6,4} of size 384
   {3,3,6,4} of size 960
   {6,3,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6,2}*96
   4-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,12,4}*384, {3,6,8}*384, {6,6,4}*384
   3-fold covers : {3,6,12}*576, {3,6,4}*576a
   4-fold covers : {3,12,8}*768, {3,6,4}*768a, {3,6,4}*768b, {3,6,16}*768, {6,12,4}*768a, {12,6,4}*768a, {6,12,4}*768b, {6,6,8}*768, {6,6,4}*768e, {12,6,4}*768b
   5-fold covers : {3,6,20}*960, {15,6,4}*960
   6-fold covers : {3,12,12}*1152, {3,6,24}*1152, {3,6,8}*1152, {3,12,4}*1152b, {6,6,12}*1152a, {6,6,4}*1152e, {6,6,4}*1152f
   7-fold covers : {3,6,28}*1344, {21,6,4}*1344
   9-fold covers : {3,6,36}*1728, {9,6,4}*1728a, {3,6,4}*1728a, {3,6,12}*1728
   10-fold covers : {3,12,20}*1920, {3,6,40}*1920, {15,6,8}*1920, {15,12,4}*1920, {6,6,20}*1920, {6,30,4}*1920, {30,6,4}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope