Polytope of Type {4,6,3}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope