Polytope of Type {4,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4}*192c
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 4
Schlafli Type : {4,6,4}
Number of vertices, edges, etc : 4, 12, 12, 4
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,4,2} of size 384
   {4,6,4,4} of size 768
   {4,6,4,6} of size 1152
   {4,6,4,3} of size 1152
   {4,6,4,6} of size 1728
   {4,6,4,10} of size 1920
Vertex Figure Of :
   {2,4,6,4} of size 384
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6,2}*96c
   4-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,4}*384d, {4,12,4}*384e, {4,6,8}*384b, {4,6,4}*384b
   3-fold covers : {4,18,4}*576c, {4,6,12}*576d, {4,6,12}*576e
   4-fold covers : {4,6,4}*768b, {4,24,4}*768g, {4,24,4}*768h, {4,12,4}*768d, {4,24,4}*768k, {4,24,4}*768l, {4,12,8}*768c, {4,12,8}*768d, {4,12,8}*768e, {4,6,16}*768b, {4,12,4}*768f, {4,6,4}*768d, {4,12,4}*768h, {4,6,8}*768a, {8,6,4}*768b, {8,6,4}*768c, {4,6,4}*768g
   5-fold covers : {4,6,20}*960b, {4,30,4}*960c
   6-fold covers : {4,36,4}*1152d, {4,36,4}*1152e, {4,18,8}*1152b, {4,18,4}*1152b, {4,6,24}*1152d, {4,12,12}*1152d, {4,12,12}*1152e, {4,12,12}*1152f, {4,12,12}*1152g, {4,6,24}*1152e, {4,6,12}*1152a, {12,6,4}*1152b, {12,6,4}*1152c, {4,6,12}*1152d
   7-fold covers : {4,6,28}*1344b, {4,42,4}*1344c
   9-fold covers : {4,54,4}*1728c, {4,6,36}*1728c, {4,18,12}*1728c, {4,6,12}*1728d, {4,18,12}*1728d, {4,6,12}*1728e, {4,6,12}*1728j, {4,6,4}*1728f
   10-fold covers : {4,6,40}*1920b, {4,12,20}*1920b, {4,12,20}*1920c, {4,60,4}*1920d, {4,60,4}*1920e, {4,30,8}*1920b, {4,6,20}*1920a, {20,6,4}*1920b, {4,30,4}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope