Polytope of Type {4,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4}*192b
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
Vertex Figure Of :
   {2,4,6,4} of size 384
   {4,4,6,4} of size 768
   {6,4,6,4} of size 1152
   {3,4,6,4} of size 1152
   {6,4,6,4} of size 1728
   {10,4,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,4}*96c
   4-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,4}*384b, {4,12,4}*384c, {8,6,4}*384b, {4,6,4}*384a
   3-fold covers : {4,18,4}*576b, {12,6,4}*576d, {12,6,4}*576e
   4-fold covers : {4,6,4}*768a, {4,24,4}*768e, {4,24,4}*768f, {4,12,4}*768c, {4,24,4}*768i, {4,24,4}*768j, {8,12,4}*768c, {8,12,4}*768d, {8,12,4}*768e, {16,6,4}*768b, {4,12,4}*768e, {4,6,4}*768c, {4,12,4}*768g, {8,6,4}*768a, {4,6,8}*768b, {4,6,8}*768c, {4,6,4}*768h
   5-fold covers : {20,6,4}*960b, {4,30,4}*960b
   6-fold covers : {4,36,4}*1152b, {4,36,4}*1152c, {8,18,4}*1152b, {4,18,4}*1152a, {24,6,4}*1152d, {12,12,4}*1152d, {12,12,4}*1152e, {12,12,4}*1152f, {12,12,4}*1152g, {24,6,4}*1152e, {12,6,4}*1152a, {4,6,12}*1152b, {4,6,12}*1152c, {12,6,4}*1152d
   7-fold covers : {28,6,4}*1344b, {4,42,4}*1344b
   9-fold covers : {4,54,4}*1728b, {36,6,4}*1728c, {12,18,4}*1728c, {12,6,4}*1728d, {12,18,4}*1728d, {12,6,4}*1728e, {12,6,4}*1728j, {4,6,4}*1728e
   10-fold covers : {40,6,4}*1920b, {20,12,4}*1920b, {20,12,4}*1920c, {4,60,4}*1920b, {4,60,4}*1920c, {8,30,4}*1920b, {20,6,4}*1920a, {4,6,20}*1920b, {4,30,4}*1920a
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, 4)( 5, 6)( 9,10)(11,12);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*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, 4)( 5, 6)( 9,10)(11,12);
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope