Polytope of Type {6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*192a
if this polytope has a name.
Group : SmallGroup(192,955)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 24, 48, 16
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {6,4,2} of size 384
Vertex Figure Of :
   {2,6,4} of size 384
   {3,6,4} of size 576
   {4,6,4} of size 768
   {4,6,4} of size 768
   {6,6,4} of size 1152
   {6,6,4} of size 1152
   {4,6,4} of size 1152
   {6,6,4} of size 1152
   {9,6,4} of size 1728
   {3,6,4} of size 1728
   {10,6,4} of size 1920
   {4,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {6,4}*48c
   8-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4}*384b, {12,4}*384c, {6,8}*384b, {6,8}*384c, {6,4}*384a
   3-fold covers : {18,4}*576a
   4-fold covers : {24,4}*768e, {24,4}*768f, {12,8}*768e, {12,8}*768f, {12,8}*768g, {12,8}*768h, {24,4}*768g, {24,4}*768h, {6,8}*768a, {6,8}*768b, {6,8}*768c, {12,8}*768i, {12,8}*768j, {6,8}*768e, {6,8}*768g, {12,4}*768b, {6,4}*768a, {12,4}*768c, {6,8}*768m, {6,8}*768n, {6,4}*768b, {6,4}*768c, {12,4}*768g, {12,4}*768h
   5-fold covers : {30,4}*960a
   6-fold covers : {36,4}*1152b, {36,4}*1152c, {18,8}*1152b, {18,8}*1152c, {18,4}*1152a, {6,12}*1152b, {6,12}*1152c
   7-fold covers : {42,4}*1344a
   9-fold covers : {54,4}*1728a
   10-fold covers : {60,4}*1920b, {60,4}*1920c, {30,8}*1920b, {30,8}*1920c, {6,20}*1920a, {30,4}*1920a
Permutation Representation (GAP) :

s0 := ( 1, 9)( 2,10)( 3,11)( 4,12);;
s1 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11);;
s2 := ( 1, 3)( 2, 4)( 9,11)(10,12);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 >;

References : None.
to this polytope