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Polytope of Type {6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3}*192
Also Known As : {6,3}(4,0), {6,3}8if this polytope has another name.
Group : SmallGroup(192,956)
Rank : 3
Schlafli Type : {6,3}
Number of vertices, edges, etc : 32, 48, 16
Order of s0s1s2 : 8
Order of s0s1s2s1 : 6
Special Properties :
   Toroidal
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,3,2} of size 384
Vertex Figure Of :
   {2,6,3} of size 384
   {4,6,3} of size 768
   {6,6,3} of size 1152
   {10,6,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {6,3}*48
   8-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,3}*384, {6,6}*384d
   3-fold covers : {6,3}*576
   4-fold covers : {24,3}*768, {6,3}*768, {12,6}*768c, {6,12}*768e, {6,6}*768d, {12,6}*768g, {6,12}*768h
   5-fold covers : {6,15}*960
   6-fold covers : {12,3}*1152a, {6,6}*1152b, {6,6}*1152f
   7-fold covers : {6,21}*1344
   9-fold covers : {6,9}*1728, {6,3}*1728
   10-fold covers : {12,15}*1920, {6,30}*1920a, {30,6}*1920c
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12);;
s1 := ( 3, 4)( 5, 9)( 6,10)( 7,11)( 8,12);;
s2 := ( 1,11)( 2,12)( 3, 9)( 4,10)( 5, 6);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
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)( 7,11)( 8,12);
s2 := Sym(12)!( 1,11)( 2,12)( 3, 9)( 4,10)( 5, 6);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >; 
 
References : None.
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