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Polytope of Type {3,6}

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