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Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*192a
Also Known As : {8,6}3if this polytope has another name.
Group : SmallGroup(192,956)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 16, 48, 12
Order of s0s1s2 : 3
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,6,2} of size 384
   {8,6,4} of size 768
   {8,6,6} of size 1152
Vertex Figure Of :
   {2,8,6} of size 384
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {4,6}*48b
   8-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,12}*384c, {8,12}*384d, {8,6}*384d
   3-fold covers : {8,18}*576a, {24,6}*576a
   4-fold covers : {16,6}*768a, {8,12}*768k, {8,6}*768f, {8,6}*768i, {8,12}*768m, {8,12}*768r, {8,12}*768v, {8,6}*768l
   5-fold covers : {40,6}*960c, {8,30}*960a
   6-fold covers : {8,36}*1152c, {8,36}*1152d, {8,18}*1152e, {24,12}*1152g, {24,12}*1152h, {24,6}*1152b, {24,6}*1152f
   7-fold covers : {56,6}*1344a, {8,42}*1344a
   9-fold covers : {8,54}*1728a, {72,6}*1728a, {24,18}*1728a, {24,6}*1728a
   10-fold covers : {40,12}*1920c, {40,12}*1920d, {8,60}*1920c, {8,60}*1920d, {40,6}*1920a, {8,30}*1920e
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12);;
s1 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)(11,12);;
s2 := ( 5,11)( 6,12)( 7, 9)( 8,10);;
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*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(12)!( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12);
s1 := Sym(12)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)(11,12);
s2 := Sym(12)!( 5,11)( 6,12)( 7, 9)( 8,10);
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*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*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 >; 
 
References : None.
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