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Polytope of Type {6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8}*192a
Also Known As : {6,8}3if this polytope has another name.
Group : SmallGroup(192,956)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 12, 48, 16
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 :
   {6,8,2} of size 384
Vertex Figure Of :
   {2,6,8} of size 384
   {4,6,8} of size 768
   {6,6,8} of size 1152
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {6,4}*48b
   8-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8}*384c, {12,8}*384d, {6,8}*384d
   3-fold covers : {18,8}*576a, {6,24}*576a
   4-fold covers : {6,16}*768a, {12,8}*768k, {6,8}*768f, {6,8}*768i, {12,8}*768m, {12,8}*768q, {12,8}*768v, {6,8}*768l
   5-fold covers : {6,40}*960c, {30,8}*960a
   6-fold covers : {36,8}*1152c, {36,8}*1152d, {18,8}*1152d, {12,24}*1152g, {12,24}*1152h, {6,24}*1152c, {6,24}*1152f
   7-fold covers : {6,56}*1344a, {42,8}*1344a
   9-fold covers : {54,8}*1728a, {6,72}*1728a, {18,24}*1728a, {6,24}*1728a
   10-fold covers : {12,40}*1920c, {12,40}*1920d, {60,8}*1920c, {60,8}*1920d, {6,40}*1920a, {30,8}*1920d
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, 3)( 2, 4)( 5, 6)( 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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 7,11)( 8,12);
s2 := Sym(12)!( 1, 3)( 2, 4)( 5, 6)( 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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
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