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Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*192b
if this polytope has a name.
Group : SmallGroup(192,1485)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 16, 48, 16
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 384
   {6,6,4} of size 768
   {6,6,6} of size 1152
   {6,6,10} of size 1920
Vertex Figure Of :
   {2,6,6} of size 384
   {4,6,6} of size 768
   {6,6,6} of size 1152
   {10,6,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*96
   4-fold quotients : {3,6}*48, {6,3}*48
   8-fold quotients : {3,3}*24
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12}*384, {12,6}*384
   3-fold covers : {6,6}*576a, {6,6}*576b
   4-fold covers : {6,6}*768b, {6,6}*768c, {6,6}*768d, {6,24}*768, {24,6}*768, {12,12}*768a
   5-fold covers : {6,30}*960, {30,6}*960
   6-fold covers : {6,12}*1152a, {12,6}*1152a, {6,12}*1152e, {12,6}*1152e
   7-fold covers : {6,42}*1344, {42,6}*1344
   9-fold covers : {6,18}*1728a, {18,6}*1728a, {6,6}*1728a, {6,6}*1728b, {6,6}*1728f
   10-fold covers : {6,60}*1920, {60,6}*1920, {12,30}*1920, {30,12}*1920
Permutation Representation (GAP) :
s0 := ( 3, 5)( 4, 6)( 7, 8)( 9,10)(11,14)(12,13);;
s1 := ( 3, 4)( 5, 7)( 6, 8)(11,12)(13,15)(14,16);;
s2 := ( 1,15)( 2,16)( 3,12)( 4,11)( 5,13)( 6,14)( 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!( 3, 5)( 4, 6)( 7, 8)( 9,10)(11,14)(12,13);
s1 := Sym(16)!( 3, 4)( 5, 7)( 6, 8)(11,12)(13,15)(14,16);
s2 := Sym(16)!( 1,15)( 2,16)( 3,12)( 4,11)( 5,13)( 6,14)( 7, 9)( 8,10);
poly := sub<Sym(16)|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*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1 >; 
 
References : None.
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