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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}*192c
if this polytope has a name.
Group : SmallGroup(192,1485)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 12, 48, 16
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,8,2} of size 384
   {6,8,4} of size 768
   {6,8,6} of size 1152
   {6,8,10} of size 1920
Vertex Figure Of :
   {2,6,8} of size 384
   {4,6,8} of size 768
   {4,6,8} of size 768
   {4,6,8} of size 768
   {6,6,8} of size 1152
   {6,6,8} of size 1152
   {10,6,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*96
   4-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   8-fold quotients : {3,4}*24, {6,2}*24
   16-fold quotients : {3,2}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8}*384f, {6,8}*384f, {12,8}*384g
   3-fold covers : {18,8}*576c, {6,24}*576c, {6,24}*576d
   4-fold covers : {6,8}*768g, {6,8}*768h, {6,8}*768i, {24,8}*768k, {24,8}*768l, {6,8}*768j, {24,8}*768m, {12,8}*768p, {24,8}*768o, {12,8}*768s
   5-fold covers : {6,40}*960d, {30,8}*960c
   6-fold covers : {36,8}*1152f, {18,8}*1152f, {36,8}*1152g, {12,24}*1152i, {12,24}*1152j, {6,24}*1152d, {12,24}*1152n, {6,24}*1152l, {12,24}*1152u
   7-fold covers : {6,56}*1344b, {42,8}*1344c
   9-fold covers : {54,8}*1728c, {6,72}*1728b, {18,24}*1728c, {18,24}*1728d, {6,24}*1728c, {6,24}*1728d, {6,24}*1728g
   10-fold covers : {12,40}*1920e, {6,40}*1920b, {12,40}*1920g, {60,8}*1920f, {30,8}*1920f, {60,8}*1920g
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)( 3,13)( 4,14)( 5,12)( 6,11)( 7,10)( 8, 9);;
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, 
s2*s0*s1*s2*s1*s2*s0*s1*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)( 3,13)( 4,14)( 5,12)( 6,11)( 7,10)( 8, 9);
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 >; 
 
References : None.
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