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Polytope of Type {8,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,3}*192
Also Known As : {8,3}6if this polytope has another name.
Group : SmallGroup(192,956)
Rank : 3
Schlafli Type : {8,3}
Number of vertices, edges, etc : 32, 48, 12
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,3,2} of size 384
   {8,3,3} of size 768
   {8,3,4} of size 768
   {8,3,6} of size 1152
Vertex Figure Of :
   {2,8,3} of size 384
   {4,8,3} of size 768
   {4,8,3} of size 768
   {6,8,3} of size 1152
   {10,8,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {4,3}*48
   8-fold quotients : {4,3}*24
   16-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,3}*384, {8,6}*384a, {8,6}*384e
   3-fold covers : {8,9}*576, {24,3}*576
   4-fold covers : {16,3}*768a, {16,3}*768b, {8,6}*768d, {8,12}*768l, {8,6}*768h, {8,12}*768n, {8,12}*768q, {8,6}*768k, {8,12}*768x
   5-fold covers : {8,15}*960a
   6-fold covers : {8,9}*1152, {8,18}*1152a, {8,18}*1152d, {24,3}*1152a, {24,6}*1152a, {24,6}*1152c, {24,6}*1152e
   7-fold covers : {8,21}*1344
   9-fold covers : {8,27}*1728, {24,9}*1728, {24,3}*1728
   10-fold covers : {8,15}*1920a, {8,30}*1920a, {40,6}*1920c, {8,30}*1920d
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 := ( 3, 4)( 5, 9)( 6,10)( 7,11)( 8,12);;
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, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*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)!( 3, 4)( 5, 9)( 6,10)( 7,11)( 8,12);
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, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >; 
 
References : None.
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