Polytope of Type {8,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*384g
if this polytope has a name.
Group : SmallGroup(384,18032)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 32, 96, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,6,2} of size 768
Vertex Figure Of :
   {2,8,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*192b
   4-fold quotients : {8,6}*96, {4,6}*96
   8-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   12-fold quotients : {8,2}*32
   16-fold quotients : {4,3}*24, {2,6}*24
   24-fold quotients : {4,2}*16
   32-fold quotients : {2,3}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,6}*768j, {8,12}*768o, {8,12}*768u, {16,6}*768b, {16,6}*768c
   3-fold covers : {8,18}*1152g, {24,6}*1152h, {24,6}*1152k
   5-fold covers : {40,6}*1920d, {8,30}*1920g
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      12 facets:
         12 of {8}*16
      16 vertex figures:
         16 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      12 facets:
         12 of {8}*16
      16 vertex figures:
         16 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 2.
      12 facets:
         12 of {8}*16
      16 vertex figures:
         16 of {6}*12
   P/N, where N=<s1*s2*s1*s2> of order 3.
      8 facets:
         8 of {8}*16
      16 vertex figures:
         8 of {2}*4
         8 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      6 facets:
         6 of {8}*16
      8 vertex figures:
         8 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 4.
      6 facets:
         6 of {8}*16
      8 vertex figures:
         8 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 4.
      6 facets:
         6 of {8}*16
      8 vertex figures:
         8 of {6}*12

Permutation Representation (GAP) : 
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,39)(26,40)(27,37)(28,38)(29,43)(30,44)(31,41)(32,42)(33,47)(34,48)(35,45)(36,46)(49,75)(50,76)(51,73)(52,74)(53,79)(54,80)(55,77)(56,78)(57,83)(58,84)(59,81)(60,82)(61,87)(62,88)(63,85)(64,86)(65,91)(66,92)(67,89)(68,90)(69,95)(70,96)(71,93)(72,94);;
s1 := ( 1,49)( 2,51)( 3,50)( 4,52)( 5,57)( 6,59)( 7,58)( 8,60)( 9,53)(10,55)(11,54)(12,56)(13,61)(14,63)(15,62)(16,64)(17,69)(18,71)(19,70)(20,72)(21,65)(22,67)(23,66)(24,68)(25,85)(26,87)(27,86)(28,88)(29,93)(30,95)(31,94)(32,96)(33,89)(34,91)(35,90)(36,92)(37,73)(38,75)(39,74)(40,76)(41,81)(42,83)(43,82)(44,84)(45,77)(46,79)(47,78)(48,80);;
s2 := ( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(13,21)(14,24)(15,23)(16,22)(18,20)(25,33)(26,36)(27,35)(28,34)(30,32)(37,45)(38,48)(39,47)(40,46)(42,44)(49,57)(50,60)(51,59)(52,58)(54,56)(61,69)(62,72)(63,71)(64,70)(66,68)(73,81)(74,84)(75,83)(76,82)(78,80)(85,93)(86,96)(87,95)(88,94)(90,92);;
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*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(96)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,39)(26,40)(27,37)(28,38)(29,43)(30,44)(31,41)(32,42)(33,47)(34,48)(35,45)(36,46)(49,75)(50,76)(51,73)(52,74)(53,79)(54,80)(55,77)(56,78)(57,83)(58,84)(59,81)(60,82)(61,87)(62,88)(63,85)(64,86)(65,91)(66,92)(67,89)(68,90)(69,95)(70,96)(71,93)(72,94);
s1 := Sym(96)!( 1,49)( 2,51)( 3,50)( 4,52)( 5,57)( 6,59)( 7,58)( 8,60)( 9,53)(10,55)(11,54)(12,56)(13,61)(14,63)(15,62)(16,64)(17,69)(18,71)(19,70)(20,72)(21,65)(22,67)(23,66)(24,68)(25,85)(26,87)(27,86)(28,88)(29,93)(30,95)(31,94)(32,96)(33,89)(34,91)(35,90)(36,92)(37,73)(38,75)(39,74)(40,76)(41,81)(42,83)(43,82)(44,84)(45,77)(46,79)(47,78)(48,80);
s2 := Sym(96)!( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(13,21)(14,24)(15,23)(16,22)(18,20)(25,33)(26,36)(27,35)(28,34)(30,32)(37,45)(38,48)(39,47)(40,46)(42,44)(49,57)(50,60)(51,59)(52,58)(54,56)(61,69)(62,72)(63,71)(64,70)(66,68)(73,81)(74,84)(75,83)(76,82)(78,80)(85,93)(86,96)(87,95)(88,94)(90,92);
poly := sub<Sym(96)|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*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;
References : None.
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