Polytope of Type {8,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768b
if this polytope has a name.
Group : SmallGroup(768,90281)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 32, 192, 48
Order of s0s1s2 : 12
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,12}*384b
   3-fold quotients : {8,4}*256b
   4-fold quotients : {4,12}*192a
   6-fold quotients : {8,4}*128b
   8-fold quotients : {4,12}*96a
   12-fold quotients : {4,4}*64
   16-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {4,4}*32
   32-fold quotients : {2,6}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   64-fold quotients : {2,3}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      36 facets:
         24 of {4}*8
         12 of {8}*16
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s0*s1> of order 4.
      30 facets:
         24 of {2}*4
         6 of {8}*16
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 4.
      18 facets:
         12 of {4}*8
         6 of {8}*16
      8 vertex figures:
         8 of {12}*24

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