Polytope of Type {12,8}

Play with this polytope as a twisty puzzle

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

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