Polytope of Type {12,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*384
if this polytope has a name.
Group : SmallGroup(384,17958)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 32, 96, 16
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,6,2} of size 768
Vertex Figure Of :
   {2,12,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6}*192a, {12,6}*192b, {6,6}*192b
   4-fold quotients : {12,3}*96, {6,6}*96
   8-fold quotients : {3,6}*48, {6,3}*48
   16-fold quotients : {3,3}*24
   24-fold quotients : {4,2}*16
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,6}*768, {12,12}*768a
   3-fold covers : {12,6}*1152a, {12,6}*1152e
   5-fold covers : {60,6}*1920, {12,30}*1920
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2*s1*s2> of order 2.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         16 of {3}*6
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      8 facets:
         4 of {4}*8
         4 of {12}*24
      16 vertex figures:
         8 of {6}*12
         8 of {2}*4

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