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}*384g
if this polytope has a name.
Group : SmallGroup(384,17958)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 16, 96, 24
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 :
   {8,12,2} of size 768
Vertex Figure Of :
   {2,8,12} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12}*192c, {8,6}*192c
   4-fold quotients : {4,6}*96
   8-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   16-fold quotients : {4,3}*24, {2,6}*24
   32-fold quotients : {2,3}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,24}*768m, {8,24}*768o, {8,12}*768s
   3-fold covers : {8,36}*1152g, {24,12}*1152n, {24,12}*1152u
   5-fold covers : {40,12}*1920g, {8,60}*1920g
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1> of order 2.
      12 facets:
         12 of {8}*16
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 2.
      12 facets:
         12 of {8}*16
      8 vertex figures:
         8 of {12}*24

Permutation Representation (GAP) :

s0 := ( 1,53)( 2,54)( 3,56)( 4,55)( 5,50)( 6,49)( 7,51)( 8,52)( 9,61)(10,62)(11,64)(12,63)(13,58)(14,57)(15,59)(16,60)(17,69)(18,70)(19,72)(20,71)(21,66)(22,65)(23,67)(24,68)(25,77)(26,78)(27,80)(28,79)(29,74)(30,73)(31,75)(32,76)(33,85)(34,86)(35,88)(36,87)(37,82)(38,81)(39,83)(40,84)(41,93)(42,94)(43,96)(44,95)(45,90)(46,89)(47,91)(48,92);;
s1 := ( 3, 6)( 4, 5)( 7, 8)( 9,17)(10,18)(11,22)(12,21)(13,20)(14,19)(15,24)(16,23)(27,30)(28,29)(31,32)(33,41)(34,42)(35,46)(36,45)(37,44)(38,43)(39,48)(40,47)(49,74)(50,73)(51,77)(52,78)(53,75)(54,76)(55,79)(56,80)(57,90)(58,89)(59,93)(60,94)(61,91)(62,92)(63,95)(64,96)(65,82)(66,81)(67,85)(68,86)(69,83)(70,84)(71,87)(72,88);;
s2 := ( 1,65)( 2,66)( 3,71)( 4,72)( 5,70)( 6,69)( 7,67)( 8,68)( 9,57)(10,58)(11,63)(12,64)(13,62)(14,61)(15,59)(16,60)(17,49)(18,50)(19,55)(20,56)(21,54)(22,53)(23,51)(24,52)(25,89)(26,90)(27,95)(28,96)(29,94)(30,93)(31,91)(32,92)(33,81)(34,82)(35,87)(36,88)(37,86)(38,85)(39,83)(40,84)(41,73)(42,74)(43,79)(44,80)(45,78)(46,77)(47,75)(48,76);;
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*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, 
s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(96)!( 1,53)( 2,54)( 3,56)( 4,55)( 5,50)( 6,49)( 7,51)( 8,52)( 9,61)(10,62)(11,64)(12,63)(13,58)(14,57)(15,59)(16,60)(17,69)(18,70)(19,72)(20,71)(21,66)(22,65)(23,67)(24,68)(25,77)(26,78)(27,80)(28,79)(29,74)(30,73)(31,75)(32,76)(33,85)(34,86)(35,88)(36,87)(37,82)(38,81)(39,83)(40,84)(41,93)(42,94)(43,96)(44,95)(45,90)(46,89)(47,91)(48,92);
s1 := Sym(96)!( 3, 6)( 4, 5)( 7, 8)( 9,17)(10,18)(11,22)(12,21)(13,20)(14,19)(15,24)(16,23)(27,30)(28,29)(31,32)(33,41)(34,42)(35,46)(36,45)(37,44)(38,43)(39,48)(40,47)(49,74)(50,73)(51,77)(52,78)(53,75)(54,76)(55,79)(56,80)(57,90)(58,89)(59,93)(60,94)(61,91)(62,92)(63,95)(64,96)(65,82)(66,81)(67,85)(68,86)(69,83)(70,84)(71,87)(72,88);
s2 := Sym(96)!( 1,65)( 2,66)( 3,71)( 4,72)( 5,70)( 6,69)( 7,67)( 8,68)( 9,57)(10,58)(11,63)(12,64)(13,62)(14,61)(15,59)(16,60)(17,49)(18,50)(19,55)(20,56)(21,54)(22,53)(23,51)(24,52)(25,89)(26,90)(27,95)(28,96)(29,94)(30,93)(31,91)(32,92)(33,81)(34,82)(35,87)(36,88)(37,86)(38,85)(39,83)(40,84)(41,73)(42,74)(43,79)(44,80)(45,78)(46,77)(47,75)(48,76);
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*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, 
s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2 >;

References : None.
to this polytope

Polytope of Type {8,12}

Twisty Puzzle