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}*384d
if this polytope has a name.
Group : SmallGroup(384,17949)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 32, 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 :
   {8,6,2} of size 768
Vertex Figure Of :
   {2,8,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,6}*192a
   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 : {8,12}*768k, {8,6}*768f, {8,6}*768i, {8,12}*768m, {8,12}*768r, {8,12}*768v, {8,6}*768l
   3-fold covers : {8,18}*1152e, {24,6}*1152b, {24,6}*1152f
   5-fold covers : {40,6}*1920a, {8,30}*1920e
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      16 facets:
         8 of {4}*8
         8 of {8}*16
      16 vertex figures:
         16 of {6}*12
   P/N, where N=<s0*s1*s0*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*s2*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*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 4.
      8 facets:
         4 of {4}*8
         4 of {8}*16
      8 vertex figures:
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1> of order 4.
      12 facets:
         8 of {2}*4
         4 of {8}*16
      8 vertex figures:
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      8 facets:
         4 of {4}*8
         4 of {8}*16
      8 vertex figures:
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      8 facets:
         4 of {4}*8
         4 of {8}*16
      8 vertex figures:
         8 of {6}*12

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {8,6}

Twisty Puzzle