Polytope of Type {6,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8}*384g
if this polytope has a name.
Group : SmallGroup(384,18032)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 24, 96, 32
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,8,2} of size 768
Vertex Figure Of :
   {2,6,8} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*192b
   4-fold quotients : {6,8}*96, {6,4}*96
   8-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   12-fold quotients : {2,8}*32
   16-fold quotients : {3,4}*24, {6,2}*24
   24-fold quotients : {2,4}*16
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,8}*768j, {12,8}*768o, {12,8}*768u, {6,16}*768b, {6,16}*768c
   3-fold covers : {18,8}*1152g, {6,24}*1152h, {6,24}*1152k
   5-fold covers : {6,40}*1920d, {30,8}*1920g
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 2.
      16 facets:
         16 of {6}*12
      12 vertex figures:
         12 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      16 facets:
         16 of {6}*12
      12 vertex figures:
         12 of {8}*16
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2> of order 2.
      16 facets:
         16 of {6}*12
      12 vertex figures:
         12 of {8}*16
   P/N, where N=<s0*s1*s0*s1> of order 3.
      16 facets:
         8 of {2}*4
         8 of {6}*12
      8 vertex figures:
         8 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {6}*12
      6 vertex figures:
         6 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {6}*12
      6 vertex figures:
         6 of {8}*16
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      8 facets:
         8 of {6}*12
      6 vertex figures:
         6 of {8}*16

Permutation Representation (GAP) :

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

References : None.
to this polytope

Polytope of Type {6,8}

Twisty Puzzle