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}*384f
if this polytope has a name.
Group : SmallGroup(384,17958)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 24, 96, 32
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
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, {6,8}*192b, {6,8}*192c
   4-fold quotients : {3,8}*96, {6,4}*96
   8-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   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}*768p, {12,8}*768s
   3-fold covers : {18,8}*1152f, {6,24}*1152d, {6,24}*1152l
   5-fold covers : {6,40}*1920b, {30,8}*1920f
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1> of order 2.
      24 facets:
         16 of {3}*6
         8 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

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,8}

Twisty Puzzle