Polytope of Type {24,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*768b
if this polytope has a name.
Group : SmallGroup(768,90280)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 96, 192, 16
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,4}*384b
   3-fold quotients : {8,4}*256b
   4-fold quotients : {12,4}*192a
   6-fold quotients : {8,4}*128b
   8-fold quotients : {12,4}*96a
   12-fold quotients : {4,4}*64
   16-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {4,4}*32
   32-fold quotients : {6,2}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   64-fold quotients : {3,2}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      12 facets:
         8 of {12}*24
         4 of {24}*48
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 4.
      6 facets:
         4 of {12}*24
         2 of {24}*48
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 4.
      10 facets:
         8 of {6}*12
         2 of {24}*48
      24 vertex figures:
         24 of {4}*8

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {24,4}

Twisty Puzzle