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}*384b
if this polytope has a name.
Group : SmallGroup(384,1706)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 48, 96, 8
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {24,4,2} of size 768
Vertex Figure Of :
   {2,24,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*192a
   3-fold quotients : {8,4}*128b
   4-fold quotients : {12,4}*96a
   6-fold quotients : {4,4}*64
   8-fold quotients : {12,2}*48, {6,4}*48a
   12-fold quotients : {4,4}*32
   16-fold quotients : {6,2}*24
   24-fold quotients : {2,4}*16, {4,2}*16
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,8}*768b, {24,4}*768a, {24,8}*768c, {24,4}*768b, {24,8}*768e, {24,4}*768d, {24,8}*768g
   3-fold covers : {72,4}*1152b, {24,12}*1152e, {24,12}*1152f
   5-fold covers : {120,4}*1920b, {24,20}*1920b
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      4 facets:
         4 of {24}*48
      24 vertex figures:
         24 of {4}*8

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {24,4}

Twisty Puzzle