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}*576b
if this polytope has a name.
Group : SmallGroup(576,5357)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 72, 144, 12
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {24,4,2} of size 1152
Vertex Figure Of :
   {2,24,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*288
   4-fold quotients : {6,4}*144
   8-fold quotients : {6,4}*72
   9-fold quotients : {8,4}*64b
   18-fold quotients : {4,4}*32
   36-fold quotients : {2,4}*16, {4,2}*16
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,4}*1152a, {24,8}*1152b, {24,8}*1152d
   3-fold covers : {24,4}*1728c, {24,12}*1728k, {24,12}*1728l, {24,4}*1728g, {24,12}*1728r, {24,12}*1728w
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 3.
      8 facets:
         6 of {8}*16
         2 of {24}*48
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 3.
      4 facets:
         4 of {24}*48
      24 vertex figures:
         24 of {4}*8

Permutation Representation (GAP) :

s0 := ( 1,46)( 2,48)( 3,47)( 4,52)( 5,54)( 6,53)( 7,49)( 8,51)( 9,50)(10,37)(11,39)(12,38)(13,43)(14,45)(15,44)(16,40)(17,42)(18,41)(19,55)(20,57)(21,56)(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,64)(29,66)(30,65)(31,70)(32,72)(33,71)(34,67)(35,69)(36,68);;
s1 := ( 1, 5)( 3, 8)( 6, 7)(10,14)(12,17)(15,16)(19,32)(20,29)(21,35)(22,31)(23,28)(24,34)(25,33)(26,30)(27,36)(37,68)(38,65)(39,71)(40,67)(41,64)(42,70)(43,69)(44,66)(45,72)(46,59)(47,56)(48,62)(49,58)(50,55)(51,61)(52,60)(53,57)(54,63);;
s2 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(19,28)(20,29)(21,30)(22,34)(23,35)(24,36)(25,31)(26,32)(27,33)(40,43)(41,44)(42,45)(49,52)(50,53)(51,54)(55,64)(56,65)(57,66)(58,70)(59,71)(60,72)(61,67)(62,68)(63,69);;
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*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(72)!( 1,46)( 2,48)( 3,47)( 4,52)( 5,54)( 6,53)( 7,49)( 8,51)( 9,50)(10,37)(11,39)(12,38)(13,43)(14,45)(15,44)(16,40)(17,42)(18,41)(19,55)(20,57)(21,56)(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,64)(29,66)(30,65)(31,70)(32,72)(33,71)(34,67)(35,69)(36,68);
s1 := Sym(72)!( 1, 5)( 3, 8)( 6, 7)(10,14)(12,17)(15,16)(19,32)(20,29)(21,35)(22,31)(23,28)(24,34)(25,33)(26,30)(27,36)(37,68)(38,65)(39,71)(40,67)(41,64)(42,70)(43,69)(44,66)(45,72)(46,59)(47,56)(48,62)(49,58)(50,55)(51,61)(52,60)(53,57)(54,63);
s2 := Sym(72)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(19,28)(20,29)(21,30)(22,34)(23,35)(24,36)(25,31)(26,32)(27,33)(40,43)(41,44)(42,45)(49,52)(50,53)(51,54)(55,64)(56,65)(57,66)(58,70)(59,71)(60,72)(61,67)(62,68)(63,69);
poly := sub<Sym(72)|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*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;

References : None.
to this polytope

Polytope of Type {24,4}

Twisty Puzzle