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}*576a
if this polytope has a name.
Group : SmallGroup(576,5339)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 72, 144, 12
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
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}*64a
   18-fold quotients : {4,4}*32, {8,2}*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}*1152a, {24,8}*1152c, {48,4}*1152a, {48,4}*1152b
   3-fold covers : {24,4}*1728a, {24,12}*1728i, {24,12}*1728j, {24,4}*1728f, {24,12}*1728q, {24,12}*1728v
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      6 facets:
         6 of {24}*48
      36 vertex figures:
         36 of {4}*8
   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*s2*s1*s0*s1*s2*s1> of order 3.
      4 facets:
         4 of {24}*48
      24 vertex figures:
         24 of {4}*8

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {24,4}

Twisty Puzzle