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}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240560)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 240, 480, 40
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 6
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 : {12,4}*960a
   4-fold quotients : {6,4}*480
   8-fold quotients : {6,4}*240a, {6,4}*240b, {6,4}*240c
   16-fold quotients : {6,4}*120
   60-fold quotients : {8,2}*32
   120-fold quotients : {4,2}*16
   240-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*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      20 facets:
         20 of {24}*48
      120 vertex figures:
         120 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      20 facets:
         20 of {24}*48
      120 vertex figures:
         120 of {4}*8
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 2.
      20 facets:
         20 of {24}*48
      128 vertex figures:
         112 of {4}*8
         16 of {2}*4
   P/N, where N=<s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      20 facets:
         20 of {24}*48
      120 vertex figures:
         120 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      16 facets:
         4 of {8}*16
         12 of {24}*48
      80 vertex figures:
         80 of {4}*8
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 4.
      10 facets:
         10 of {24}*48
      72 vertex figures:
         48 of {4}*8
         24 of {2}*4
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1, s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 4.
      10 facets:
         10 of {24}*48
      64 vertex figures:
         56 of {4}*8
         8 of {2}*4
   P/N, where N=<s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 6.
      8 facets:
         2 of {8}*16
         6 of {24}*48
      48 vertex figures:
         32 of {4}*8
         16 of {2}*4
   P/N, where N=<s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2> of order 6.
      8 facets:
         2 of {8}*16
         6 of {24}*48
      40 vertex figures:
         40 of {4}*8
   P/N, where N=<s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 6.
      8 facets:
         2 of {8}*16
         6 of {24}*48
      40 vertex figures:
         40 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 12.
      6 facets:
         4 of {8}*16
         2 of {24}*48
      24 vertex figures:
         16 of {4}*8
         8 of {2}*4

Permutation Representation (GAP) :

s0 := ( 3, 5)( 6,14)( 7,15)( 8,17)( 9,16)(10,18)(11,19)(12,21)(13,20)(22,30)(23,31)(24,33)(25,32)(26,34)(27,35)(28,37)(29,36);;
s1 := ( 1, 2)( 4, 5)( 6,26)( 7,27)( 8,29)( 9,28)(10,22)(11,23)(12,25)(13,24)(14,36)(15,37)(16,34)(17,35)(18,32)(19,33)(20,30)(21,31);;
s2 := ( 2, 4)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);;
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*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*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(37)!( 3, 5)( 6,14)( 7,15)( 8,17)( 9,16)(10,18)(11,19)(12,21)(13,20)(22,30)(23,31)(24,33)(25,32)(26,34)(27,35)(28,37)(29,36);
s1 := Sym(37)!( 1, 2)( 4, 5)( 6,26)( 7,27)( 8,29)( 9,28)(10,22)(11,23)(12,25)(13,24)(14,36)(15,37)(16,34)(17,35)(18,32)(19,33)(20,30)(21,31);
s2 := Sym(37)!( 2, 4)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);
poly := sub<Sym(37)|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*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*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