Polytope of Type {4,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240809)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 40, 480, 240
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,24}*960a, {4,24}*960b, {4,12}*960b
   4-fold quotients : {4,12}*480a, {4,12}*480b, {4,6}*480
   8-fold quotients : {4,6}*240a, {4,6}*240b, {4,6}*240c
   16-fold quotients : {4,6}*120
   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=<s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 2.
      120 facets:
         120 of {4}*8
      20 vertex figures:
         20 of {24}*48
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
      80 facets:
         80 of {4}*8
      16 vertex figures:
         12 of {24}*48
         4 of {8}*16
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
      40 facets:
         40 of {4}*8
      8 vertex figures:
         6 of {24}*48
         2 of {8}*16

Permutation Representation (GAP) :

s0 := ( 1,27)( 2,28)( 3,35)( 4,36)( 5,50)( 6,49)( 7,46)( 8,45)( 9,34)(10,33)(11,52)(12,51)(13,43)(14,44)(15,38)(16,37)(17,31)(18,32)(19,30)(20,29)(21,42)(22,41)(23,39)(24,40)(25,47)(26,48);;
s1 := ( 1,27)( 2,28)( 3,29)( 4,30)( 5,32)( 6,31)( 7,33)( 8,34)( 9,43)(10,44)(11,52)(12,51)(13,40)(14,39)(15,48)(16,47)(17,35)(18,36)(19,50)(20,49)(21,42)(22,41)(23,46)(24,45)(25,38)(26,37);;
s2 := ( 1,28)( 2,27)( 3,35)( 4,36)( 5,48)( 6,47)( 7,46)( 8,45)( 9,42)(10,41)(11,30)(12,29)(13,37)(14,38)(15,44)(16,43)(17,32)(18,31)(19,52)(20,51)(21,34)(22,33)(23,40)(24,39)(25,49)(26,50);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!( 1,27)( 2,28)( 3,35)( 4,36)( 5,50)( 6,49)( 7,46)( 8,45)( 9,34)(10,33)(11,52)(12,51)(13,43)(14,44)(15,38)(16,37)(17,31)(18,32)(19,30)(20,29)(21,42)(22,41)(23,39)(24,40)(25,47)(26,48);
s1 := Sym(52)!( 1,27)( 2,28)( 3,29)( 4,30)( 5,32)( 6,31)( 7,33)( 8,34)( 9,43)(10,44)(11,52)(12,51)(13,40)(14,39)(15,48)(16,47)(17,35)(18,36)(19,50)(20,49)(21,42)(22,41)(23,46)(24,45)(25,38)(26,37);
s2 := Sym(52)!( 1,28)( 2,27)( 3,35)( 4,36)( 5,48)( 6,47)( 7,46)( 8,45)( 9,42)(10,41)(11,30)(12,29)(13,37)(14,38)(15,44)(16,43)(17,32)(18,31)(19,52)(20,51)(21,34)(22,33)(23,40)(24,39)(25,49)(26,50);
poly := sub<Sym(52)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1 >;

References : None.
to this polytope

Polytope of Type {4,24}

Twisty Puzzle