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}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240816)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 40, 480, 240
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      120 facets:
         120 of {4}*8
      20 vertex figures:
         20 of {24}*48
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 2.
      120 facets:
         120 of {4}*8
      20 vertex figures:
         20 of {24}*48
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1> of order 3.
      80 facets:
         80 of {4}*8
      16 vertex figures:
         4 of {8}*16
         12 of {24}*48

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {4,24}

Twisty Puzzle