Polytope of Type {6,40}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,40}*1920h
if this polytope has a name.
Group : SmallGroup(1920,240882)
Rank : 3
Schlafli Type : {6,40}
Number of vertices, edges, etc : 24, 480, 160
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 20
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 : {6,20}*960c
   4-fold quotients : {6,20}*480a, {6,20}*480b, {6,10}*480c
   8-fold quotients : {3,10}*240, {6,5}*240b, {6,10}*240c, {6,10}*240d, {6,10}*240e, {6,10}*240f
   16-fold quotients : {3,5}*120, {3,10}*120a, {3,10}*120b, {6,5}*120b, {6,5}*120c
   32-fold quotients : {3,5}*60
   120-fold quotients : {2,4}*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=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      80 facets:
         80 of {6}*12
      12 vertex figures:
         12 of {40}*80

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,40}

Twisty Puzzle