Polytope of Type {6,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240864)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 240, 480, 160
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 12
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 : {6,4}*960
   4-fold quotients : {6,4}*480
   8-fold quotients : {6,4}*240a, {6,4}*240b, {6,4}*240c
   16-fold quotients : {6,4}*120
   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*s2*s1*s2> of order 2.
      80 facets:
         80 of {6}*12
      124 vertex figures:
         8 of {2}*4
         116 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      82 facets:
         78 of {6}*12
         4 of {3}*6
      120 vertex figures:
         120 of {4}*8
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1> of order 3.
      64 facets:
         48 of {6}*12
         16 of {2}*4
      80 vertex figures:
         80 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0> of order 4.
      40 facets:
         40 of {6}*12
      62 vertex figures:
         4 of {2}*4
         58 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0> of order 4.
      42 facets:
         38 of {6}*12
         4 of {3}*6
      62 vertex figures:
         4 of {2}*4
         58 of {4}*8
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 5.
      32 facets:
         32 of {6}*12
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2> of order 6.
      32 facets:
         24 of {6}*12
         8 of {2}*4
      44 vertex figures:
         8 of {2}*4
         36 of {4}*8
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 6.
      34 facets:
         22 of {6}*12
         4 of {3}*6
         8 of {2}*4
      40 vertex figures:
         40 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 10.
      16 facets:
         16 of {6}*12
      28 vertex figures:
         8 of {2}*4
         20 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2> of order 20.
      8 facets:
         8 of {6}*12
      14 vertex figures:
         4 of {2}*4
         10 of {4}*8

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,4}

Twisty Puzzle