Polytope of Type {8,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240800)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 80, 480, 120
Order of s₀s₁s₂ : 20
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 : {8,6}*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*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1> of order 2.
      60 facets:
         60 of {8}*16
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 3.
      40 facets:
         40 of {8}*16
      32 vertex figures:
         24 of {12}*24
         8 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
      20 facets:
         20 of {8}*16
      16 vertex figures:
         12 of {12}*24
         4 of {4}*8

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {8,12}

Twisty Puzzle