Polytope of Type {6,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8}*960b
if this polytope has a name.
Group : SmallGroup(960,10877)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 60, 240, 80
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,8,2} of size 1920
Vertex Figure Of :
   {2,6,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*480
   4-fold quotients : {6,4}*240a, {6,4}*240b, {6,4}*240c
   8-fold quotients : {6,4}*120
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8}*1920b, {12,8}*1920c, {6,8}*1920b
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1> of order 2.
      40 facets:
         40 of {6}*12
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 3.
      32 facets:
         24 of {6}*12
         8 of {2}*4
      20 vertex figures:
         20 of {8}*16
   P/N, where N=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1> of order 6.
      16 facets:
         12 of {6}*12
         4 of {2}*4
      10 vertex figures:
         10 of {8}*16

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,8}

Twisty Puzzle