Polytope of Type {12,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*960a
if this polytope has a name.
Group : SmallGroup(960,10877)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 80, 240, 40
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,6,2} of size 1920
Vertex Figure Of :
   {2,12,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*480
   4-fold quotients : {6,6}*240a, {6,6}*240b, {6,6}*240c
   8-fold quotients : {6,6}*120
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6}*1920a, {12,12}*1920b, {12,12}*1920d
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      20 facets:
         20 of {12}*24
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 5.
      8 facets:
         8 of {12}*24
      16 vertex figures:
         16 of {6}*12

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {12,6}

Twisty Puzzle