Polytope of Type {6,12}

Play with this polytope as a twisty puzzle

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

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

References : None.
to this polytope

Polytope of Type {6,12}

Twisty Puzzle