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}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240800)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 80, 480, 160
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 20
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 : {6,6}*960, {6,12}*960a, {6,12}*960b
   4-fold quotients : {6,12}*480a, {6,12}*480b, {6,6}*480
   8-fold quotients : {6,6}*240a, {6,6}*240b, {6,6}*240c
   16-fold quotients : {6,6}*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=<s0*s1*s0*s1> of order 3.
      64 facets:
         16 of {2}*4
         48 of {6}*12
      32 vertex figures:
         24 of {12}*24
         8 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 5.
      32 facets:
         32 of {6}*12
      16 vertex figures:
         16 of {12}*24

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,12}

Twisty Puzzle