Polytope of Type {12,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240857)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 240, 480, 80
Order of s₀s₁s₂ : 40
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 : {6,4}*960
   4-fold quotients : {6,4}*480
   8-fold quotients : {6,4}*240a, {6,4}*240b, {6,4}*240c
   16-fold quotients : {6,4}*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*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 3.
      32 facets:
         24 of {12}*24
         8 of {4}*8
      80 vertex figures:
         80 of {4}*8
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 5.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8

Permutation Representation (GAP) :

s0 := ( 1,35)( 2,36)( 3,11)( 4,12)( 5,18)( 6,17)( 7,15)( 8,16)( 9,43)(10,44)(13,29)(14,30)(19,33)(20,34)(21,37)(22,38)(23,28)(24,27)(25,32)(26,31)(39,48)(40,47)(41,45)(42,46)(49,86)(50,85)(51,64)(52,63)(53,80)(54,79)(55,59)(56,60)(57,72)(58,71)(61,96)(62,95)(65,73)(66,74)(67,93)(68,94)(69,83)(70,84)(75,92)(76,91)(77,88)(78,87)(81,90)(82,89);;
s1 := ( 1,51)( 2,52)( 3,57)( 4,58)( 5,63)( 6,64)( 7,69)( 8,70)( 9,55)(10,56)(11,77)(12,78)(13,76)(14,75)(15,74)(16,73)(17,81)(18,82)(19,60)(20,59)(21,80)(22,79)(23,84)(24,83)(25,72)(26,71)(27,93)(28,94)(29,90)(30,89)(31,49)(32,50)(33,62)(34,61)(35,92)(36,91)(37,96)(38,95)(39,65)(40,66)(41,86)(42,85)(43,54)(44,53)(45,88)(46,87)(47,68)(48,67);;
s2 := ( 1,57)( 2,58)( 3,87)( 4,88)( 5,89)( 6,90)( 7,80)( 8,79)( 9,52)(10,51)(11,78)(12,77)(13,66)(14,65)(15,53)(16,54)(17,81)(18,82)(19,86)(20,85)(21,62)(22,61)(23,68)(24,67)(25,84)(26,83)(27,93)(28,94)(29,74)(30,73)(31,69)(32,70)(33,49)(34,50)(35,72)(36,71)(37,95)(38,96)(39,76)(40,75)(41,59)(42,60)(43,63)(44,64)(45,55)(46,56)(47,92)(48,91);;
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, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(96)!( 1,35)( 2,36)( 3,11)( 4,12)( 5,18)( 6,17)( 7,15)( 8,16)( 9,43)(10,44)(13,29)(14,30)(19,33)(20,34)(21,37)(22,38)(23,28)(24,27)(25,32)(26,31)(39,48)(40,47)(41,45)(42,46)(49,86)(50,85)(51,64)(52,63)(53,80)(54,79)(55,59)(56,60)(57,72)(58,71)(61,96)(62,95)(65,73)(66,74)(67,93)(68,94)(69,83)(70,84)(75,92)(76,91)(77,88)(78,87)(81,90)(82,89);
s1 := Sym(96)!( 1,51)( 2,52)( 3,57)( 4,58)( 5,63)( 6,64)( 7,69)( 8,70)( 9,55)(10,56)(11,77)(12,78)(13,76)(14,75)(15,74)(16,73)(17,81)(18,82)(19,60)(20,59)(21,80)(22,79)(23,84)(24,83)(25,72)(26,71)(27,93)(28,94)(29,90)(30,89)(31,49)(32,50)(33,62)(34,61)(35,92)(36,91)(37,96)(38,95)(39,65)(40,66)(41,86)(42,85)(43,54)(44,53)(45,88)(46,87)(47,68)(48,67);
s2 := Sym(96)!( 1,57)( 2,58)( 3,87)( 4,88)( 5,89)( 6,90)( 7,80)( 8,79)( 9,52)(10,51)(11,78)(12,77)(13,66)(14,65)(15,53)(16,54)(17,81)(18,82)(19,86)(20,85)(21,62)(22,61)(23,68)(24,67)(25,84)(26,83)(27,93)(28,94)(29,74)(30,73)(31,69)(32,70)(33,49)(34,50)(35,72)(36,71)(37,95)(38,96)(39,76)(40,75)(41,59)(42,60)(43,63)(44,64)(45,55)(46,56)(47,92)(48,91);
poly := sub<Sym(96)|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, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope

Polytope of Type {12,4}

Twisty Puzzle