Polytope of Type {12,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240806)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 80, 480, 80
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6}*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*s2*s1*s0*s1*s2*s1*s0*s1> of order 5.
      16 facets:
         16 of {12}*24
      16 vertex figures:
         16 of {12}*24

Permutation Representation (GAP) :

s0 := (  1, 53)(  2, 54)(  3, 55)(  4, 56)(  5, 63)(  6, 64)(  7,103)(  8,104)(  9, 74)( 10, 73)( 11, 58)( 12, 57)( 13, 67)( 14, 68)( 15, 66)( 16, 65)( 17, 99)( 18,100)( 19, 89)( 20, 90)( 21, 61)( 22, 62)( 23, 97)( 24, 98)( 25,101)( 26,102)( 27, 81)( 28, 82)( 29, 80)( 30, 79)( 31, 86)( 32, 85)( 33, 83)( 34, 84)( 35, 93)( 36, 94)( 37, 72)( 38, 71)( 39, 95)( 40, 96)( 41, 88)( 42, 87)( 43, 92)( 44, 91)( 45, 76)( 46, 75)( 47, 70)( 48, 69)( 49, 78)( 50, 77)( 51, 60)( 52, 59);;
s1 := (  1, 55)(  2, 56)(  3, 53)(  4, 54)(  5, 69)(  6, 70)(  7, 64)(  8, 63)(  9, 84)( 10, 83)( 11, 59)( 12, 60)( 13,101)( 14,102)( 15, 97)( 16, 98)( 17, 58)( 18, 57)( 19, 73)( 20, 74)( 21, 72)( 22, 71)( 23, 89)( 24, 90)( 25, 86)( 26, 85)( 27, 92)( 28, 91)( 29, 88)( 30, 87)( 31, 61)( 32, 62)( 33, 77)( 34, 78)( 35, 81)( 36, 82)( 37, 76)( 38, 75)( 39, 79)( 40, 80)( 41, 99)( 42,100)( 43,103)( 44,104)( 45, 68)( 46, 67)( 47, 94)( 48, 93)( 49, 66)( 50, 65)( 51, 96)( 52, 95);;
s2 := (  3,  4)(  5, 13)(  6, 14)(  7,  8)(  9, 28)( 10, 27)( 11, 16)( 12, 15)( 17, 18)( 21, 30)( 22, 29)( 23, 45)( 24, 46)( 25, 49)( 26, 50)( 33, 34)( 35, 41)( 36, 42)( 37, 38)( 39, 43)( 40, 44)( 55, 56)( 57, 66)( 58, 65)( 61, 79)( 62, 80)( 63, 67)( 64, 68)( 71, 72)( 73, 81)( 74, 82)( 75, 98)( 76, 97)( 77,102)( 78,101)( 83, 84)( 87, 94)( 88, 93)( 91, 96)( 92, 95)( 99,100)(103,104);;
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*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*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(104)!(  1, 53)(  2, 54)(  3, 55)(  4, 56)(  5, 63)(  6, 64)(  7,103)(  8,104)(  9, 74)( 10, 73)( 11, 58)( 12, 57)( 13, 67)( 14, 68)( 15, 66)( 16, 65)( 17, 99)( 18,100)( 19, 89)( 20, 90)( 21, 61)( 22, 62)( 23, 97)( 24, 98)( 25,101)( 26,102)( 27, 81)( 28, 82)( 29, 80)( 30, 79)( 31, 86)( 32, 85)( 33, 83)( 34, 84)( 35, 93)( 36, 94)( 37, 72)( 38, 71)( 39, 95)( 40, 96)( 41, 88)( 42, 87)( 43, 92)( 44, 91)( 45, 76)( 46, 75)( 47, 70)( 48, 69)( 49, 78)( 50, 77)( 51, 60)( 52, 59);
s1 := Sym(104)!(  1, 55)(  2, 56)(  3, 53)(  4, 54)(  5, 69)(  6, 70)(  7, 64)(  8, 63)(  9, 84)( 10, 83)( 11, 59)( 12, 60)( 13,101)( 14,102)( 15, 97)( 16, 98)( 17, 58)( 18, 57)( 19, 73)( 20, 74)( 21, 72)( 22, 71)( 23, 89)( 24, 90)( 25, 86)( 26, 85)( 27, 92)( 28, 91)( 29, 88)( 30, 87)( 31, 61)( 32, 62)( 33, 77)( 34, 78)( 35, 81)( 36, 82)( 37, 76)( 38, 75)( 39, 79)( 40, 80)( 41, 99)( 42,100)( 43,103)( 44,104)( 45, 68)( 46, 67)( 47, 94)( 48, 93)( 49, 66)( 50, 65)( 51, 96)( 52, 95);
s2 := Sym(104)!(  3,  4)(  5, 13)(  6, 14)(  7,  8)(  9, 28)( 10, 27)( 11, 16)( 12, 15)( 17, 18)( 21, 30)( 22, 29)( 23, 45)( 24, 46)( 25, 49)( 26, 50)( 33, 34)( 35, 41)( 36, 42)( 37, 38)( 39, 43)( 40, 44)( 55, 56)( 57, 66)( 58, 65)( 61, 79)( 62, 80)( 63, 67)( 64, 68)( 71, 72)( 73, 81)( 74, 82)( 75, 98)( 76, 97)( 77,102)( 78,101)( 83, 84)( 87, 94)( 88, 93)( 91, 96)( 92, 95)( 99,100)(103,104);
poly := sub<Sym(104)|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*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*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 {12,12}

Twisty Puzzle