Polytope of Type {20,3}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,3}*1200
Also Known As : {20,3}6. if this polytope has another name.
Group : SmallGroup(1200,985)
Rank : 3
Schlafli Type : {20,3}
Number of vertices, edges, etc : 200, 300, 30
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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {10,3}*300
   25-fold quotients : {4,3}*48
   50-fold quotients : {4,3}*24
   100-fold quotients : {2,3}*12
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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 2.
      15 facets:
         15 of {20}*40
      100 vertex figures:
         100 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      20 facets:
         10 of {10}*20
         10 of {20}*40
      100 vertex figures:
         100 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 5.
      6 facets:
         6 of {20}*40
      40 vertex figures:
         40 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 5.
      14 facets:
         10 of {4}*8
         4 of {20}*40
      40 vertex figures:
         40 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 10.
      4 facets:
         2 of {20}*40
         2 of {10}*20
      20 vertex figures:
         20 of {3}*6
   P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2> of order 10.
      3 facets:
         3 of {20}*40
      20 vertex figures:
         20 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 10.
      7 facets:
         5 of {4}*8
         2 of {20}*40
      20 vertex figures:
         20 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 10.
      8 facets:
         5 of {4}*8
         2 of {10}*20
         1 of {20}*40
      20 vertex figures:
         20 of {3}*6
   P/N, where N=<s0*s1*s0*s1> of order 10.
      12 facets:
         10 of {2}*4
         2 of {20}*40
      20 vertex figures:
         20 of {3}*6
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1> of order 10.
      4 facets:
         2 of {10}*20
         2 of {20}*40
      20 vertex figures:
         20 of {3}*6

Permutation Representation (GAP) : 
s0 := (  1, 51)(  2, 55)(  3, 54)(  4, 53)(  5, 52)(  6, 71)(  7, 75)(  8, 74)(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 61)( 17, 65)( 18, 64)( 19, 63)( 20, 62)( 21, 56)( 22, 60)( 23, 59)( 24, 58)( 25, 57)( 26, 76)( 27, 80)( 28, 79)( 29, 78)( 30, 77)( 31, 96)( 32,100)( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)( 41, 86)( 42, 90)( 43, 89)( 44, 88)( 45, 87)( 46, 81)( 47, 85)( 48, 84)( 49, 83)( 50, 82);;
s1 := (  1,  2)(  3,  5)(  6,  8)(  9, 10)( 11, 14)( 12, 13)( 16, 20)( 17, 19)( 22, 25)( 23, 24)( 26, 27)( 28, 30)( 31, 33)( 34, 35)( 36, 39)( 37, 38)( 41, 45)( 42, 44)( 47, 50)( 48, 49)( 51, 77)( 52, 76)( 53, 80)( 54, 79)( 55, 78)( 56, 83)( 57, 82)( 58, 81)( 59, 85)( 60, 84)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 90)( 66, 95)( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97);;
s2 := (  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)( 11, 16)( 12, 22)( 18, 23)( 26, 76)( 27, 82)( 28, 88)( 29, 94)( 30,100)( 31, 96)( 32, 77)( 33, 83)( 34, 89)( 35, 95)( 36, 91)( 37, 97)( 38, 78)( 39, 84)( 40, 90)( 41, 86)( 42, 92)( 43, 98)( 44, 79)( 45, 85)( 46, 81)( 47, 87)( 48, 93)( 49, 99)( 50, 80)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)( 60, 70)( 61, 66)( 62, 72)( 68, 73);;
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, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(100)!(  1, 51)(  2, 55)(  3, 54)(  4, 53)(  5, 52)(  6, 71)(  7, 75)(  8, 74)(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 61)( 17, 65)( 18, 64)( 19, 63)( 20, 62)( 21, 56)( 22, 60)( 23, 59)( 24, 58)( 25, 57)( 26, 76)( 27, 80)( 28, 79)( 29, 78)( 30, 77)( 31, 96)( 32,100)( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)( 41, 86)( 42, 90)( 43, 89)( 44, 88)( 45, 87)( 46, 81)( 47, 85)( 48, 84)( 49, 83)( 50, 82);
s1 := Sym(100)!(  1,  2)(  3,  5)(  6,  8)(  9, 10)( 11, 14)( 12, 13)( 16, 20)( 17, 19)( 22, 25)( 23, 24)( 26, 27)( 28, 30)( 31, 33)( 34, 35)( 36, 39)( 37, 38)( 41, 45)( 42, 44)( 47, 50)( 48, 49)( 51, 77)( 52, 76)( 53, 80)( 54, 79)( 55, 78)( 56, 83)( 57, 82)( 58, 81)( 59, 85)( 60, 84)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 90)( 66, 95)( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97);
s2 := Sym(100)!(  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)( 11, 16)( 12, 22)( 18, 23)( 26, 76)( 27, 82)( 28, 88)( 29, 94)( 30,100)( 31, 96)( 32, 77)( 33, 83)( 34, 89)( 35, 95)( 36, 91)( 37, 97)( 38, 78)( 39, 84)( 40, 90)( 41, 86)( 42, 92)( 43, 98)( 44, 79)( 45, 85)( 46, 81)( 47, 87)( 48, 93)( 49, 99)( 50, 80)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)( 60, 70)( 61, 66)( 62, 72)( 68, 73);
poly := sub<Sym(100)|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, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
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