Polytope of Type {20,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4}*800
if this polytope has a name.
Group : SmallGroup(800,1058)
Rank : 3
Schlafli Type : {20,4}
Number of vertices, edges, etc : 100, 200, 20
Order of s0s1s2 : 4
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {20,4,2} of size 1600
Vertex Figure Of :
   {2,20,4} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,4}*400
   4-fold quotients : {10,4}*200
   25-fold quotients : {4,4}*32
   50-fold quotients : {2,4}*16, {4,2}*16
   100-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,4}*1600, {20,8}*1600a, {40,4}*1600a, {40,4}*1600b, {20,8}*1600b
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2> of order 2.
      10 facets:
         10 of {20}*40
      50 vertex figures:
         50 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 5.
      12 facets:
         10 of {4}*8
         2 of {20}*40
      20 vertex figures:
         20 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 5.
      4 facets:
         4 of {20}*40
      20 vertex figures:
         20 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 5.
      4 facets:
         4 of {20}*40
      20 vertex figures:
         20 of {4}*8

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