Polytope of Type {20,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10}*2000i
if this polytope has a name.
Group : SmallGroup(2000,919)
Rank : 3
Schlafli Type : {20,10}
Number of vertices, edges, etc : 100, 500, 50
Order of s0s1s2 : 4
Order of s0s1s2s1 : 10
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) :
   5-fold quotients : {4,10}*400
   10-fold quotients : {4,10}*200
   125-fold quotients : {4,2}*16
   250-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*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      25 facets:
         25 of {20}*40
      50 vertex figures:
         50 of {10}*20
   P/N, where N=<s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      25 facets:
         25 of {20}*40
      55 vertex figures:
         45 of {10}*20
         10 of {5}*10
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2> of order 5.
      10 facets:
         10 of {20}*40
      20 vertex figures:
         20 of {10}*20
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1> of order 5.
      10 facets:
         10 of {20}*40
      20 vertex figures:
         20 of {10}*20
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 5.
      10 facets:
         10 of {20}*40
      20 vertex figures:
         20 of {10}*20
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1> of order 5.
      10 facets:
         10 of {20}*40
      20 vertex figures:
         20 of {10}*20
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 5.
      10 facets:
         10 of {20}*40
      20 vertex figures:
         20 of {10}*20

Permutation Representation (GAP) : 
s0 := (  2,  5)(  3,  4)(  6, 26)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21,101)( 22,105)( 23,104)( 24,103)( 25,102)( 32, 35)( 33, 34)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 81)( 42, 85)( 43, 84)( 44, 83)( 45, 82)( 46,106)( 47,110)( 48,109)( 49,108)( 50,107)( 62, 65)( 63, 64)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 92, 95)( 93, 94)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(122,125)(123,124);;
s1 := (  1,  2)(  3,  5)(  6, 77)(  7, 76)(  8, 80)(  9, 79)( 10, 78)( 11, 27)( 12, 26)( 13, 30)( 14, 29)( 15, 28)( 16,102)( 17,101)( 18,105)( 19,104)( 20,103)( 21, 52)( 22, 51)( 23, 55)( 24, 54)( 25, 53)( 31, 87)( 32, 86)( 33, 90)( 34, 89)( 35, 88)( 36, 37)( 38, 40)( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46, 62)( 47, 61)( 48, 65)( 49, 64)( 50, 63)( 56, 97)( 57, 96)( 58,100)( 59, 99)( 60, 98)( 66,122)( 67,121)( 68,125)( 69,124)( 70,123)( 71, 72)( 73, 75)( 81, 82)( 83, 85)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)(116,117)(118,120);;
s2 := (  1, 31)(  2, 35)(  3, 34)(  4, 33)(  5, 32)(  6, 26)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)( 24, 38)( 25, 37)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)( 61,121)( 62,125)( 63,124)( 64,123)( 65,122)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)( 93, 94);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(125)!(  2,  5)(  3,  4)(  6, 26)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21,101)( 22,105)( 23,104)( 24,103)( 25,102)( 32, 35)( 33, 34)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 81)( 42, 85)( 43, 84)( 44, 83)( 45, 82)( 46,106)( 47,110)( 48,109)( 49,108)( 50,107)( 62, 65)( 63, 64)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 92, 95)( 93, 94)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(122,125)(123,124);
s1 := Sym(125)!(  1,  2)(  3,  5)(  6, 77)(  7, 76)(  8, 80)(  9, 79)( 10, 78)( 11, 27)( 12, 26)( 13, 30)( 14, 29)( 15, 28)( 16,102)( 17,101)( 18,105)( 19,104)( 20,103)( 21, 52)( 22, 51)( 23, 55)( 24, 54)( 25, 53)( 31, 87)( 32, 86)( 33, 90)( 34, 89)( 35, 88)( 36, 37)( 38, 40)( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46, 62)( 47, 61)( 48, 65)( 49, 64)( 50, 63)( 56, 97)( 57, 96)( 58,100)( 59, 99)( 60, 98)( 66,122)( 67,121)( 68,125)( 69,124)( 70,123)( 71, 72)( 73, 75)( 81, 82)( 83, 85)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)(116,117)(118,120);
s2 := Sym(125)!(  1, 31)(  2, 35)(  3, 34)(  4, 33)(  5, 32)(  6, 26)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)( 24, 38)( 25, 37)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)( 61,121)( 62,125)( 63,124)( 64,123)( 65,122)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)( 93, 94);
poly := sub<Sym(125)|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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
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