Polytope of Type {4,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10}*2000a
if this polytope has a name.
Group : SmallGroup(2000,482)
Rank : 3
Schlafli Type : {4,10}
Number of vertices, edges, etc : 100, 500, 250
Order of s0s1s2 : 20
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,10}*1000
   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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      125 facets:
         125 of {4}*8
      51 vertex figures:
         49 of {10}*20
         2 of {5}*10
   P/N, where N=<s0*s1*s0*s1> of order 2.
      130 facets:
         10 of {2}*4
         120 of {4}*8
      50 vertex figures:
         50 of {10}*20
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      65 facets:
         5 of {2}*4
         60 of {4}*8
      26 vertex figures:
         24 of {10}*20
         2 of {5}*10
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1> of order 5.
      50 facets:
         50 of {4}*8
      20 vertex figures:
         20 of {10}*20
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0> of order 5.
      50 facets:
         50 of {4}*8
      28 vertex figures:
         18 of {10}*20
         10 of {2}*4
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1> of order 5.
      50 facets:
         50 of {4}*8
      20 vertex figures:
         20 of {10}*20
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1> of order 10.
      30 facets:
         10 of {2}*4
         20 of {4}*8
      10 vertex figures:
         10 of {10}*20
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0, s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1> of order 10.
      25 facets:
         25 of {4}*8
      15 vertex figures:
         8 of {10}*20
         2 of {5}*10
         5 of {2}*4
   P/N, where N=<s0*s1*s0*s1, s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 10.
      30 facets:
         10 of {2}*4
         20 of {4}*8
      14 vertex figures:
         9 of {10}*20
         5 of {2}*4
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1> of order 10.
      30 facets:
         10 of {2}*4
         20 of {4}*8
      10 vertex figures:
         10 of {10}*20

Permutation Representation (GAP) : 
s0 := (  2,  5)(  3,  4)(  6, 59)(  7, 58)(  8, 57)(  9, 56)( 10, 60)( 11,114)( 12,113)( 13,112)( 14,111)( 15,115)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21,100)( 22, 99)( 23, 98)( 24, 97)( 25, 96)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31, 34)( 32, 33)( 36, 89)( 37, 88)( 38, 87)( 39, 86)( 40, 90)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 61, 64)( 62, 63)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 81,109)( 82,108)( 83,107)( 84,106)( 85,110)( 92, 95)( 93, 94)(121,125)(122,124)(127,130)(128,129)(131,184)(132,183)(133,182)(134,181)(135,185)(136,239)(137,238)(138,237)(139,236)(140,240)(141,166)(142,170)(143,169)(144,168)(145,167)(146,225)(147,224)(148,223)(149,222)(150,221)(151,226)(152,230)(153,229)(154,228)(155,227)(156,159)(157,158)(161,214)(162,213)(163,212)(164,211)(165,215)(171,200)(172,199)(173,198)(174,197)(175,196)(176,201)(177,205)(178,204)(179,203)(180,202)(186,189)(187,188)(191,241)(192,245)(193,244)(194,243)(195,242)(206,234)(207,233)(208,232)(209,231)(210,235)(217,220)(218,219)(246,250)(247,249);;
s1 := (  2,  5)(  3,  4)(  6, 41)(  7, 45)(  8, 44)(  9, 43)( 10, 42)( 11, 59)( 12, 58)( 13, 57)( 14, 56)( 15, 60)( 16,100)( 17, 99)( 18, 98)( 19, 97)( 20, 96)( 21,114)( 22,113)( 23,112)( 24,111)( 25,115)( 26, 61)( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 78)( 32, 77)( 33, 76)( 34, 80)( 35, 79)( 36,118)( 37,117)( 38,116)( 39,120)( 40,119)( 46, 47)( 48, 50)( 51,125)( 52,124)( 53,123)( 54,122)( 55,121)( 67, 70)( 68, 69)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 85)( 86, 88)( 89, 90)( 91,105)( 92,104)( 93,103)( 94,102)( 95,101)(106,108)(109,110)(127,130)(128,129)(131,166)(132,170)(133,169)(134,168)(135,167)(136,184)(137,183)(138,182)(139,181)(140,185)(141,225)(142,224)(143,223)(144,222)(145,221)(146,239)(147,238)(148,237)(149,236)(150,240)(151,186)(152,190)(153,189)(154,188)(155,187)(156,203)(157,202)(158,201)(159,205)(160,204)(161,243)(162,242)(163,241)(164,245)(165,244)(171,172)(173,175)(176,250)(177,249)(178,248)(179,247)(180,246)(192,195)(193,194)(196,209)(197,208)(198,207)(199,206)(200,210)(211,213)(214,215)(216,230)(217,229)(218,228)(219,227)(220,226)(231,233)(234,235);;
s2 := (  1,216)(  2,217)(  3,218)(  4,219)(  5,220)(  6,213)(  7,214)(  8,215)(  9,211)( 10,212)( 11,210)( 12,206)( 13,207)( 14,208)( 15,209)( 16,202)( 17,203)( 18,204)( 19,205)( 20,201)( 21,224)( 22,225)( 23,221)( 24,222)( 25,223)( 26,194)( 27,195)( 28,191)( 29,192)( 30,193)( 31,186)( 32,187)( 33,188)( 34,189)( 35,190)( 36,183)( 37,184)( 38,185)( 39,181)( 40,182)( 41,180)( 42,176)( 43,177)( 44,178)( 45,179)( 46,197)( 47,198)( 48,199)( 49,200)( 50,196)( 51,167)( 52,168)( 53,169)( 54,170)( 55,166)( 56,164)( 57,165)( 58,161)( 59,162)( 60,163)( 61,156)( 62,157)( 63,158)( 64,159)( 65,160)( 66,153)( 67,154)( 68,155)( 69,151)( 70,152)( 71,175)( 72,171)( 73,172)( 74,173)( 75,174)( 76,145)( 77,141)( 78,142)( 79,143)( 80,144)( 81,137)( 82,138)( 83,139)( 84,140)( 85,136)( 86,134)( 87,135)( 88,131)( 89,132)( 90,133)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,148)( 97,149)( 98,150)( 99,146)(100,147)(101,243)(102,244)(103,245)(104,241)(105,242)(106,240)(107,236)(108,237)(109,238)(110,239)(111,232)(112,233)(113,234)(114,235)(115,231)(116,229)(117,230)(118,226)(119,227)(120,228)(121,246)(122,247)(123,248)(124,249)(125,250);;
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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(250)!(  2,  5)(  3,  4)(  6, 59)(  7, 58)(  8, 57)(  9, 56)( 10, 60)( 11,114)( 12,113)( 13,112)( 14,111)( 15,115)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21,100)( 22, 99)( 23, 98)( 24, 97)( 25, 96)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31, 34)( 32, 33)( 36, 89)( 37, 88)( 38, 87)( 39, 86)( 40, 90)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 61, 64)( 62, 63)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 81,109)( 82,108)( 83,107)( 84,106)( 85,110)( 92, 95)( 93, 94)(121,125)(122,124)(127,130)(128,129)(131,184)(132,183)(133,182)(134,181)(135,185)(136,239)(137,238)(138,237)(139,236)(140,240)(141,166)(142,170)(143,169)(144,168)(145,167)(146,225)(147,224)(148,223)(149,222)(150,221)(151,226)(152,230)(153,229)(154,228)(155,227)(156,159)(157,158)(161,214)(162,213)(163,212)(164,211)(165,215)(171,200)(172,199)(173,198)(174,197)(175,196)(176,201)(177,205)(178,204)(179,203)(180,202)(186,189)(187,188)(191,241)(192,245)(193,244)(194,243)(195,242)(206,234)(207,233)(208,232)(209,231)(210,235)(217,220)(218,219)(246,250)(247,249);
s1 := Sym(250)!(  2,  5)(  3,  4)(  6, 41)(  7, 45)(  8, 44)(  9, 43)( 10, 42)( 11, 59)( 12, 58)( 13, 57)( 14, 56)( 15, 60)( 16,100)( 17, 99)( 18, 98)( 19, 97)( 20, 96)( 21,114)( 22,113)( 23,112)( 24,111)( 25,115)( 26, 61)( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 78)( 32, 77)( 33, 76)( 34, 80)( 35, 79)( 36,118)( 37,117)( 38,116)( 39,120)( 40,119)( 46, 47)( 48, 50)( 51,125)( 52,124)( 53,123)( 54,122)( 55,121)( 67, 70)( 68, 69)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 85)( 86, 88)( 89, 90)( 91,105)( 92,104)( 93,103)( 94,102)( 95,101)(106,108)(109,110)(127,130)(128,129)(131,166)(132,170)(133,169)(134,168)(135,167)(136,184)(137,183)(138,182)(139,181)(140,185)(141,225)(142,224)(143,223)(144,222)(145,221)(146,239)(147,238)(148,237)(149,236)(150,240)(151,186)(152,190)(153,189)(154,188)(155,187)(156,203)(157,202)(158,201)(159,205)(160,204)(161,243)(162,242)(163,241)(164,245)(165,244)(171,172)(173,175)(176,250)(177,249)(178,248)(179,247)(180,246)(192,195)(193,194)(196,209)(197,208)(198,207)(199,206)(200,210)(211,213)(214,215)(216,230)(217,229)(218,228)(219,227)(220,226)(231,233)(234,235);
s2 := Sym(250)!(  1,216)(  2,217)(  3,218)(  4,219)(  5,220)(  6,213)(  7,214)(  8,215)(  9,211)( 10,212)( 11,210)( 12,206)( 13,207)( 14,208)( 15,209)( 16,202)( 17,203)( 18,204)( 19,205)( 20,201)( 21,224)( 22,225)( 23,221)( 24,222)( 25,223)( 26,194)( 27,195)( 28,191)( 29,192)( 30,193)( 31,186)( 32,187)( 33,188)( 34,189)( 35,190)( 36,183)( 37,184)( 38,185)( 39,181)( 40,182)( 41,180)( 42,176)( 43,177)( 44,178)( 45,179)( 46,197)( 47,198)( 48,199)( 49,200)( 50,196)( 51,167)( 52,168)( 53,169)( 54,170)( 55,166)( 56,164)( 57,165)( 58,161)( 59,162)( 60,163)( 61,156)( 62,157)( 63,158)( 64,159)( 65,160)( 66,153)( 67,154)( 68,155)( 69,151)( 70,152)( 71,175)( 72,171)( 73,172)( 74,173)( 75,174)( 76,145)( 77,141)( 78,142)( 79,143)( 80,144)( 81,137)( 82,138)( 83,139)( 84,140)( 85,136)( 86,134)( 87,135)( 88,131)( 89,132)( 90,133)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,148)( 97,149)( 98,150)( 99,146)(100,147)(101,243)(102,244)(103,245)(104,241)(105,242)(106,240)(107,236)(108,237)(109,238)(110,239)(111,232)(112,233)(113,234)(114,235)(115,231)(116,229)(117,230)(118,226)(119,227)(120,228)(121,246)(122,247)(123,248)(124,249)(125,250);
poly := sub<Sym(250)|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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle