Polytope of Type {10,20}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,20}*2000d
if this polytope has a name.
Group : SmallGroup(2000,482)
Rank : 3
Schlafli Type : {10,20}
Number of vertices, edges, etc : 50, 500, 100
Order of s0s1s2 : 20
Order of s0s1s2s1 : 10
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 : {10,20}*1000d
   5-fold quotients : {10,4}*400
   10-fold quotients : {10,4}*200
   125-fold quotients : {2,4}*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*s0*s2> of order 5.
      20 facets:
         20 of {10}*20
      10 vertex figures:
         10 of {20}*40
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1> of order 5.
      20 facets:
         20 of {10}*20
      10 vertex figures:
         10 of {20}*40

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