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}*2000f
if this polytope has a name.
Group : SmallGroup(2000,482)
Rank : 3
Schlafli Type : {20,10}
Number of vertices, edges, etc : 100, 500, 50
Order of s0s1s2 : 20
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) :
   2-fold quotients : {20,10}*1000b
   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*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 5.
      10 facets:
         10 of {20}*40
      20 vertex figures:
         20 of {10}*20
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1> 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, 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 := (  1,  3)(  4,  5)(  6, 43)(  7, 42)(  8, 41)(  9, 45)( 10, 44)( 11, 56)( 12, 60)( 13, 59)( 14, 58)( 15, 57)( 16, 97)( 17, 96)( 18,100)( 19, 99)( 20, 98)( 21,111)( 22,115)( 23,114)( 24,113)( 25,112)( 26, 63)( 27, 62)( 28, 61)( 29, 65)( 30, 64)( 31, 80)( 32, 79)( 33, 78)( 34, 77)( 35, 76)( 36,120)( 37,119)( 38,118)( 39,117)( 40,116)( 46, 49)( 47, 48)( 51,122)( 52,121)( 53,125)( 54,124)( 55,123)( 66, 68)( 69, 70)( 71, 81)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,105)( 94,104)( 95,103)(106,110)(107,109)(126,128)(129,130)(131,168)(132,167)(133,166)(134,170)(135,169)(136,181)(137,185)(138,184)(139,183)(140,182)(141,222)(142,221)(143,225)(144,224)(145,223)(146,236)(147,240)(148,239)(149,238)(150,237)(151,188)(152,187)(153,186)(154,190)(155,189)(156,205)(157,204)(158,203)(159,202)(160,201)(161,245)(162,244)(163,243)(164,242)(165,241)(171,174)(172,173)(176,247)(177,246)(178,250)(179,249)(180,248)(191,193)(194,195)(196,206)(197,210)(198,209)(199,208)(200,207)(211,215)(212,214)(216,227)(217,226)(218,230)(219,229)(220,228)(231,235)(232,234);;
s2 := (  1,160)(  2,156)(  3,157)(  4,158)(  5,159)(  6,154)(  7,155)(  8,151)(  9,152)( 10,153)( 11,173)( 12,174)( 13,175)( 14,171)( 15,172)( 16,167)( 17,168)( 18,169)( 19,170)( 20,166)( 21,161)( 22,162)( 23,163)( 24,164)( 25,165)( 26,133)( 27,134)( 28,135)( 29,131)( 30,132)( 31,127)( 32,128)( 33,129)( 34,130)( 35,126)( 36,146)( 37,147)( 38,148)( 39,149)( 40,150)( 41,145)( 42,141)( 43,142)( 44,143)( 45,144)( 46,139)( 47,140)( 48,136)( 49,137)( 50,138)( 51,231)( 52,232)( 53,233)( 54,234)( 55,235)( 56,230)( 57,226)( 58,227)( 59,228)( 60,229)( 61,249)( 62,250)( 63,246)( 64,247)( 65,248)( 66,243)( 67,244)( 68,245)( 69,241)( 70,242)( 71,237)( 72,238)( 73,239)( 74,240)( 75,236)( 76,209)( 77,210)( 78,206)( 79,207)( 80,208)( 81,203)( 82,204)( 83,205)( 84,201)( 85,202)( 86,222)( 87,223)( 88,224)( 89,225)( 90,221)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,215)( 97,211)( 98,212)( 99,213)(100,214)(101,182)(102,183)(103,184)(104,185)(105,181)(106,176)(107,177)(108,178)(109,179)(110,180)(111,200)(112,196)(113,197)(114,198)(115,199)(116,194)(117,195)(118,191)(119,192)(120,193)(121,188)(122,189)(123,190)(124,186)(125,187);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*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(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)!(  1,  3)(  4,  5)(  6, 43)(  7, 42)(  8, 41)(  9, 45)( 10, 44)( 11, 56)( 12, 60)( 13, 59)( 14, 58)( 15, 57)( 16, 97)( 17, 96)( 18,100)( 19, 99)( 20, 98)( 21,111)( 22,115)( 23,114)( 24,113)( 25,112)( 26, 63)( 27, 62)( 28, 61)( 29, 65)( 30, 64)( 31, 80)( 32, 79)( 33, 78)( 34, 77)( 35, 76)( 36,120)( 37,119)( 38,118)( 39,117)( 40,116)( 46, 49)( 47, 48)( 51,122)( 52,121)( 53,125)( 54,124)( 55,123)( 66, 68)( 69, 70)( 71, 81)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,105)( 94,104)( 95,103)(106,110)(107,109)(126,128)(129,130)(131,168)(132,167)(133,166)(134,170)(135,169)(136,181)(137,185)(138,184)(139,183)(140,182)(141,222)(142,221)(143,225)(144,224)(145,223)(146,236)(147,240)(148,239)(149,238)(150,237)(151,188)(152,187)(153,186)(154,190)(155,189)(156,205)(157,204)(158,203)(159,202)(160,201)(161,245)(162,244)(163,243)(164,242)(165,241)(171,174)(172,173)(176,247)(177,246)(178,250)(179,249)(180,248)(191,193)(194,195)(196,206)(197,210)(198,209)(199,208)(200,207)(211,215)(212,214)(216,227)(217,226)(218,230)(219,229)(220,228)(231,235)(232,234);
s2 := Sym(250)!(  1,160)(  2,156)(  3,157)(  4,158)(  5,159)(  6,154)(  7,155)(  8,151)(  9,152)( 10,153)( 11,173)( 12,174)( 13,175)( 14,171)( 15,172)( 16,167)( 17,168)( 18,169)( 19,170)( 20,166)( 21,161)( 22,162)( 23,163)( 24,164)( 25,165)( 26,133)( 27,134)( 28,135)( 29,131)( 30,132)( 31,127)( 32,128)( 33,129)( 34,130)( 35,126)( 36,146)( 37,147)( 38,148)( 39,149)( 40,150)( 41,145)( 42,141)( 43,142)( 44,143)( 45,144)( 46,139)( 47,140)( 48,136)( 49,137)( 50,138)( 51,231)( 52,232)( 53,233)( 54,234)( 55,235)( 56,230)( 57,226)( 58,227)( 59,228)( 60,229)( 61,249)( 62,250)( 63,246)( 64,247)( 65,248)( 66,243)( 67,244)( 68,245)( 69,241)( 70,242)( 71,237)( 72,238)( 73,239)( 74,240)( 75,236)( 76,209)( 77,210)( 78,206)( 79,207)( 80,208)( 81,203)( 82,204)( 83,205)( 84,201)( 85,202)( 86,222)( 87,223)( 88,224)( 89,225)( 90,221)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,215)( 97,211)( 98,212)( 99,213)(100,214)(101,182)(102,183)(103,184)(104,185)(105,181)(106,176)(107,177)(108,178)(109,179)(110,180)(111,200)(112,196)(113,197)(114,198)(115,199)(116,194)(117,195)(118,191)(119,192)(120,193)(121,188)(122,189)(123,190)(124,186)(125,187);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*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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