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}*2000j
if this polytope has a name.
Group : SmallGroup(2000,942)
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
   Self-Petrie
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}*1000e
   5-fold quotients : {4,10}*400
   10-fold quotients : {4,10}*200
   25-fold quotients : {20,2}*80
   50-fold quotients : {10,2}*40
   100-fold quotients : {5,2}*20
   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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*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*s2*s1*s0*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*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1> of order 5.
      10 facets:
         10 of {20}*40
      20 vertex figures:
         20 of {10}*20
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 5.
      10 facets:
         10 of {20}*40
      20 vertex figures:
         20 of {10}*20
   P/N, where N=<s1*s2*s1*s2> of order 5.
      10 facets:
         10 of {20}*40
      60 vertex figures:
         50 of {2}*4
         10 of {10}*20
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*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, 56)(  7, 60)(  8, 59)(  9, 58)( 10, 57)( 11,111)( 12,115)( 13,114)( 14,113)( 15,112)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 96)( 22,100)( 23, 99)( 24, 98)( 25, 97)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 32, 35)( 33, 34)( 36, 86)( 37, 90)( 38, 89)( 39, 88)( 40, 87)( 46, 71)( 47, 75)( 48, 74)( 49, 73)( 50, 72)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 62, 65)( 63, 64)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 81,106)( 82,110)( 83,109)( 84,108)( 85,107)( 92, 95)( 93, 94)(122,125)(123,124)(127,130)(128,129)(131,181)(132,185)(133,184)(134,183)(135,182)(136,236)(137,240)(138,239)(139,238)(140,237)(141,166)(142,170)(143,169)(144,168)(145,167)(146,221)(147,225)(148,224)(149,223)(150,222)(151,226)(152,230)(153,229)(154,228)(155,227)(157,160)(158,159)(161,211)(162,215)(163,214)(164,213)(165,212)(171,196)(172,200)(173,199)(174,198)(175,197)(176,201)(177,205)(178,204)(179,203)(180,202)(187,190)(188,189)(191,241)(192,245)(193,244)(194,243)(195,242)(206,231)(207,235)(208,234)(209,233)(210,232)(217,220)(218,219)(247,250)(248,249);;
s1 := (  1,  2)(  3,  5)(  6, 42)(  7, 41)(  8, 45)(  9, 44)( 10, 43)( 11, 57)( 12, 56)( 13, 60)( 14, 59)( 15, 58)( 16, 97)( 17, 96)( 18,100)( 19, 99)( 20, 98)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26, 62)( 27, 61)( 28, 65)( 29, 64)( 30, 63)( 31, 77)( 32, 76)( 33, 80)( 34, 79)( 35, 78)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 46, 47)( 48, 50)( 51,122)( 52,121)( 53,125)( 54,124)( 55,123)( 66, 67)( 68, 70)( 71, 82)( 72, 81)( 73, 85)( 74, 84)( 75, 83)( 86, 87)( 88, 90)( 91,102)( 92,101)( 93,105)( 94,104)( 95,103)(106,107)(108,110)(126,127)(128,130)(131,167)(132,166)(133,170)(134,169)(135,168)(136,182)(137,181)(138,185)(139,184)(140,183)(141,222)(142,221)(143,225)(144,224)(145,223)(146,237)(147,236)(148,240)(149,239)(150,238)(151,187)(152,186)(153,190)(154,189)(155,188)(156,202)(157,201)(158,205)(159,204)(160,203)(161,242)(162,241)(163,245)(164,244)(165,243)(171,172)(173,175)(176,247)(177,246)(178,250)(179,249)(180,248)(191,192)(193,195)(196,207)(197,206)(198,210)(199,209)(200,208)(211,212)(213,215)(216,227)(217,226)(218,230)(219,229)(220,228)(231,232)(233,235);;
s2 := (  1,156)(  2,157)(  3,158)(  4,159)(  5,160)(  6,151)(  7,152)(  8,153)(  9,154)( 10,155)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)( 16,166)( 17,167)( 18,168)( 19,169)( 20,170)( 21,161)( 22,162)( 23,163)( 24,164)( 25,165)( 26,131)( 27,132)( 28,133)( 29,134)( 30,135)( 31,126)( 32,127)( 33,128)( 34,129)( 35,130)( 36,146)( 37,147)( 38,148)( 39,149)( 40,150)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)( 51,231)( 52,232)( 53,233)( 54,234)( 55,235)( 56,226)( 57,227)( 58,228)( 59,229)( 60,230)( 61,246)( 62,247)( 63,248)( 64,249)( 65,250)( 66,241)( 67,242)( 68,243)( 69,244)( 70,245)( 71,236)( 72,237)( 73,238)( 74,239)( 75,240)( 76,206)( 77,207)( 78,208)( 79,209)( 80,210)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,221)( 87,222)( 88,223)( 89,224)( 90,225)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,181)(102,182)(103,183)(104,184)(105,185)(106,176)(107,177)(108,178)(109,179)(110,180)(111,196)(112,197)(113,198)(114,199)(115,200)(116,191)(117,192)(118,193)(119,194)(120,195)(121,186)(122,187)(123,188)(124,189)(125,190);;
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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(250)!(  2,  5)(  3,  4)(  6, 56)(  7, 60)(  8, 59)(  9, 58)( 10, 57)( 11,111)( 12,115)( 13,114)( 14,113)( 15,112)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 96)( 22,100)( 23, 99)( 24, 98)( 25, 97)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 32, 35)( 33, 34)( 36, 86)( 37, 90)( 38, 89)( 39, 88)( 40, 87)( 46, 71)( 47, 75)( 48, 74)( 49, 73)( 50, 72)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 62, 65)( 63, 64)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 81,106)( 82,110)( 83,109)( 84,108)( 85,107)( 92, 95)( 93, 94)(122,125)(123,124)(127,130)(128,129)(131,181)(132,185)(133,184)(134,183)(135,182)(136,236)(137,240)(138,239)(139,238)(140,237)(141,166)(142,170)(143,169)(144,168)(145,167)(146,221)(147,225)(148,224)(149,223)(150,222)(151,226)(152,230)(153,229)(154,228)(155,227)(157,160)(158,159)(161,211)(162,215)(163,214)(164,213)(165,212)(171,196)(172,200)(173,199)(174,198)(175,197)(176,201)(177,205)(178,204)(179,203)(180,202)(187,190)(188,189)(191,241)(192,245)(193,244)(194,243)(195,242)(206,231)(207,235)(208,234)(209,233)(210,232)(217,220)(218,219)(247,250)(248,249);
s1 := Sym(250)!(  1,  2)(  3,  5)(  6, 42)(  7, 41)(  8, 45)(  9, 44)( 10, 43)( 11, 57)( 12, 56)( 13, 60)( 14, 59)( 15, 58)( 16, 97)( 17, 96)( 18,100)( 19, 99)( 20, 98)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26, 62)( 27, 61)( 28, 65)( 29, 64)( 30, 63)( 31, 77)( 32, 76)( 33, 80)( 34, 79)( 35, 78)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 46, 47)( 48, 50)( 51,122)( 52,121)( 53,125)( 54,124)( 55,123)( 66, 67)( 68, 70)( 71, 82)( 72, 81)( 73, 85)( 74, 84)( 75, 83)( 86, 87)( 88, 90)( 91,102)( 92,101)( 93,105)( 94,104)( 95,103)(106,107)(108,110)(126,127)(128,130)(131,167)(132,166)(133,170)(134,169)(135,168)(136,182)(137,181)(138,185)(139,184)(140,183)(141,222)(142,221)(143,225)(144,224)(145,223)(146,237)(147,236)(148,240)(149,239)(150,238)(151,187)(152,186)(153,190)(154,189)(155,188)(156,202)(157,201)(158,205)(159,204)(160,203)(161,242)(162,241)(163,245)(164,244)(165,243)(171,172)(173,175)(176,247)(177,246)(178,250)(179,249)(180,248)(191,192)(193,195)(196,207)(197,206)(198,210)(199,209)(200,208)(211,212)(213,215)(216,227)(217,226)(218,230)(219,229)(220,228)(231,232)(233,235);
s2 := Sym(250)!(  1,156)(  2,157)(  3,158)(  4,159)(  5,160)(  6,151)(  7,152)(  8,153)(  9,154)( 10,155)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)( 16,166)( 17,167)( 18,168)( 19,169)( 20,170)( 21,161)( 22,162)( 23,163)( 24,164)( 25,165)( 26,131)( 27,132)( 28,133)( 29,134)( 30,135)( 31,126)( 32,127)( 33,128)( 34,129)( 35,130)( 36,146)( 37,147)( 38,148)( 39,149)( 40,150)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)( 51,231)( 52,232)( 53,233)( 54,234)( 55,235)( 56,226)( 57,227)( 58,228)( 59,229)( 60,230)( 61,246)( 62,247)( 63,248)( 64,249)( 65,250)( 66,241)( 67,242)( 68,243)( 69,244)( 70,245)( 71,236)( 72,237)( 73,238)( 74,239)( 75,240)( 76,206)( 77,207)( 78,208)( 79,209)( 80,210)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,221)( 87,222)( 88,223)( 89,224)( 90,225)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,181)(102,182)(103,183)(104,184)(105,185)(106,176)(107,177)(108,178)(109,179)(110,180)(111,196)(112,197)(113,198)(114,199)(115,200)(116,191)(117,192)(118,193)(119,194)(120,195)(121,186)(122,187)(123,188)(124,189)(125,190);
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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope

Twisty Puzzle