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

Twisty Puzzle