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Polytope of Type {20,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10}*2000a
if this polytope has a name.
Group : SmallGroup(2000,372)
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 : {10,10}*1000a
   4-fold quotients : {5,10}*500
   5-fold quotients : {20,10}*400b
   10-fold quotients : {10,10}*200c
   20-fold quotients : {5,10}*100
   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.
Permutation Representation (GAP) :
s0 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,121)
( 32,122)( 33,123)( 34,124)( 35,125)( 36,116)( 37,117)( 38,118)( 39,119)
( 40,120)( 41,111)( 42,112)( 43,113)( 44,114)( 45,115)( 46,106)( 47,107)
( 48,108)( 49,109)( 50,110)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)
( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)( 63, 93)
( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)
( 72, 82)( 73, 83)( 74, 84)( 75, 85)(131,146)(132,147)(133,148)(134,149)
(135,150)(136,141)(137,142)(138,143)(139,144)(140,145)(151,226)(152,227)
(153,228)(154,229)(155,230)(156,246)(157,247)(158,248)(159,249)(160,250)
(161,241)(162,242)(163,243)(164,244)(165,245)(166,236)(167,237)(168,238)
(169,239)(170,240)(171,231)(172,232)(173,233)(174,234)(175,235)(176,201)
(177,202)(178,203)(179,204)(180,205)(181,221)(182,222)(183,223)(184,224)
(185,225)(186,216)(187,217)(188,218)(189,219)(190,220)(191,211)(192,212)
(193,213)(194,214)(195,215)(196,206)(197,207)(198,208)(199,209)(200,210)
(251,376)(252,377)(253,378)(254,379)(255,380)(256,396)(257,397)(258,398)
(259,399)(260,400)(261,391)(262,392)(263,393)(264,394)(265,395)(266,386)
(267,387)(268,388)(269,389)(270,390)(271,381)(272,382)(273,383)(274,384)
(275,385)(276,476)(277,477)(278,478)(279,479)(280,480)(281,496)(282,497)
(283,498)(284,499)(285,500)(286,491)(287,492)(288,493)(289,494)(290,495)
(291,486)(292,487)(293,488)(294,489)(295,490)(296,481)(297,482)(298,483)
(299,484)(300,485)(301,451)(302,452)(303,453)(304,454)(305,455)(306,471)
(307,472)(308,473)(309,474)(310,475)(311,466)(312,467)(313,468)(314,469)
(315,470)(316,461)(317,462)(318,463)(319,464)(320,465)(321,456)(322,457)
(323,458)(324,459)(325,460)(326,426)(327,427)(328,428)(329,429)(330,430)
(331,446)(332,447)(333,448)(334,449)(335,450)(336,441)(337,442)(338,443)
(339,444)(340,445)(341,436)(342,437)(343,438)(344,439)(345,440)(346,431)
(347,432)(348,433)(349,434)(350,435)(351,401)(352,402)(353,403)(354,404)
(355,405)(356,421)(357,422)(358,423)(359,424)(360,425)(361,416)(362,417)
(363,418)(364,419)(365,420)(366,411)(367,412)(368,413)(369,414)(370,415)
(371,406)(372,407)(373,408)(374,409)(375,410);;
s1 := (  1,307)(  2,308)(  3,309)(  4,310)(  5,306)(  6,305)(  7,301)(  8,302)
(  9,303)( 10,304)( 11,323)( 12,324)( 13,325)( 14,321)( 15,322)( 16,316)
( 17,317)( 18,318)( 19,319)( 20,320)( 21,314)( 22,315)( 23,311)( 24,312)
( 25,313)( 26,282)( 27,283)( 28,284)( 29,285)( 30,281)( 31,280)( 32,276)
( 33,277)( 34,278)( 35,279)( 36,298)( 37,299)( 38,300)( 39,296)( 40,297)
( 41,291)( 42,292)( 43,293)( 44,294)( 45,295)( 46,289)( 47,290)( 48,286)
( 49,287)( 50,288)( 51,257)( 52,258)( 53,259)( 54,260)( 55,256)( 56,255)
( 57,251)( 58,252)( 59,253)( 60,254)( 61,273)( 62,274)( 63,275)( 64,271)
( 65,272)( 66,266)( 67,267)( 68,268)( 69,269)( 70,270)( 71,264)( 72,265)
( 73,261)( 74,262)( 75,263)( 76,357)( 77,358)( 78,359)( 79,360)( 80,356)
( 81,355)( 82,351)( 83,352)( 84,353)( 85,354)( 86,373)( 87,374)( 88,375)
( 89,371)( 90,372)( 91,366)( 92,367)( 93,368)( 94,369)( 95,370)( 96,364)
( 97,365)( 98,361)( 99,362)(100,363)(101,332)(102,333)(103,334)(104,335)
(105,331)(106,330)(107,326)(108,327)(109,328)(110,329)(111,348)(112,349)
(113,350)(114,346)(115,347)(116,341)(117,342)(118,343)(119,344)(120,345)
(121,339)(122,340)(123,336)(124,337)(125,338)(126,432)(127,433)(128,434)
(129,435)(130,431)(131,430)(132,426)(133,427)(134,428)(135,429)(136,448)
(137,449)(138,450)(139,446)(140,447)(141,441)(142,442)(143,443)(144,444)
(145,445)(146,439)(147,440)(148,436)(149,437)(150,438)(151,407)(152,408)
(153,409)(154,410)(155,406)(156,405)(157,401)(158,402)(159,403)(160,404)
(161,423)(162,424)(163,425)(164,421)(165,422)(166,416)(167,417)(168,418)
(169,419)(170,420)(171,414)(172,415)(173,411)(174,412)(175,413)(176,382)
(177,383)(178,384)(179,385)(180,381)(181,380)(182,376)(183,377)(184,378)
(185,379)(186,398)(187,399)(188,400)(189,396)(190,397)(191,391)(192,392)
(193,393)(194,394)(195,395)(196,389)(197,390)(198,386)(199,387)(200,388)
(201,482)(202,483)(203,484)(204,485)(205,481)(206,480)(207,476)(208,477)
(209,478)(210,479)(211,498)(212,499)(213,500)(214,496)(215,497)(216,491)
(217,492)(218,493)(219,494)(220,495)(221,489)(222,490)(223,486)(224,487)
(225,488)(226,457)(227,458)(228,459)(229,460)(230,456)(231,455)(232,451)
(233,452)(234,453)(235,454)(236,473)(237,474)(238,475)(239,471)(240,472)
(241,466)(242,467)(243,468)(244,469)(245,470)(246,464)(247,465)(248,461)
(249,462)(250,463);;
s2 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,106)
( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)( 39,113)
( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)( 47,125)
( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)
( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)( 63, 89)
( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 96)
( 72,100)( 73, 99)( 74, 98)( 75, 97)(127,130)(128,129)(132,135)(133,134)
(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)
(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)
(161,236)(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)
(169,243)(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)(176,201)
(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)(184,208)
(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)(192,220)
(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)(200,222)
(252,255)(253,254)(257,260)(258,259)(262,265)(263,264)(267,270)(268,269)
(272,275)(273,274)(276,351)(277,355)(278,354)(279,353)(280,352)(281,356)
(282,360)(283,359)(284,358)(285,357)(286,361)(287,365)(288,364)(289,363)
(290,362)(291,366)(292,370)(293,369)(294,368)(295,367)(296,371)(297,375)
(298,374)(299,373)(300,372)(301,326)(302,330)(303,329)(304,328)(305,327)
(306,331)(307,335)(308,334)(309,333)(310,332)(311,336)(312,340)(313,339)
(314,338)(315,337)(316,341)(317,345)(318,344)(319,343)(320,342)(321,346)
(322,350)(323,349)(324,348)(325,347)(377,380)(378,379)(382,385)(383,384)
(387,390)(388,389)(392,395)(393,394)(397,400)(398,399)(401,476)(402,480)
(403,479)(404,478)(405,477)(406,481)(407,485)(408,484)(409,483)(410,482)
(411,486)(412,490)(413,489)(414,488)(415,487)(416,491)(417,495)(418,494)
(419,493)(420,492)(421,496)(422,500)(423,499)(424,498)(425,497)(426,451)
(427,455)(428,454)(429,453)(430,452)(431,456)(432,460)(433,459)(434,458)
(435,457)(436,461)(437,465)(438,464)(439,463)(440,462)(441,466)(442,470)
(443,469)(444,468)(445,467)(446,471)(447,475)(448,474)(449,473)(450,472);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(500)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)
( 31,121)( 32,122)( 33,123)( 34,124)( 35,125)( 36,116)( 37,117)( 38,118)
( 39,119)( 40,120)( 41,111)( 42,112)( 43,113)( 44,114)( 45,115)( 46,106)
( 47,107)( 48,108)( 49,109)( 50,110)( 51, 76)( 52, 77)( 53, 78)( 54, 79)
( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)
( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)
( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(131,146)(132,147)(133,148)
(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)(140,145)(151,226)
(152,227)(153,228)(154,229)(155,230)(156,246)(157,247)(158,248)(159,249)
(160,250)(161,241)(162,242)(163,243)(164,244)(165,245)(166,236)(167,237)
(168,238)(169,239)(170,240)(171,231)(172,232)(173,233)(174,234)(175,235)
(176,201)(177,202)(178,203)(179,204)(180,205)(181,221)(182,222)(183,223)
(184,224)(185,225)(186,216)(187,217)(188,218)(189,219)(190,220)(191,211)
(192,212)(193,213)(194,214)(195,215)(196,206)(197,207)(198,208)(199,209)
(200,210)(251,376)(252,377)(253,378)(254,379)(255,380)(256,396)(257,397)
(258,398)(259,399)(260,400)(261,391)(262,392)(263,393)(264,394)(265,395)
(266,386)(267,387)(268,388)(269,389)(270,390)(271,381)(272,382)(273,383)
(274,384)(275,385)(276,476)(277,477)(278,478)(279,479)(280,480)(281,496)
(282,497)(283,498)(284,499)(285,500)(286,491)(287,492)(288,493)(289,494)
(290,495)(291,486)(292,487)(293,488)(294,489)(295,490)(296,481)(297,482)
(298,483)(299,484)(300,485)(301,451)(302,452)(303,453)(304,454)(305,455)
(306,471)(307,472)(308,473)(309,474)(310,475)(311,466)(312,467)(313,468)
(314,469)(315,470)(316,461)(317,462)(318,463)(319,464)(320,465)(321,456)
(322,457)(323,458)(324,459)(325,460)(326,426)(327,427)(328,428)(329,429)
(330,430)(331,446)(332,447)(333,448)(334,449)(335,450)(336,441)(337,442)
(338,443)(339,444)(340,445)(341,436)(342,437)(343,438)(344,439)(345,440)
(346,431)(347,432)(348,433)(349,434)(350,435)(351,401)(352,402)(353,403)
(354,404)(355,405)(356,421)(357,422)(358,423)(359,424)(360,425)(361,416)
(362,417)(363,418)(364,419)(365,420)(366,411)(367,412)(368,413)(369,414)
(370,415)(371,406)(372,407)(373,408)(374,409)(375,410);
s1 := Sym(500)!(  1,307)(  2,308)(  3,309)(  4,310)(  5,306)(  6,305)(  7,301)
(  8,302)(  9,303)( 10,304)( 11,323)( 12,324)( 13,325)( 14,321)( 15,322)
( 16,316)( 17,317)( 18,318)( 19,319)( 20,320)( 21,314)( 22,315)( 23,311)
( 24,312)( 25,313)( 26,282)( 27,283)( 28,284)( 29,285)( 30,281)( 31,280)
( 32,276)( 33,277)( 34,278)( 35,279)( 36,298)( 37,299)( 38,300)( 39,296)
( 40,297)( 41,291)( 42,292)( 43,293)( 44,294)( 45,295)( 46,289)( 47,290)
( 48,286)( 49,287)( 50,288)( 51,257)( 52,258)( 53,259)( 54,260)( 55,256)
( 56,255)( 57,251)( 58,252)( 59,253)( 60,254)( 61,273)( 62,274)( 63,275)
( 64,271)( 65,272)( 66,266)( 67,267)( 68,268)( 69,269)( 70,270)( 71,264)
( 72,265)( 73,261)( 74,262)( 75,263)( 76,357)( 77,358)( 78,359)( 79,360)
( 80,356)( 81,355)( 82,351)( 83,352)( 84,353)( 85,354)( 86,373)( 87,374)
( 88,375)( 89,371)( 90,372)( 91,366)( 92,367)( 93,368)( 94,369)( 95,370)
( 96,364)( 97,365)( 98,361)( 99,362)(100,363)(101,332)(102,333)(103,334)
(104,335)(105,331)(106,330)(107,326)(108,327)(109,328)(110,329)(111,348)
(112,349)(113,350)(114,346)(115,347)(116,341)(117,342)(118,343)(119,344)
(120,345)(121,339)(122,340)(123,336)(124,337)(125,338)(126,432)(127,433)
(128,434)(129,435)(130,431)(131,430)(132,426)(133,427)(134,428)(135,429)
(136,448)(137,449)(138,450)(139,446)(140,447)(141,441)(142,442)(143,443)
(144,444)(145,445)(146,439)(147,440)(148,436)(149,437)(150,438)(151,407)
(152,408)(153,409)(154,410)(155,406)(156,405)(157,401)(158,402)(159,403)
(160,404)(161,423)(162,424)(163,425)(164,421)(165,422)(166,416)(167,417)
(168,418)(169,419)(170,420)(171,414)(172,415)(173,411)(174,412)(175,413)
(176,382)(177,383)(178,384)(179,385)(180,381)(181,380)(182,376)(183,377)
(184,378)(185,379)(186,398)(187,399)(188,400)(189,396)(190,397)(191,391)
(192,392)(193,393)(194,394)(195,395)(196,389)(197,390)(198,386)(199,387)
(200,388)(201,482)(202,483)(203,484)(204,485)(205,481)(206,480)(207,476)
(208,477)(209,478)(210,479)(211,498)(212,499)(213,500)(214,496)(215,497)
(216,491)(217,492)(218,493)(219,494)(220,495)(221,489)(222,490)(223,486)
(224,487)(225,488)(226,457)(227,458)(228,459)(229,460)(230,456)(231,455)
(232,451)(233,452)(234,453)(235,454)(236,473)(237,474)(238,475)(239,471)
(240,472)(241,466)(242,467)(243,468)(244,469)(245,470)(246,464)(247,465)
(248,461)(249,462)(250,463);
s2 := Sym(500)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)
( 31,106)( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)
( 39,113)( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)
( 47,125)( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)
( 55, 77)( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)
( 63, 89)( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)
( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)(127,130)(128,129)(132,135)
(133,134)(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)
(152,230)(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)
(160,232)(161,236)(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)
(168,244)(169,243)(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)
(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)
(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)
(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)
(200,222)(252,255)(253,254)(257,260)(258,259)(262,265)(263,264)(267,270)
(268,269)(272,275)(273,274)(276,351)(277,355)(278,354)(279,353)(280,352)
(281,356)(282,360)(283,359)(284,358)(285,357)(286,361)(287,365)(288,364)
(289,363)(290,362)(291,366)(292,370)(293,369)(294,368)(295,367)(296,371)
(297,375)(298,374)(299,373)(300,372)(301,326)(302,330)(303,329)(304,328)
(305,327)(306,331)(307,335)(308,334)(309,333)(310,332)(311,336)(312,340)
(313,339)(314,338)(315,337)(316,341)(317,345)(318,344)(319,343)(320,342)
(321,346)(322,350)(323,349)(324,348)(325,347)(377,380)(378,379)(382,385)
(383,384)(387,390)(388,389)(392,395)(393,394)(397,400)(398,399)(401,476)
(402,480)(403,479)(404,478)(405,477)(406,481)(407,485)(408,484)(409,483)
(410,482)(411,486)(412,490)(413,489)(414,488)(415,487)(416,491)(417,495)
(418,494)(419,493)(420,492)(421,496)(422,500)(423,499)(424,498)(425,497)
(426,451)(427,455)(428,454)(429,453)(430,452)(431,456)(432,460)(433,459)
(434,458)(435,457)(436,461)(437,465)(438,464)(439,463)(440,462)(441,466)
(442,470)(443,469)(444,468)(445,467)(446,471)(447,475)(448,474)(449,473)
(450,472);
poly := sub<Sym(500)|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, s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope