Polytope of Type {50,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,20}*2000b
if this polytope has a name.
Group : SmallGroup(2000,386)
Rank : 3
Schlafli Type : {50,20}
Number of vertices, edges, etc : 50, 500, 20
Order of s0s1s2 : 100
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {50,10}*1000b
4-fold quotients : {25,10}*500
5-fold quotients : {50,4}*400, {10,20}*400c
10-fold quotients : {50,2}*200, {10,10}*200c
20-fold quotients : {25,2}*100, {5,10}*100
25-fold quotients : {10,4}*80
50-fold quotients : {10,2}*40
100-fold quotients : {5,2}*20
125-fold quotients : {2,4}*16
250-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26,105)( 27,104)( 28,103)( 29,102)
( 30,101)( 31,125)( 32,124)( 33,123)( 34,122)( 35,121)( 36,120)( 37,119)
( 38,118)( 39,117)( 40,116)( 41,115)( 42,114)( 43,113)( 44,112)( 45,111)
( 46,110)( 47,109)( 48,108)( 49,107)( 50,106)( 51, 80)( 52, 79)( 53, 78)
( 54, 77)( 55, 76)( 56,100)( 57, 99)( 58, 98)( 59, 97)( 60, 96)( 61, 95)
( 62, 94)( 63, 93)( 64, 92)( 65, 91)( 66, 90)( 67, 89)( 68, 88)( 69, 87)
( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)(127,130)(128,129)
(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)
(139,143)(140,142)(151,230)(152,229)(153,228)(154,227)(155,226)(156,250)
(157,249)(158,248)(159,247)(160,246)(161,245)(162,244)(163,243)(164,242)
(165,241)(166,240)(167,239)(168,238)(169,237)(170,236)(171,235)(172,234)
(173,233)(174,232)(175,231)(176,205)(177,204)(178,203)(179,202)(180,201)
(181,225)(182,224)(183,223)(184,222)(185,221)(186,220)(187,219)(188,218)
(189,217)(190,216)(191,215)(192,214)(193,213)(194,212)(195,211)(196,210)
(197,209)(198,208)(199,207)(200,206)(252,255)(253,254)(256,271)(257,275)
(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)(265,267)
(276,355)(277,354)(278,353)(279,352)(280,351)(281,375)(282,374)(283,373)
(284,372)(285,371)(286,370)(287,369)(288,368)(289,367)(290,366)(291,365)
(292,364)(293,363)(294,362)(295,361)(296,360)(297,359)(298,358)(299,357)
(300,356)(301,330)(302,329)(303,328)(304,327)(305,326)(306,350)(307,349)
(308,348)(309,347)(310,346)(311,345)(312,344)(313,343)(314,342)(315,341)
(316,340)(317,339)(318,338)(319,337)(320,336)(321,335)(322,334)(323,333)
(324,332)(325,331)(377,380)(378,379)(381,396)(382,400)(383,399)(384,398)
(385,397)(386,391)(387,395)(388,394)(389,393)(390,392)(401,480)(402,479)
(403,478)(404,477)(405,476)(406,500)(407,499)(408,498)(409,497)(410,496)
(411,495)(412,494)(413,493)(414,492)(415,491)(416,490)(417,489)(418,488)
(419,487)(420,486)(421,485)(422,484)(423,483)(424,482)(425,481)(426,455)
(427,454)(428,453)(429,452)(430,451)(431,475)(432,474)(433,473)(434,472)
(435,471)(436,470)(437,469)(438,468)(439,467)(440,466)(441,465)(442,464)
(443,463)(444,462)(445,461)(446,460)(447,459)(448,458)(449,457)(450,456);;
s1 := ( 1,281)( 2,285)( 3,284)( 4,283)( 5,282)( 6,276)( 7,280)( 8,279)
( 9,278)( 10,277)( 11,296)( 12,300)( 13,299)( 14,298)( 15,297)( 16,291)
( 17,295)( 18,294)( 19,293)( 20,292)( 21,286)( 22,290)( 23,289)( 24,288)
( 25,287)( 26,256)( 27,260)( 28,259)( 29,258)( 30,257)( 31,251)( 32,255)
( 33,254)( 34,253)( 35,252)( 36,271)( 37,275)( 38,274)( 39,273)( 40,272)
( 41,266)( 42,270)( 43,269)( 44,268)( 45,267)( 46,261)( 47,265)( 48,264)
( 49,263)( 50,262)( 51,360)( 52,359)( 53,358)( 54,357)( 55,356)( 56,355)
( 57,354)( 58,353)( 59,352)( 60,351)( 61,375)( 62,374)( 63,373)( 64,372)
( 65,371)( 66,370)( 67,369)( 68,368)( 69,367)( 70,366)( 71,365)( 72,364)
( 73,363)( 74,362)( 75,361)( 76,335)( 77,334)( 78,333)( 79,332)( 80,331)
( 81,330)( 82,329)( 83,328)( 84,327)( 85,326)( 86,350)( 87,349)( 88,348)
( 89,347)( 90,346)( 91,345)( 92,344)( 93,343)( 94,342)( 95,341)( 96,340)
( 97,339)( 98,338)( 99,337)(100,336)(101,310)(102,309)(103,308)(104,307)
(105,306)(106,305)(107,304)(108,303)(109,302)(110,301)(111,325)(112,324)
(113,323)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)(120,316)
(121,315)(122,314)(123,313)(124,312)(125,311)(126,406)(127,410)(128,409)
(129,408)(130,407)(131,401)(132,405)(133,404)(134,403)(135,402)(136,421)
(137,425)(138,424)(139,423)(140,422)(141,416)(142,420)(143,419)(144,418)
(145,417)(146,411)(147,415)(148,414)(149,413)(150,412)(151,381)(152,385)
(153,384)(154,383)(155,382)(156,376)(157,380)(158,379)(159,378)(160,377)
(161,396)(162,400)(163,399)(164,398)(165,397)(166,391)(167,395)(168,394)
(169,393)(170,392)(171,386)(172,390)(173,389)(174,388)(175,387)(176,485)
(177,484)(178,483)(179,482)(180,481)(181,480)(182,479)(183,478)(184,477)
(185,476)(186,500)(187,499)(188,498)(189,497)(190,496)(191,495)(192,494)
(193,493)(194,492)(195,491)(196,490)(197,489)(198,488)(199,487)(200,486)
(201,460)(202,459)(203,458)(204,457)(205,456)(206,455)(207,454)(208,453)
(209,452)(210,451)(211,475)(212,474)(213,473)(214,472)(215,471)(216,470)
(217,469)(218,468)(219,467)(220,466)(221,465)(222,464)(223,463)(224,462)
(225,461)(226,435)(227,434)(228,433)(229,432)(230,431)(231,430)(232,429)
(233,428)(234,427)(235,426)(236,450)(237,449)(238,448)(239,447)(240,446)
(241,445)(242,444)(243,443)(244,442)(245,441)(246,440)(247,439)(248,438)
(249,437)(250,436);;
s2 := ( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)
( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)
(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)
(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)
(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)
(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)
(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195)
(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)(213,218)
(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)
(237,242)(238,243)(239,244)(240,245)(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)(276,401)(277,402)(278,403)
(279,404)(280,405)(281,421)(282,422)(283,423)(284,424)(285,425)(286,416)
(287,417)(288,418)(289,419)(290,420)(291,411)(292,412)(293,413)(294,414)
(295,415)(296,406)(297,407)(298,408)(299,409)(300,410)(301,426)(302,427)
(303,428)(304,429)(305,430)(306,446)(307,447)(308,448)(309,449)(310,450)
(311,441)(312,442)(313,443)(314,444)(315,445)(316,436)(317,437)(318,438)
(319,439)(320,440)(321,431)(322,432)(323,433)(324,434)(325,435)(326,451)
(327,452)(328,453)(329,454)(330,455)(331,471)(332,472)(333,473)(334,474)
(335,475)(336,466)(337,467)(338,468)(339,469)(340,470)(341,461)(342,462)
(343,463)(344,464)(345,465)(346,456)(347,457)(348,458)(349,459)(350,460)
(351,476)(352,477)(353,478)(354,479)(355,480)(356,496)(357,497)(358,498)
(359,499)(360,500)(361,491)(362,492)(363,493)(364,494)(365,495)(366,486)
(367,487)(368,488)(369,489)(370,490)(371,481)(372,482)(373,483)(374,484)
(375,485);;
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*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*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)!( 2, 5)( 3, 4)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26,105)( 27,104)( 28,103)
( 29,102)( 30,101)( 31,125)( 32,124)( 33,123)( 34,122)( 35,121)( 36,120)
( 37,119)( 38,118)( 39,117)( 40,116)( 41,115)( 42,114)( 43,113)( 44,112)
( 45,111)( 46,110)( 47,109)( 48,108)( 49,107)( 50,106)( 51, 80)( 52, 79)
( 53, 78)( 54, 77)( 55, 76)( 56,100)( 57, 99)( 58, 98)( 59, 97)( 60, 96)
( 61, 95)( 62, 94)( 63, 93)( 64, 92)( 65, 91)( 66, 90)( 67, 89)( 68, 88)
( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)(127,130)
(128,129)(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)
(138,144)(139,143)(140,142)(151,230)(152,229)(153,228)(154,227)(155,226)
(156,250)(157,249)(158,248)(159,247)(160,246)(161,245)(162,244)(163,243)
(164,242)(165,241)(166,240)(167,239)(168,238)(169,237)(170,236)(171,235)
(172,234)(173,233)(174,232)(175,231)(176,205)(177,204)(178,203)(179,202)
(180,201)(181,225)(182,224)(183,223)(184,222)(185,221)(186,220)(187,219)
(188,218)(189,217)(190,216)(191,215)(192,214)(193,213)(194,212)(195,211)
(196,210)(197,209)(198,208)(199,207)(200,206)(252,255)(253,254)(256,271)
(257,275)(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)
(265,267)(276,355)(277,354)(278,353)(279,352)(280,351)(281,375)(282,374)
(283,373)(284,372)(285,371)(286,370)(287,369)(288,368)(289,367)(290,366)
(291,365)(292,364)(293,363)(294,362)(295,361)(296,360)(297,359)(298,358)
(299,357)(300,356)(301,330)(302,329)(303,328)(304,327)(305,326)(306,350)
(307,349)(308,348)(309,347)(310,346)(311,345)(312,344)(313,343)(314,342)
(315,341)(316,340)(317,339)(318,338)(319,337)(320,336)(321,335)(322,334)
(323,333)(324,332)(325,331)(377,380)(378,379)(381,396)(382,400)(383,399)
(384,398)(385,397)(386,391)(387,395)(388,394)(389,393)(390,392)(401,480)
(402,479)(403,478)(404,477)(405,476)(406,500)(407,499)(408,498)(409,497)
(410,496)(411,495)(412,494)(413,493)(414,492)(415,491)(416,490)(417,489)
(418,488)(419,487)(420,486)(421,485)(422,484)(423,483)(424,482)(425,481)
(426,455)(427,454)(428,453)(429,452)(430,451)(431,475)(432,474)(433,473)
(434,472)(435,471)(436,470)(437,469)(438,468)(439,467)(440,466)(441,465)
(442,464)(443,463)(444,462)(445,461)(446,460)(447,459)(448,458)(449,457)
(450,456);
s1 := Sym(500)!( 1,281)( 2,285)( 3,284)( 4,283)( 5,282)( 6,276)( 7,280)
( 8,279)( 9,278)( 10,277)( 11,296)( 12,300)( 13,299)( 14,298)( 15,297)
( 16,291)( 17,295)( 18,294)( 19,293)( 20,292)( 21,286)( 22,290)( 23,289)
( 24,288)( 25,287)( 26,256)( 27,260)( 28,259)( 29,258)( 30,257)( 31,251)
( 32,255)( 33,254)( 34,253)( 35,252)( 36,271)( 37,275)( 38,274)( 39,273)
( 40,272)( 41,266)( 42,270)( 43,269)( 44,268)( 45,267)( 46,261)( 47,265)
( 48,264)( 49,263)( 50,262)( 51,360)( 52,359)( 53,358)( 54,357)( 55,356)
( 56,355)( 57,354)( 58,353)( 59,352)( 60,351)( 61,375)( 62,374)( 63,373)
( 64,372)( 65,371)( 66,370)( 67,369)( 68,368)( 69,367)( 70,366)( 71,365)
( 72,364)( 73,363)( 74,362)( 75,361)( 76,335)( 77,334)( 78,333)( 79,332)
( 80,331)( 81,330)( 82,329)( 83,328)( 84,327)( 85,326)( 86,350)( 87,349)
( 88,348)( 89,347)( 90,346)( 91,345)( 92,344)( 93,343)( 94,342)( 95,341)
( 96,340)( 97,339)( 98,338)( 99,337)(100,336)(101,310)(102,309)(103,308)
(104,307)(105,306)(106,305)(107,304)(108,303)(109,302)(110,301)(111,325)
(112,324)(113,323)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)
(120,316)(121,315)(122,314)(123,313)(124,312)(125,311)(126,406)(127,410)
(128,409)(129,408)(130,407)(131,401)(132,405)(133,404)(134,403)(135,402)
(136,421)(137,425)(138,424)(139,423)(140,422)(141,416)(142,420)(143,419)
(144,418)(145,417)(146,411)(147,415)(148,414)(149,413)(150,412)(151,381)
(152,385)(153,384)(154,383)(155,382)(156,376)(157,380)(158,379)(159,378)
(160,377)(161,396)(162,400)(163,399)(164,398)(165,397)(166,391)(167,395)
(168,394)(169,393)(170,392)(171,386)(172,390)(173,389)(174,388)(175,387)
(176,485)(177,484)(178,483)(179,482)(180,481)(181,480)(182,479)(183,478)
(184,477)(185,476)(186,500)(187,499)(188,498)(189,497)(190,496)(191,495)
(192,494)(193,493)(194,492)(195,491)(196,490)(197,489)(198,488)(199,487)
(200,486)(201,460)(202,459)(203,458)(204,457)(205,456)(206,455)(207,454)
(208,453)(209,452)(210,451)(211,475)(212,474)(213,473)(214,472)(215,471)
(216,470)(217,469)(218,468)(219,467)(220,466)(221,465)(222,464)(223,463)
(224,462)(225,461)(226,435)(227,434)(228,433)(229,432)(230,431)(231,430)
(232,429)(233,428)(234,427)(235,426)(236,450)(237,449)(238,448)(239,447)
(240,446)(241,445)(242,444)(243,443)(244,442)(245,441)(246,440)(247,439)
(248,438)(249,437)(250,436);
s2 := Sym(500)!( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)
( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)
(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)
(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)
(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)
(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)
(190,195)(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)
(213,218)(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)
(236,241)(237,242)(238,243)(239,244)(240,245)(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)(276,401)(277,402)
(278,403)(279,404)(280,405)(281,421)(282,422)(283,423)(284,424)(285,425)
(286,416)(287,417)(288,418)(289,419)(290,420)(291,411)(292,412)(293,413)
(294,414)(295,415)(296,406)(297,407)(298,408)(299,409)(300,410)(301,426)
(302,427)(303,428)(304,429)(305,430)(306,446)(307,447)(308,448)(309,449)
(310,450)(311,441)(312,442)(313,443)(314,444)(315,445)(316,436)(317,437)
(318,438)(319,439)(320,440)(321,431)(322,432)(323,433)(324,434)(325,435)
(326,451)(327,452)(328,453)(329,454)(330,455)(331,471)(332,472)(333,473)
(334,474)(335,475)(336,466)(337,467)(338,468)(339,469)(340,470)(341,461)
(342,462)(343,463)(344,464)(345,465)(346,456)(347,457)(348,458)(349,459)
(350,460)(351,476)(352,477)(353,478)(354,479)(355,480)(356,496)(357,497)
(358,498)(359,499)(360,500)(361,491)(362,492)(363,493)(364,494)(365,495)
(366,486)(367,487)(368,488)(369,489)(370,490)(371,481)(372,482)(373,483)
(374,484)(375,485);
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*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*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