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