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