Polytope of Type {10,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,20}*2000c
if this polytope has a name.
Group : SmallGroup(2000,395)
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}*1000a
4-fold quotients : {5,10}*500
5-fold quotients : {10,20}*400c
10-fold quotients : {10,10}*200c
20-fold quotients : {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 := ( 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)
(256,271)(257,272)(258,273)(259,274)(260,275)(261,266)(262,267)(263,268)
(264,269)(265,270)(276,351)(277,352)(278,353)(279,354)(280,355)(281,371)
(282,372)(283,373)(284,374)(285,375)(286,366)(287,367)(288,368)(289,369)
(290,370)(291,361)(292,362)(293,363)(294,364)(295,365)(296,356)(297,357)
(298,358)(299,359)(300,360)(301,326)(302,327)(303,328)(304,329)(305,330)
(306,346)(307,347)(308,348)(309,349)(310,350)(311,341)(312,342)(313,343)
(314,344)(315,345)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)
(322,332)(323,333)(324,334)(325,335)(381,396)(382,397)(383,398)(384,399)
(385,400)(386,391)(387,392)(388,393)(389,394)(390,395)(401,476)(402,477)
(403,478)(404,479)(405,480)(406,496)(407,497)(408,498)(409,499)(410,500)
(411,491)(412,492)(413,493)(414,494)(415,495)(416,486)(417,487)(418,488)
(419,489)(420,490)(421,481)(422,482)(423,483)(424,484)(425,485)(426,451)
(427,452)(428,453)(429,454)(430,455)(431,471)(432,472)(433,473)(434,474)
(435,475)(436,466)(437,467)(438,468)(439,469)(440,470)(441,461)(442,462)
(443,463)(444,464)(445,465)(446,456)(447,457)(448,458)(449,459)(450,460);;
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)
(251,376)(252,380)(253,379)(254,378)(255,377)(256,381)(257,385)(258,384)
(259,383)(260,382)(261,386)(262,390)(263,389)(264,388)(265,387)(266,391)
(267,395)(268,394)(269,393)(270,392)(271,396)(272,400)(273,399)(274,398)
(275,397)(276,476)(277,480)(278,479)(279,478)(280,477)(281,481)(282,485)
(283,484)(284,483)(285,482)(286,486)(287,490)(288,489)(289,488)(290,487)
(291,491)(292,495)(293,494)(294,493)(295,492)(296,496)(297,500)(298,499)
(299,498)(300,497)(301,451)(302,455)(303,454)(304,453)(305,452)(306,456)
(307,460)(308,459)(309,458)(310,457)(311,461)(312,465)(313,464)(314,463)
(315,462)(316,466)(317,470)(318,469)(319,468)(320,467)(321,471)(322,475)
(323,474)(324,473)(325,472)(326,426)(327,430)(328,429)(329,428)(330,427)
(331,431)(332,435)(333,434)(334,433)(335,432)(336,436)(337,440)(338,439)
(339,438)(340,437)(341,441)(342,445)(343,444)(344,443)(345,442)(346,446)
(347,450)(348,449)(349,448)(350,447)(351,401)(352,405)(353,404)(354,403)
(355,402)(356,406)(357,410)(358,409)(359,408)(360,407)(361,411)(362,415)
(363,414)(364,413)(365,412)(366,416)(367,420)(368,419)(369,418)(370,417)
(371,421)(372,425)(373,424)(374,423)(375,422);;
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,
s1*s2*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*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)(256,271)(257,272)(258,273)(259,274)(260,275)(261,266)(262,267)
(263,268)(264,269)(265,270)(276,351)(277,352)(278,353)(279,354)(280,355)
(281,371)(282,372)(283,373)(284,374)(285,375)(286,366)(287,367)(288,368)
(289,369)(290,370)(291,361)(292,362)(293,363)(294,364)(295,365)(296,356)
(297,357)(298,358)(299,359)(300,360)(301,326)(302,327)(303,328)(304,329)
(305,330)(306,346)(307,347)(308,348)(309,349)(310,350)(311,341)(312,342)
(313,343)(314,344)(315,345)(316,336)(317,337)(318,338)(319,339)(320,340)
(321,331)(322,332)(323,333)(324,334)(325,335)(381,396)(382,397)(383,398)
(384,399)(385,400)(386,391)(387,392)(388,393)(389,394)(390,395)(401,476)
(402,477)(403,478)(404,479)(405,480)(406,496)(407,497)(408,498)(409,499)
(410,500)(411,491)(412,492)(413,493)(414,494)(415,495)(416,486)(417,487)
(418,488)(419,489)(420,490)(421,481)(422,482)(423,483)(424,484)(425,485)
(426,451)(427,452)(428,453)(429,454)(430,455)(431,471)(432,472)(433,473)
(434,474)(435,475)(436,466)(437,467)(438,468)(439,469)(440,470)(441,461)
(442,462)(443,463)(444,464)(445,465)(446,456)(447,457)(448,458)(449,459)
(450,460);
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)(251,376)(252,380)(253,379)(254,378)(255,377)(256,381)(257,385)
(258,384)(259,383)(260,382)(261,386)(262,390)(263,389)(264,388)(265,387)
(266,391)(267,395)(268,394)(269,393)(270,392)(271,396)(272,400)(273,399)
(274,398)(275,397)(276,476)(277,480)(278,479)(279,478)(280,477)(281,481)
(282,485)(283,484)(284,483)(285,482)(286,486)(287,490)(288,489)(289,488)
(290,487)(291,491)(292,495)(293,494)(294,493)(295,492)(296,496)(297,500)
(298,499)(299,498)(300,497)(301,451)(302,455)(303,454)(304,453)(305,452)
(306,456)(307,460)(308,459)(309,458)(310,457)(311,461)(312,465)(313,464)
(314,463)(315,462)(316,466)(317,470)(318,469)(319,468)(320,467)(321,471)
(322,475)(323,474)(324,473)(325,472)(326,426)(327,430)(328,429)(329,428)
(330,427)(331,431)(332,435)(333,434)(334,433)(335,432)(336,436)(337,440)
(338,439)(339,438)(340,437)(341,441)(342,445)(343,444)(344,443)(345,442)
(346,446)(347,450)(348,449)(349,448)(350,447)(351,401)(352,405)(353,404)
(354,403)(355,402)(356,406)(357,410)(358,409)(359,408)(360,407)(361,411)
(362,415)(363,414)(364,413)(365,412)(366,416)(367,420)(368,419)(369,418)
(370,417)(371,421)(372,425)(373,424)(374,423)(375,422);
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,
s1*s2*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1 >;
References : None.
to this polytope