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