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