Polytope of Type {100,10}

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