Polytope of Type {98,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {98,10}*1960
Also Known As : {98,10|2}. if this polytope has another name.
Group : SmallGroup(1960,36)
Rank : 3
Schlafli Type : {98,10}
Number of vertices, edges, etc : 98, 490, 10
Order of s0s1s2 : 490
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) :
5-fold quotients : {98,2}*392
7-fold quotients : {14,10}*280
10-fold quotients : {49,2}*196
35-fold quotients : {14,2}*56
49-fold quotients : {2,10}*40
70-fold quotients : {7,2}*28
98-fold quotients : {2,5}*20
245-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8, 44)( 9, 43)( 10, 49)( 11, 48)( 12, 47)
( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)( 20, 39)
( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)
( 51, 56)( 52, 55)( 53, 54)( 57, 93)( 58, 92)( 59, 98)( 60, 97)( 61, 96)
( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)( 69, 88)
( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)
(100,105)(101,104)(102,103)(106,142)(107,141)(108,147)(109,146)(110,145)
(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)(118,137)
(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)(126,129)
(149,154)(150,153)(151,152)(155,191)(156,190)(157,196)(158,195)(159,194)
(160,193)(161,192)(162,184)(163,183)(164,189)(165,188)(166,187)(167,186)
(168,185)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)(175,178)
(198,203)(199,202)(200,201)(204,240)(205,239)(206,245)(207,244)(208,243)
(209,242)(210,241)(211,233)(212,232)(213,238)(214,237)(215,236)(216,235)
(217,234)(218,226)(219,225)(220,231)(221,230)(222,229)(223,228)(224,227)
(247,252)(248,251)(249,250)(253,289)(254,288)(255,294)(256,293)(257,292)
(258,291)(259,290)(260,282)(261,281)(262,287)(263,286)(264,285)(265,284)
(266,283)(267,275)(268,274)(269,280)(270,279)(271,278)(272,277)(273,276)
(296,301)(297,300)(298,299)(302,338)(303,337)(304,343)(305,342)(306,341)
(307,340)(308,339)(309,331)(310,330)(311,336)(312,335)(313,334)(314,333)
(315,332)(316,324)(317,323)(318,329)(319,328)(320,327)(321,326)(322,325)
(345,350)(346,349)(347,348)(351,387)(352,386)(353,392)(354,391)(355,390)
(356,389)(357,388)(358,380)(359,379)(360,385)(361,384)(362,383)(363,382)
(364,381)(365,373)(366,372)(367,378)(368,377)(369,376)(370,375)(371,374)
(394,399)(395,398)(396,397)(400,436)(401,435)(402,441)(403,440)(404,439)
(405,438)(406,437)(407,429)(408,428)(409,434)(410,433)(411,432)(412,431)
(413,430)(414,422)(415,421)(416,427)(417,426)(418,425)(419,424)(420,423)
(443,448)(444,447)(445,446)(449,485)(450,484)(451,490)(452,489)(453,488)
(454,487)(455,486)(456,478)(457,477)(458,483)(459,482)(460,481)(461,480)
(462,479)(463,471)(464,470)(465,476)(466,475)(467,474)(468,473)(469,472);;
s1 := ( 1, 8)( 2, 14)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 15, 44)
( 16, 43)( 17, 49)( 18, 48)( 19, 47)( 20, 46)( 21, 45)( 22, 37)( 23, 36)
( 24, 42)( 25, 41)( 26, 40)( 27, 39)( 28, 38)( 29, 30)( 31, 35)( 32, 34)
( 50,204)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)( 56,205)( 57,197)
( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)( 64,240)( 65,239)
( 66,245)( 67,244)( 68,243)( 69,242)( 70,241)( 71,233)( 72,232)( 73,238)
( 74,237)( 75,236)( 76,235)( 77,234)( 78,226)( 79,225)( 80,231)( 81,230)
( 82,229)( 83,228)( 84,227)( 85,219)( 86,218)( 87,224)( 88,223)( 89,222)
( 90,221)( 91,220)( 92,212)( 93,211)( 94,217)( 95,216)( 96,215)( 97,214)
( 98,213)( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)(105,156)
(106,148)(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)(113,191)
(114,190)(115,196)(116,195)(117,194)(118,193)(119,192)(120,184)(121,183)
(122,189)(123,188)(124,187)(125,186)(126,185)(127,177)(128,176)(129,182)
(130,181)(131,180)(132,179)(133,178)(134,170)(135,169)(136,175)(137,174)
(138,173)(139,172)(140,171)(141,163)(142,162)(143,168)(144,167)(145,166)
(146,165)(147,164)(246,253)(247,259)(248,258)(249,257)(250,256)(251,255)
(252,254)(260,289)(261,288)(262,294)(263,293)(264,292)(265,291)(266,290)
(267,282)(268,281)(269,287)(270,286)(271,285)(272,284)(273,283)(274,275)
(276,280)(277,279)(295,449)(296,455)(297,454)(298,453)(299,452)(300,451)
(301,450)(302,442)(303,448)(304,447)(305,446)(306,445)(307,444)(308,443)
(309,485)(310,484)(311,490)(312,489)(313,488)(314,487)(315,486)(316,478)
(317,477)(318,483)(319,482)(320,481)(321,480)(322,479)(323,471)(324,470)
(325,476)(326,475)(327,474)(328,473)(329,472)(330,464)(331,463)(332,469)
(333,468)(334,467)(335,466)(336,465)(337,457)(338,456)(339,462)(340,461)
(341,460)(342,459)(343,458)(344,400)(345,406)(346,405)(347,404)(348,403)
(349,402)(350,401)(351,393)(352,399)(353,398)(354,397)(355,396)(356,395)
(357,394)(358,436)(359,435)(360,441)(361,440)(362,439)(363,438)(364,437)
(365,429)(366,428)(367,434)(368,433)(369,432)(370,431)(371,430)(372,422)
(373,421)(374,427)(375,426)(376,425)(377,424)(378,423)(379,415)(380,414)
(381,420)(382,419)(383,418)(384,417)(385,416)(386,408)(387,407)(388,413)
(389,412)(390,411)(391,410)(392,409);;
s2 := ( 1,295)( 2,296)( 3,297)( 4,298)( 5,299)( 6,300)( 7,301)( 8,302)
( 9,303)( 10,304)( 11,305)( 12,306)( 13,307)( 14,308)( 15,309)( 16,310)
( 17,311)( 18,312)( 19,313)( 20,314)( 21,315)( 22,316)( 23,317)( 24,318)
( 25,319)( 26,320)( 27,321)( 28,322)( 29,323)( 30,324)( 31,325)( 32,326)
( 33,327)( 34,328)( 35,329)( 36,330)( 37,331)( 38,332)( 39,333)( 40,334)
( 41,335)( 42,336)( 43,337)( 44,338)( 45,339)( 46,340)( 47,341)( 48,342)
( 49,343)( 50,246)( 51,247)( 52,248)( 53,249)( 54,250)( 55,251)( 56,252)
( 57,253)( 58,254)( 59,255)( 60,256)( 61,257)( 62,258)( 63,259)( 64,260)
( 65,261)( 66,262)( 67,263)( 68,264)( 69,265)( 70,266)( 71,267)( 72,268)
( 73,269)( 74,270)( 75,271)( 76,272)( 77,273)( 78,274)( 79,275)( 80,276)
( 81,277)( 82,278)( 83,279)( 84,280)( 85,281)( 86,282)( 87,283)( 88,284)
( 89,285)( 90,286)( 91,287)( 92,288)( 93,289)( 94,290)( 95,291)( 96,292)
( 97,293)( 98,294)( 99,442)(100,443)(101,444)(102,445)(103,446)(104,447)
(105,448)(106,449)(107,450)(108,451)(109,452)(110,453)(111,454)(112,455)
(113,456)(114,457)(115,458)(116,459)(117,460)(118,461)(119,462)(120,463)
(121,464)(122,465)(123,466)(124,467)(125,468)(126,469)(127,470)(128,471)
(129,472)(130,473)(131,474)(132,475)(133,476)(134,477)(135,478)(136,479)
(137,480)(138,481)(139,482)(140,483)(141,484)(142,485)(143,486)(144,487)
(145,488)(146,489)(147,490)(148,393)(149,394)(150,395)(151,396)(152,397)
(153,398)(154,399)(155,400)(156,401)(157,402)(158,403)(159,404)(160,405)
(161,406)(162,407)(163,408)(164,409)(165,410)(166,411)(167,412)(168,413)
(169,414)(170,415)(171,416)(172,417)(173,418)(174,419)(175,420)(176,421)
(177,422)(178,423)(179,424)(180,425)(181,426)(182,427)(183,428)(184,429)
(185,430)(186,431)(187,432)(188,433)(189,434)(190,435)(191,436)(192,437)
(193,438)(194,439)(195,440)(196,441)(197,344)(198,345)(199,346)(200,347)
(201,348)(202,349)(203,350)(204,351)(205,352)(206,353)(207,354)(208,355)
(209,356)(210,357)(211,358)(212,359)(213,360)(214,361)(215,362)(216,363)
(217,364)(218,365)(219,366)(220,367)(221,368)(222,369)(223,370)(224,371)
(225,372)(226,373)(227,374)(228,375)(229,376)(230,377)(231,378)(232,379)
(233,380)(234,381)(235,382)(236,383)(237,384)(238,385)(239,386)(240,387)
(241,388)(242,389)(243,390)(244,391)(245,392);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(490)!( 2, 7)( 3, 6)( 4, 5)( 8, 44)( 9, 43)( 10, 49)( 11, 48)
( 12, 47)( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)
( 20, 39)( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 51, 56)( 52, 55)( 53, 54)( 57, 93)( 58, 92)( 59, 98)( 60, 97)
( 61, 96)( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)
( 69, 88)( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)
( 77, 80)(100,105)(101,104)(102,103)(106,142)(107,141)(108,147)(109,146)
(110,145)(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)
(118,137)(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)
(126,129)(149,154)(150,153)(151,152)(155,191)(156,190)(157,196)(158,195)
(159,194)(160,193)(161,192)(162,184)(163,183)(164,189)(165,188)(166,187)
(167,186)(168,185)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)
(175,178)(198,203)(199,202)(200,201)(204,240)(205,239)(206,245)(207,244)
(208,243)(209,242)(210,241)(211,233)(212,232)(213,238)(214,237)(215,236)
(216,235)(217,234)(218,226)(219,225)(220,231)(221,230)(222,229)(223,228)
(224,227)(247,252)(248,251)(249,250)(253,289)(254,288)(255,294)(256,293)
(257,292)(258,291)(259,290)(260,282)(261,281)(262,287)(263,286)(264,285)
(265,284)(266,283)(267,275)(268,274)(269,280)(270,279)(271,278)(272,277)
(273,276)(296,301)(297,300)(298,299)(302,338)(303,337)(304,343)(305,342)
(306,341)(307,340)(308,339)(309,331)(310,330)(311,336)(312,335)(313,334)
(314,333)(315,332)(316,324)(317,323)(318,329)(319,328)(320,327)(321,326)
(322,325)(345,350)(346,349)(347,348)(351,387)(352,386)(353,392)(354,391)
(355,390)(356,389)(357,388)(358,380)(359,379)(360,385)(361,384)(362,383)
(363,382)(364,381)(365,373)(366,372)(367,378)(368,377)(369,376)(370,375)
(371,374)(394,399)(395,398)(396,397)(400,436)(401,435)(402,441)(403,440)
(404,439)(405,438)(406,437)(407,429)(408,428)(409,434)(410,433)(411,432)
(412,431)(413,430)(414,422)(415,421)(416,427)(417,426)(418,425)(419,424)
(420,423)(443,448)(444,447)(445,446)(449,485)(450,484)(451,490)(452,489)
(453,488)(454,487)(455,486)(456,478)(457,477)(458,483)(459,482)(460,481)
(461,480)(462,479)(463,471)(464,470)(465,476)(466,475)(467,474)(468,473)
(469,472);
s1 := Sym(490)!( 1, 8)( 2, 14)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)
( 15, 44)( 16, 43)( 17, 49)( 18, 48)( 19, 47)( 20, 46)( 21, 45)( 22, 37)
( 23, 36)( 24, 42)( 25, 41)( 26, 40)( 27, 39)( 28, 38)( 29, 30)( 31, 35)
( 32, 34)( 50,204)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)( 56,205)
( 57,197)( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)( 64,240)
( 65,239)( 66,245)( 67,244)( 68,243)( 69,242)( 70,241)( 71,233)( 72,232)
( 73,238)( 74,237)( 75,236)( 76,235)( 77,234)( 78,226)( 79,225)( 80,231)
( 81,230)( 82,229)( 83,228)( 84,227)( 85,219)( 86,218)( 87,224)( 88,223)
( 89,222)( 90,221)( 91,220)( 92,212)( 93,211)( 94,217)( 95,216)( 96,215)
( 97,214)( 98,213)( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)
(105,156)(106,148)(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)
(113,191)(114,190)(115,196)(116,195)(117,194)(118,193)(119,192)(120,184)
(121,183)(122,189)(123,188)(124,187)(125,186)(126,185)(127,177)(128,176)
(129,182)(130,181)(131,180)(132,179)(133,178)(134,170)(135,169)(136,175)
(137,174)(138,173)(139,172)(140,171)(141,163)(142,162)(143,168)(144,167)
(145,166)(146,165)(147,164)(246,253)(247,259)(248,258)(249,257)(250,256)
(251,255)(252,254)(260,289)(261,288)(262,294)(263,293)(264,292)(265,291)
(266,290)(267,282)(268,281)(269,287)(270,286)(271,285)(272,284)(273,283)
(274,275)(276,280)(277,279)(295,449)(296,455)(297,454)(298,453)(299,452)
(300,451)(301,450)(302,442)(303,448)(304,447)(305,446)(306,445)(307,444)
(308,443)(309,485)(310,484)(311,490)(312,489)(313,488)(314,487)(315,486)
(316,478)(317,477)(318,483)(319,482)(320,481)(321,480)(322,479)(323,471)
(324,470)(325,476)(326,475)(327,474)(328,473)(329,472)(330,464)(331,463)
(332,469)(333,468)(334,467)(335,466)(336,465)(337,457)(338,456)(339,462)
(340,461)(341,460)(342,459)(343,458)(344,400)(345,406)(346,405)(347,404)
(348,403)(349,402)(350,401)(351,393)(352,399)(353,398)(354,397)(355,396)
(356,395)(357,394)(358,436)(359,435)(360,441)(361,440)(362,439)(363,438)
(364,437)(365,429)(366,428)(367,434)(368,433)(369,432)(370,431)(371,430)
(372,422)(373,421)(374,427)(375,426)(376,425)(377,424)(378,423)(379,415)
(380,414)(381,420)(382,419)(383,418)(384,417)(385,416)(386,408)(387,407)
(388,413)(389,412)(390,411)(391,410)(392,409);
s2 := Sym(490)!( 1,295)( 2,296)( 3,297)( 4,298)( 5,299)( 6,300)( 7,301)
( 8,302)( 9,303)( 10,304)( 11,305)( 12,306)( 13,307)( 14,308)( 15,309)
( 16,310)( 17,311)( 18,312)( 19,313)( 20,314)( 21,315)( 22,316)( 23,317)
( 24,318)( 25,319)( 26,320)( 27,321)( 28,322)( 29,323)( 30,324)( 31,325)
( 32,326)( 33,327)( 34,328)( 35,329)( 36,330)( 37,331)( 38,332)( 39,333)
( 40,334)( 41,335)( 42,336)( 43,337)( 44,338)( 45,339)( 46,340)( 47,341)
( 48,342)( 49,343)( 50,246)( 51,247)( 52,248)( 53,249)( 54,250)( 55,251)
( 56,252)( 57,253)( 58,254)( 59,255)( 60,256)( 61,257)( 62,258)( 63,259)
( 64,260)( 65,261)( 66,262)( 67,263)( 68,264)( 69,265)( 70,266)( 71,267)
( 72,268)( 73,269)( 74,270)( 75,271)( 76,272)( 77,273)( 78,274)( 79,275)
( 80,276)( 81,277)( 82,278)( 83,279)( 84,280)( 85,281)( 86,282)( 87,283)
( 88,284)( 89,285)( 90,286)( 91,287)( 92,288)( 93,289)( 94,290)( 95,291)
( 96,292)( 97,293)( 98,294)( 99,442)(100,443)(101,444)(102,445)(103,446)
(104,447)(105,448)(106,449)(107,450)(108,451)(109,452)(110,453)(111,454)
(112,455)(113,456)(114,457)(115,458)(116,459)(117,460)(118,461)(119,462)
(120,463)(121,464)(122,465)(123,466)(124,467)(125,468)(126,469)(127,470)
(128,471)(129,472)(130,473)(131,474)(132,475)(133,476)(134,477)(135,478)
(136,479)(137,480)(138,481)(139,482)(140,483)(141,484)(142,485)(143,486)
(144,487)(145,488)(146,489)(147,490)(148,393)(149,394)(150,395)(151,396)
(152,397)(153,398)(154,399)(155,400)(156,401)(157,402)(158,403)(159,404)
(160,405)(161,406)(162,407)(163,408)(164,409)(165,410)(166,411)(167,412)
(168,413)(169,414)(170,415)(171,416)(172,417)(173,418)(174,419)(175,420)
(176,421)(177,422)(178,423)(179,424)(180,425)(181,426)(182,427)(183,428)
(184,429)(185,430)(186,431)(187,432)(188,433)(189,434)(190,435)(191,436)
(192,437)(193,438)(194,439)(195,440)(196,441)(197,344)(198,345)(199,346)
(200,347)(201,348)(202,349)(203,350)(204,351)(205,352)(206,353)(207,354)
(208,355)(209,356)(210,357)(211,358)(212,359)(213,360)(214,361)(215,362)
(216,363)(217,364)(218,365)(219,366)(220,367)(221,368)(222,369)(223,370)
(224,371)(225,372)(226,373)(227,374)(228,375)(229,376)(230,377)(231,378)
(232,379)(233,380)(234,381)(235,382)(236,383)(237,384)(238,385)(239,386)
(240,387)(241,388)(242,389)(243,390)(244,391)(245,392);
poly := sub<Sym(490)|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 >;
References : None.
to this polytope