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