Polytope of Type {4,142}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,142}*1136
Also Known As : {4,142|2}. if this polytope has another name.
Group : SmallGroup(1136,34)
Rank : 3
Schlafli Type : {4,142}
Number of vertices, edges, etc : 4, 284, 142
Order of s0s1s2 : 284
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 : {2,142}*568
4-fold quotients : {2,71}*284
71-fold quotients : {4,2}*16
142-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (285,356)(286,357)(287,358)(288,359)(289,360)(290,361)(291,362)(292,363)
(293,364)(294,365)(295,366)(296,367)(297,368)(298,369)(299,370)(300,371)
(301,372)(302,373)(303,374)(304,375)(305,376)(306,377)(307,378)(308,379)
(309,380)(310,381)(311,382)(312,383)(313,384)(314,385)(315,386)(316,387)
(317,388)(318,389)(319,390)(320,391)(321,392)(322,393)(323,394)(324,395)
(325,396)(326,397)(327,398)(328,399)(329,400)(330,401)(331,402)(332,403)
(333,404)(334,405)(335,406)(336,407)(337,408)(338,409)(339,410)(340,411)
(341,412)(342,413)(343,414)(344,415)(345,416)(346,417)(347,418)(348,419)
(349,420)(350,421)(351,422)(352,423)(353,424)(354,425)(355,426)(427,498)
(428,499)(429,500)(430,501)(431,502)(432,503)(433,504)(434,505)(435,506)
(436,507)(437,508)(438,509)(439,510)(440,511)(441,512)(442,513)(443,514)
(444,515)(445,516)(446,517)(447,518)(448,519)(449,520)(450,521)(451,522)
(452,523)(453,524)(454,525)(455,526)(456,527)(457,528)(458,529)(459,530)
(460,531)(461,532)(462,533)(463,534)(464,535)(465,536)(466,537)(467,538)
(468,539)(469,540)(470,541)(471,542)(472,543)(473,544)(474,545)(475,546)
(476,547)(477,548)(478,549)(479,550)(480,551)(481,552)(482,553)(483,554)
(484,555)(485,556)(486,557)(487,558)(488,559)(489,560)(490,561)(491,562)
(492,563)(493,564)(494,565)(495,566)(496,567)(497,568);;
s1 := ( 1,427)( 2,497)( 3,496)( 4,495)( 5,494)( 6,493)( 7,492)( 8,491)
( 9,490)( 10,489)( 11,488)( 12,487)( 13,486)( 14,485)( 15,484)( 16,483)
( 17,482)( 18,481)( 19,480)( 20,479)( 21,478)( 22,477)( 23,476)( 24,475)
( 25,474)( 26,473)( 27,472)( 28,471)( 29,470)( 30,469)( 31,468)( 32,467)
( 33,466)( 34,465)( 35,464)( 36,463)( 37,462)( 38,461)( 39,460)( 40,459)
( 41,458)( 42,457)( 43,456)( 44,455)( 45,454)( 46,453)( 47,452)( 48,451)
( 49,450)( 50,449)( 51,448)( 52,447)( 53,446)( 54,445)( 55,444)( 56,443)
( 57,442)( 58,441)( 59,440)( 60,439)( 61,438)( 62,437)( 63,436)( 64,435)
( 65,434)( 66,433)( 67,432)( 68,431)( 69,430)( 70,429)( 71,428)( 72,498)
( 73,568)( 74,567)( 75,566)( 76,565)( 77,564)( 78,563)( 79,562)( 80,561)
( 81,560)( 82,559)( 83,558)( 84,557)( 85,556)( 86,555)( 87,554)( 88,553)
( 89,552)( 90,551)( 91,550)( 92,549)( 93,548)( 94,547)( 95,546)( 96,545)
( 97,544)( 98,543)( 99,542)(100,541)(101,540)(102,539)(103,538)(104,537)
(105,536)(106,535)(107,534)(108,533)(109,532)(110,531)(111,530)(112,529)
(113,528)(114,527)(115,526)(116,525)(117,524)(118,523)(119,522)(120,521)
(121,520)(122,519)(123,518)(124,517)(125,516)(126,515)(127,514)(128,513)
(129,512)(130,511)(131,510)(132,509)(133,508)(134,507)(135,506)(136,505)
(137,504)(138,503)(139,502)(140,501)(141,500)(142,499)(143,285)(144,355)
(145,354)(146,353)(147,352)(148,351)(149,350)(150,349)(151,348)(152,347)
(153,346)(154,345)(155,344)(156,343)(157,342)(158,341)(159,340)(160,339)
(161,338)(162,337)(163,336)(164,335)(165,334)(166,333)(167,332)(168,331)
(169,330)(170,329)(171,328)(172,327)(173,326)(174,325)(175,324)(176,323)
(177,322)(178,321)(179,320)(180,319)(181,318)(182,317)(183,316)(184,315)
(185,314)(186,313)(187,312)(188,311)(189,310)(190,309)(191,308)(192,307)
(193,306)(194,305)(195,304)(196,303)(197,302)(198,301)(199,300)(200,299)
(201,298)(202,297)(203,296)(204,295)(205,294)(206,293)(207,292)(208,291)
(209,290)(210,289)(211,288)(212,287)(213,286)(214,356)(215,426)(216,425)
(217,424)(218,423)(219,422)(220,421)(221,420)(222,419)(223,418)(224,417)
(225,416)(226,415)(227,414)(228,413)(229,412)(230,411)(231,410)(232,409)
(233,408)(234,407)(235,406)(236,405)(237,404)(238,403)(239,402)(240,401)
(241,400)(242,399)(243,398)(244,397)(245,396)(246,395)(247,394)(248,393)
(249,392)(250,391)(251,390)(252,389)(253,388)(254,387)(255,386)(256,385)
(257,384)(258,383)(259,382)(260,381)(261,380)(262,379)(263,378)(264,377)
(265,376)(266,375)(267,374)(268,373)(269,372)(270,371)(271,370)(272,369)
(273,368)(274,367)(275,366)(276,365)(277,364)(278,363)(279,362)(280,361)
(281,360)(282,359)(283,358)(284,357);;
s2 := ( 1,144)( 2,143)( 3,213)( 4,212)( 5,211)( 6,210)( 7,209)( 8,208)
( 9,207)( 10,206)( 11,205)( 12,204)( 13,203)( 14,202)( 15,201)( 16,200)
( 17,199)( 18,198)( 19,197)( 20,196)( 21,195)( 22,194)( 23,193)( 24,192)
( 25,191)( 26,190)( 27,189)( 28,188)( 29,187)( 30,186)( 31,185)( 32,184)
( 33,183)( 34,182)( 35,181)( 36,180)( 37,179)( 38,178)( 39,177)( 40,176)
( 41,175)( 42,174)( 43,173)( 44,172)( 45,171)( 46,170)( 47,169)( 48,168)
( 49,167)( 50,166)( 51,165)( 52,164)( 53,163)( 54,162)( 55,161)( 56,160)
( 57,159)( 58,158)( 59,157)( 60,156)( 61,155)( 62,154)( 63,153)( 64,152)
( 65,151)( 66,150)( 67,149)( 68,148)( 69,147)( 70,146)( 71,145)( 72,215)
( 73,214)( 74,284)( 75,283)( 76,282)( 77,281)( 78,280)( 79,279)( 80,278)
( 81,277)( 82,276)( 83,275)( 84,274)( 85,273)( 86,272)( 87,271)( 88,270)
( 89,269)( 90,268)( 91,267)( 92,266)( 93,265)( 94,264)( 95,263)( 96,262)
( 97,261)( 98,260)( 99,259)(100,258)(101,257)(102,256)(103,255)(104,254)
(105,253)(106,252)(107,251)(108,250)(109,249)(110,248)(111,247)(112,246)
(113,245)(114,244)(115,243)(116,242)(117,241)(118,240)(119,239)(120,238)
(121,237)(122,236)(123,235)(124,234)(125,233)(126,232)(127,231)(128,230)
(129,229)(130,228)(131,227)(132,226)(133,225)(134,224)(135,223)(136,222)
(137,221)(138,220)(139,219)(140,218)(141,217)(142,216)(285,428)(286,427)
(287,497)(288,496)(289,495)(290,494)(291,493)(292,492)(293,491)(294,490)
(295,489)(296,488)(297,487)(298,486)(299,485)(300,484)(301,483)(302,482)
(303,481)(304,480)(305,479)(306,478)(307,477)(308,476)(309,475)(310,474)
(311,473)(312,472)(313,471)(314,470)(315,469)(316,468)(317,467)(318,466)
(319,465)(320,464)(321,463)(322,462)(323,461)(324,460)(325,459)(326,458)
(327,457)(328,456)(329,455)(330,454)(331,453)(332,452)(333,451)(334,450)
(335,449)(336,448)(337,447)(338,446)(339,445)(340,444)(341,443)(342,442)
(343,441)(344,440)(345,439)(346,438)(347,437)(348,436)(349,435)(350,434)
(351,433)(352,432)(353,431)(354,430)(355,429)(356,499)(357,498)(358,568)
(359,567)(360,566)(361,565)(362,564)(363,563)(364,562)(365,561)(366,560)
(367,559)(368,558)(369,557)(370,556)(371,555)(372,554)(373,553)(374,552)
(375,551)(376,550)(377,549)(378,548)(379,547)(380,546)(381,545)(382,544)
(383,543)(384,542)(385,541)(386,540)(387,539)(388,538)(389,537)(390,536)
(391,535)(392,534)(393,533)(394,532)(395,531)(396,530)(397,529)(398,528)
(399,527)(400,526)(401,525)(402,524)(403,523)(404,522)(405,521)(406,520)
(407,519)(408,518)(409,517)(410,516)(411,515)(412,514)(413,513)(414,512)
(415,511)(416,510)(417,509)(418,508)(419,507)(420,506)(421,505)(422,504)
(423,503)(424,502)(425,501)(426,500);;
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*s0*s1*s0*s1*s0*s1,
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(568)!(285,356)(286,357)(287,358)(288,359)(289,360)(290,361)(291,362)
(292,363)(293,364)(294,365)(295,366)(296,367)(297,368)(298,369)(299,370)
(300,371)(301,372)(302,373)(303,374)(304,375)(305,376)(306,377)(307,378)
(308,379)(309,380)(310,381)(311,382)(312,383)(313,384)(314,385)(315,386)
(316,387)(317,388)(318,389)(319,390)(320,391)(321,392)(322,393)(323,394)
(324,395)(325,396)(326,397)(327,398)(328,399)(329,400)(330,401)(331,402)
(332,403)(333,404)(334,405)(335,406)(336,407)(337,408)(338,409)(339,410)
(340,411)(341,412)(342,413)(343,414)(344,415)(345,416)(346,417)(347,418)
(348,419)(349,420)(350,421)(351,422)(352,423)(353,424)(354,425)(355,426)
(427,498)(428,499)(429,500)(430,501)(431,502)(432,503)(433,504)(434,505)
(435,506)(436,507)(437,508)(438,509)(439,510)(440,511)(441,512)(442,513)
(443,514)(444,515)(445,516)(446,517)(447,518)(448,519)(449,520)(450,521)
(451,522)(452,523)(453,524)(454,525)(455,526)(456,527)(457,528)(458,529)
(459,530)(460,531)(461,532)(462,533)(463,534)(464,535)(465,536)(466,537)
(467,538)(468,539)(469,540)(470,541)(471,542)(472,543)(473,544)(474,545)
(475,546)(476,547)(477,548)(478,549)(479,550)(480,551)(481,552)(482,553)
(483,554)(484,555)(485,556)(486,557)(487,558)(488,559)(489,560)(490,561)
(491,562)(492,563)(493,564)(494,565)(495,566)(496,567)(497,568);
s1 := Sym(568)!( 1,427)( 2,497)( 3,496)( 4,495)( 5,494)( 6,493)( 7,492)
( 8,491)( 9,490)( 10,489)( 11,488)( 12,487)( 13,486)( 14,485)( 15,484)
( 16,483)( 17,482)( 18,481)( 19,480)( 20,479)( 21,478)( 22,477)( 23,476)
( 24,475)( 25,474)( 26,473)( 27,472)( 28,471)( 29,470)( 30,469)( 31,468)
( 32,467)( 33,466)( 34,465)( 35,464)( 36,463)( 37,462)( 38,461)( 39,460)
( 40,459)( 41,458)( 42,457)( 43,456)( 44,455)( 45,454)( 46,453)( 47,452)
( 48,451)( 49,450)( 50,449)( 51,448)( 52,447)( 53,446)( 54,445)( 55,444)
( 56,443)( 57,442)( 58,441)( 59,440)( 60,439)( 61,438)( 62,437)( 63,436)
( 64,435)( 65,434)( 66,433)( 67,432)( 68,431)( 69,430)( 70,429)( 71,428)
( 72,498)( 73,568)( 74,567)( 75,566)( 76,565)( 77,564)( 78,563)( 79,562)
( 80,561)( 81,560)( 82,559)( 83,558)( 84,557)( 85,556)( 86,555)( 87,554)
( 88,553)( 89,552)( 90,551)( 91,550)( 92,549)( 93,548)( 94,547)( 95,546)
( 96,545)( 97,544)( 98,543)( 99,542)(100,541)(101,540)(102,539)(103,538)
(104,537)(105,536)(106,535)(107,534)(108,533)(109,532)(110,531)(111,530)
(112,529)(113,528)(114,527)(115,526)(116,525)(117,524)(118,523)(119,522)
(120,521)(121,520)(122,519)(123,518)(124,517)(125,516)(126,515)(127,514)
(128,513)(129,512)(130,511)(131,510)(132,509)(133,508)(134,507)(135,506)
(136,505)(137,504)(138,503)(139,502)(140,501)(141,500)(142,499)(143,285)
(144,355)(145,354)(146,353)(147,352)(148,351)(149,350)(150,349)(151,348)
(152,347)(153,346)(154,345)(155,344)(156,343)(157,342)(158,341)(159,340)
(160,339)(161,338)(162,337)(163,336)(164,335)(165,334)(166,333)(167,332)
(168,331)(169,330)(170,329)(171,328)(172,327)(173,326)(174,325)(175,324)
(176,323)(177,322)(178,321)(179,320)(180,319)(181,318)(182,317)(183,316)
(184,315)(185,314)(186,313)(187,312)(188,311)(189,310)(190,309)(191,308)
(192,307)(193,306)(194,305)(195,304)(196,303)(197,302)(198,301)(199,300)
(200,299)(201,298)(202,297)(203,296)(204,295)(205,294)(206,293)(207,292)
(208,291)(209,290)(210,289)(211,288)(212,287)(213,286)(214,356)(215,426)
(216,425)(217,424)(218,423)(219,422)(220,421)(221,420)(222,419)(223,418)
(224,417)(225,416)(226,415)(227,414)(228,413)(229,412)(230,411)(231,410)
(232,409)(233,408)(234,407)(235,406)(236,405)(237,404)(238,403)(239,402)
(240,401)(241,400)(242,399)(243,398)(244,397)(245,396)(246,395)(247,394)
(248,393)(249,392)(250,391)(251,390)(252,389)(253,388)(254,387)(255,386)
(256,385)(257,384)(258,383)(259,382)(260,381)(261,380)(262,379)(263,378)
(264,377)(265,376)(266,375)(267,374)(268,373)(269,372)(270,371)(271,370)
(272,369)(273,368)(274,367)(275,366)(276,365)(277,364)(278,363)(279,362)
(280,361)(281,360)(282,359)(283,358)(284,357);
s2 := Sym(568)!( 1,144)( 2,143)( 3,213)( 4,212)( 5,211)( 6,210)( 7,209)
( 8,208)( 9,207)( 10,206)( 11,205)( 12,204)( 13,203)( 14,202)( 15,201)
( 16,200)( 17,199)( 18,198)( 19,197)( 20,196)( 21,195)( 22,194)( 23,193)
( 24,192)( 25,191)( 26,190)( 27,189)( 28,188)( 29,187)( 30,186)( 31,185)
( 32,184)( 33,183)( 34,182)( 35,181)( 36,180)( 37,179)( 38,178)( 39,177)
( 40,176)( 41,175)( 42,174)( 43,173)( 44,172)( 45,171)( 46,170)( 47,169)
( 48,168)( 49,167)( 50,166)( 51,165)( 52,164)( 53,163)( 54,162)( 55,161)
( 56,160)( 57,159)( 58,158)( 59,157)( 60,156)( 61,155)( 62,154)( 63,153)
( 64,152)( 65,151)( 66,150)( 67,149)( 68,148)( 69,147)( 70,146)( 71,145)
( 72,215)( 73,214)( 74,284)( 75,283)( 76,282)( 77,281)( 78,280)( 79,279)
( 80,278)( 81,277)( 82,276)( 83,275)( 84,274)( 85,273)( 86,272)( 87,271)
( 88,270)( 89,269)( 90,268)( 91,267)( 92,266)( 93,265)( 94,264)( 95,263)
( 96,262)( 97,261)( 98,260)( 99,259)(100,258)(101,257)(102,256)(103,255)
(104,254)(105,253)(106,252)(107,251)(108,250)(109,249)(110,248)(111,247)
(112,246)(113,245)(114,244)(115,243)(116,242)(117,241)(118,240)(119,239)
(120,238)(121,237)(122,236)(123,235)(124,234)(125,233)(126,232)(127,231)
(128,230)(129,229)(130,228)(131,227)(132,226)(133,225)(134,224)(135,223)
(136,222)(137,221)(138,220)(139,219)(140,218)(141,217)(142,216)(285,428)
(286,427)(287,497)(288,496)(289,495)(290,494)(291,493)(292,492)(293,491)
(294,490)(295,489)(296,488)(297,487)(298,486)(299,485)(300,484)(301,483)
(302,482)(303,481)(304,480)(305,479)(306,478)(307,477)(308,476)(309,475)
(310,474)(311,473)(312,472)(313,471)(314,470)(315,469)(316,468)(317,467)
(318,466)(319,465)(320,464)(321,463)(322,462)(323,461)(324,460)(325,459)
(326,458)(327,457)(328,456)(329,455)(330,454)(331,453)(332,452)(333,451)
(334,450)(335,449)(336,448)(337,447)(338,446)(339,445)(340,444)(341,443)
(342,442)(343,441)(344,440)(345,439)(346,438)(347,437)(348,436)(349,435)
(350,434)(351,433)(352,432)(353,431)(354,430)(355,429)(356,499)(357,498)
(358,568)(359,567)(360,566)(361,565)(362,564)(363,563)(364,562)(365,561)
(366,560)(367,559)(368,558)(369,557)(370,556)(371,555)(372,554)(373,553)
(374,552)(375,551)(376,550)(377,549)(378,548)(379,547)(380,546)(381,545)
(382,544)(383,543)(384,542)(385,541)(386,540)(387,539)(388,538)(389,537)
(390,536)(391,535)(392,534)(393,533)(394,532)(395,531)(396,530)(397,529)
(398,528)(399,527)(400,526)(401,525)(402,524)(403,523)(404,522)(405,521)
(406,520)(407,519)(408,518)(409,517)(410,516)(411,515)(412,514)(413,513)
(414,512)(415,511)(416,510)(417,509)(418,508)(419,507)(420,506)(421,505)
(422,504)(423,503)(424,502)(425,501)(426,500);
poly := sub<Sym(568)|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*s0*s1*s0*s1*s0*s1,
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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