Polytope of Type {4,134}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,134}*1072
Also Known As : {4,134|2}. if this polytope has another name.
Group : SmallGroup(1072,34)
Rank : 3
Schlafli Type : {4,134}
Number of vertices, edges, etc : 4, 268, 134
Order of s0s1s2 : 268
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 : {2,134}*536
4-fold quotients : {2,67}*268
67-fold quotients : {4,2}*16
134-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (269,336)(270,337)(271,338)(272,339)(273,340)(274,341)(275,342)(276,343)
(277,344)(278,345)(279,346)(280,347)(281,348)(282,349)(283,350)(284,351)
(285,352)(286,353)(287,354)(288,355)(289,356)(290,357)(291,358)(292,359)
(293,360)(294,361)(295,362)(296,363)(297,364)(298,365)(299,366)(300,367)
(301,368)(302,369)(303,370)(304,371)(305,372)(306,373)(307,374)(308,375)
(309,376)(310,377)(311,378)(312,379)(313,380)(314,381)(315,382)(316,383)
(317,384)(318,385)(319,386)(320,387)(321,388)(322,389)(323,390)(324,391)
(325,392)(326,393)(327,394)(328,395)(329,396)(330,397)(331,398)(332,399)
(333,400)(334,401)(335,402)(403,470)(404,471)(405,472)(406,473)(407,474)
(408,475)(409,476)(410,477)(411,478)(412,479)(413,480)(414,481)(415,482)
(416,483)(417,484)(418,485)(419,486)(420,487)(421,488)(422,489)(423,490)
(424,491)(425,492)(426,493)(427,494)(428,495)(429,496)(430,497)(431,498)
(432,499)(433,500)(434,501)(435,502)(436,503)(437,504)(438,505)(439,506)
(440,507)(441,508)(442,509)(443,510)(444,511)(445,512)(446,513)(447,514)
(448,515)(449,516)(450,517)(451,518)(452,519)(453,520)(454,521)(455,522)
(456,523)(457,524)(458,525)(459,526)(460,527)(461,528)(462,529)(463,530)
(464,531)(465,532)(466,533)(467,534)(468,535)(469,536);;
s1 := ( 1,403)( 2,469)( 3,468)( 4,467)( 5,466)( 6,465)( 7,464)( 8,463)
( 9,462)( 10,461)( 11,460)( 12,459)( 13,458)( 14,457)( 15,456)( 16,455)
( 17,454)( 18,453)( 19,452)( 20,451)( 21,450)( 22,449)( 23,448)( 24,447)
( 25,446)( 26,445)( 27,444)( 28,443)( 29,442)( 30,441)( 31,440)( 32,439)
( 33,438)( 34,437)( 35,436)( 36,435)( 37,434)( 38,433)( 39,432)( 40,431)
( 41,430)( 42,429)( 43,428)( 44,427)( 45,426)( 46,425)( 47,424)( 48,423)
( 49,422)( 50,421)( 51,420)( 52,419)( 53,418)( 54,417)( 55,416)( 56,415)
( 57,414)( 58,413)( 59,412)( 60,411)( 61,410)( 62,409)( 63,408)( 64,407)
( 65,406)( 66,405)( 67,404)( 68,470)( 69,536)( 70,535)( 71,534)( 72,533)
( 73,532)( 74,531)( 75,530)( 76,529)( 77,528)( 78,527)( 79,526)( 80,525)
( 81,524)( 82,523)( 83,522)( 84,521)( 85,520)( 86,519)( 87,518)( 88,517)
( 89,516)( 90,515)( 91,514)( 92,513)( 93,512)( 94,511)( 95,510)( 96,509)
( 97,508)( 98,507)( 99,506)(100,505)(101,504)(102,503)(103,502)(104,501)
(105,500)(106,499)(107,498)(108,497)(109,496)(110,495)(111,494)(112,493)
(113,492)(114,491)(115,490)(116,489)(117,488)(118,487)(119,486)(120,485)
(121,484)(122,483)(123,482)(124,481)(125,480)(126,479)(127,478)(128,477)
(129,476)(130,475)(131,474)(132,473)(133,472)(134,471)(135,269)(136,335)
(137,334)(138,333)(139,332)(140,331)(141,330)(142,329)(143,328)(144,327)
(145,326)(146,325)(147,324)(148,323)(149,322)(150,321)(151,320)(152,319)
(153,318)(154,317)(155,316)(156,315)(157,314)(158,313)(159,312)(160,311)
(161,310)(162,309)(163,308)(164,307)(165,306)(166,305)(167,304)(168,303)
(169,302)(170,301)(171,300)(172,299)(173,298)(174,297)(175,296)(176,295)
(177,294)(178,293)(179,292)(180,291)(181,290)(182,289)(183,288)(184,287)
(185,286)(186,285)(187,284)(188,283)(189,282)(190,281)(191,280)(192,279)
(193,278)(194,277)(195,276)(196,275)(197,274)(198,273)(199,272)(200,271)
(201,270)(202,336)(203,402)(204,401)(205,400)(206,399)(207,398)(208,397)
(209,396)(210,395)(211,394)(212,393)(213,392)(214,391)(215,390)(216,389)
(217,388)(218,387)(219,386)(220,385)(221,384)(222,383)(223,382)(224,381)
(225,380)(226,379)(227,378)(228,377)(229,376)(230,375)(231,374)(232,373)
(233,372)(234,371)(235,370)(236,369)(237,368)(238,367)(239,366)(240,365)
(241,364)(242,363)(243,362)(244,361)(245,360)(246,359)(247,358)(248,357)
(249,356)(250,355)(251,354)(252,353)(253,352)(254,351)(255,350)(256,349)
(257,348)(258,347)(259,346)(260,345)(261,344)(262,343)(263,342)(264,341)
(265,340)(266,339)(267,338)(268,337);;
s2 := ( 1,136)( 2,135)( 3,201)( 4,200)( 5,199)( 6,198)( 7,197)( 8,196)
( 9,195)( 10,194)( 11,193)( 12,192)( 13,191)( 14,190)( 15,189)( 16,188)
( 17,187)( 18,186)( 19,185)( 20,184)( 21,183)( 22,182)( 23,181)( 24,180)
( 25,179)( 26,178)( 27,177)( 28,176)( 29,175)( 30,174)( 31,173)( 32,172)
( 33,171)( 34,170)( 35,169)( 36,168)( 37,167)( 38,166)( 39,165)( 40,164)
( 41,163)( 42,162)( 43,161)( 44,160)( 45,159)( 46,158)( 47,157)( 48,156)
( 49,155)( 50,154)( 51,153)( 52,152)( 53,151)( 54,150)( 55,149)( 56,148)
( 57,147)( 58,146)( 59,145)( 60,144)( 61,143)( 62,142)( 63,141)( 64,140)
( 65,139)( 66,138)( 67,137)( 68,203)( 69,202)( 70,268)( 71,267)( 72,266)
( 73,265)( 74,264)( 75,263)( 76,262)( 77,261)( 78,260)( 79,259)( 80,258)
( 81,257)( 82,256)( 83,255)( 84,254)( 85,253)( 86,252)( 87,251)( 88,250)
( 89,249)( 90,248)( 91,247)( 92,246)( 93,245)( 94,244)( 95,243)( 96,242)
( 97,241)( 98,240)( 99,239)(100,238)(101,237)(102,236)(103,235)(104,234)
(105,233)(106,232)(107,231)(108,230)(109,229)(110,228)(111,227)(112,226)
(113,225)(114,224)(115,223)(116,222)(117,221)(118,220)(119,219)(120,218)
(121,217)(122,216)(123,215)(124,214)(125,213)(126,212)(127,211)(128,210)
(129,209)(130,208)(131,207)(132,206)(133,205)(134,204)(269,404)(270,403)
(271,469)(272,468)(273,467)(274,466)(275,465)(276,464)(277,463)(278,462)
(279,461)(280,460)(281,459)(282,458)(283,457)(284,456)(285,455)(286,454)
(287,453)(288,452)(289,451)(290,450)(291,449)(292,448)(293,447)(294,446)
(295,445)(296,444)(297,443)(298,442)(299,441)(300,440)(301,439)(302,438)
(303,437)(304,436)(305,435)(306,434)(307,433)(308,432)(309,431)(310,430)
(311,429)(312,428)(313,427)(314,426)(315,425)(316,424)(317,423)(318,422)
(319,421)(320,420)(321,419)(322,418)(323,417)(324,416)(325,415)(326,414)
(327,413)(328,412)(329,411)(330,410)(331,409)(332,408)(333,407)(334,406)
(335,405)(336,471)(337,470)(338,536)(339,535)(340,534)(341,533)(342,532)
(343,531)(344,530)(345,529)(346,528)(347,527)(348,526)(349,525)(350,524)
(351,523)(352,522)(353,521)(354,520)(355,519)(356,518)(357,517)(358,516)
(359,515)(360,514)(361,513)(362,512)(363,511)(364,510)(365,509)(366,508)
(367,507)(368,506)(369,505)(370,504)(371,503)(372,502)(373,501)(374,500)
(375,499)(376,498)(377,497)(378,496)(379,495)(380,494)(381,493)(382,492)
(383,491)(384,490)(385,489)(386,488)(387,487)(388,486)(389,485)(390,484)
(391,483)(392,482)(393,481)(394,480)(395,479)(396,478)(397,477)(398,476)
(399,475)(400,474)(401,473)(402,472);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(536)!(269,336)(270,337)(271,338)(272,339)(273,340)(274,341)(275,342)
(276,343)(277,344)(278,345)(279,346)(280,347)(281,348)(282,349)(283,350)
(284,351)(285,352)(286,353)(287,354)(288,355)(289,356)(290,357)(291,358)
(292,359)(293,360)(294,361)(295,362)(296,363)(297,364)(298,365)(299,366)
(300,367)(301,368)(302,369)(303,370)(304,371)(305,372)(306,373)(307,374)
(308,375)(309,376)(310,377)(311,378)(312,379)(313,380)(314,381)(315,382)
(316,383)(317,384)(318,385)(319,386)(320,387)(321,388)(322,389)(323,390)
(324,391)(325,392)(326,393)(327,394)(328,395)(329,396)(330,397)(331,398)
(332,399)(333,400)(334,401)(335,402)(403,470)(404,471)(405,472)(406,473)
(407,474)(408,475)(409,476)(410,477)(411,478)(412,479)(413,480)(414,481)
(415,482)(416,483)(417,484)(418,485)(419,486)(420,487)(421,488)(422,489)
(423,490)(424,491)(425,492)(426,493)(427,494)(428,495)(429,496)(430,497)
(431,498)(432,499)(433,500)(434,501)(435,502)(436,503)(437,504)(438,505)
(439,506)(440,507)(441,508)(442,509)(443,510)(444,511)(445,512)(446,513)
(447,514)(448,515)(449,516)(450,517)(451,518)(452,519)(453,520)(454,521)
(455,522)(456,523)(457,524)(458,525)(459,526)(460,527)(461,528)(462,529)
(463,530)(464,531)(465,532)(466,533)(467,534)(468,535)(469,536);
s1 := Sym(536)!( 1,403)( 2,469)( 3,468)( 4,467)( 5,466)( 6,465)( 7,464)
( 8,463)( 9,462)( 10,461)( 11,460)( 12,459)( 13,458)( 14,457)( 15,456)
( 16,455)( 17,454)( 18,453)( 19,452)( 20,451)( 21,450)( 22,449)( 23,448)
( 24,447)( 25,446)( 26,445)( 27,444)( 28,443)( 29,442)( 30,441)( 31,440)
( 32,439)( 33,438)( 34,437)( 35,436)( 36,435)( 37,434)( 38,433)( 39,432)
( 40,431)( 41,430)( 42,429)( 43,428)( 44,427)( 45,426)( 46,425)( 47,424)
( 48,423)( 49,422)( 50,421)( 51,420)( 52,419)( 53,418)( 54,417)( 55,416)
( 56,415)( 57,414)( 58,413)( 59,412)( 60,411)( 61,410)( 62,409)( 63,408)
( 64,407)( 65,406)( 66,405)( 67,404)( 68,470)( 69,536)( 70,535)( 71,534)
( 72,533)( 73,532)( 74,531)( 75,530)( 76,529)( 77,528)( 78,527)( 79,526)
( 80,525)( 81,524)( 82,523)( 83,522)( 84,521)( 85,520)( 86,519)( 87,518)
( 88,517)( 89,516)( 90,515)( 91,514)( 92,513)( 93,512)( 94,511)( 95,510)
( 96,509)( 97,508)( 98,507)( 99,506)(100,505)(101,504)(102,503)(103,502)
(104,501)(105,500)(106,499)(107,498)(108,497)(109,496)(110,495)(111,494)
(112,493)(113,492)(114,491)(115,490)(116,489)(117,488)(118,487)(119,486)
(120,485)(121,484)(122,483)(123,482)(124,481)(125,480)(126,479)(127,478)
(128,477)(129,476)(130,475)(131,474)(132,473)(133,472)(134,471)(135,269)
(136,335)(137,334)(138,333)(139,332)(140,331)(141,330)(142,329)(143,328)
(144,327)(145,326)(146,325)(147,324)(148,323)(149,322)(150,321)(151,320)
(152,319)(153,318)(154,317)(155,316)(156,315)(157,314)(158,313)(159,312)
(160,311)(161,310)(162,309)(163,308)(164,307)(165,306)(166,305)(167,304)
(168,303)(169,302)(170,301)(171,300)(172,299)(173,298)(174,297)(175,296)
(176,295)(177,294)(178,293)(179,292)(180,291)(181,290)(182,289)(183,288)
(184,287)(185,286)(186,285)(187,284)(188,283)(189,282)(190,281)(191,280)
(192,279)(193,278)(194,277)(195,276)(196,275)(197,274)(198,273)(199,272)
(200,271)(201,270)(202,336)(203,402)(204,401)(205,400)(206,399)(207,398)
(208,397)(209,396)(210,395)(211,394)(212,393)(213,392)(214,391)(215,390)
(216,389)(217,388)(218,387)(219,386)(220,385)(221,384)(222,383)(223,382)
(224,381)(225,380)(226,379)(227,378)(228,377)(229,376)(230,375)(231,374)
(232,373)(233,372)(234,371)(235,370)(236,369)(237,368)(238,367)(239,366)
(240,365)(241,364)(242,363)(243,362)(244,361)(245,360)(246,359)(247,358)
(248,357)(249,356)(250,355)(251,354)(252,353)(253,352)(254,351)(255,350)
(256,349)(257,348)(258,347)(259,346)(260,345)(261,344)(262,343)(263,342)
(264,341)(265,340)(266,339)(267,338)(268,337);
s2 := Sym(536)!( 1,136)( 2,135)( 3,201)( 4,200)( 5,199)( 6,198)( 7,197)
( 8,196)( 9,195)( 10,194)( 11,193)( 12,192)( 13,191)( 14,190)( 15,189)
( 16,188)( 17,187)( 18,186)( 19,185)( 20,184)( 21,183)( 22,182)( 23,181)
( 24,180)( 25,179)( 26,178)( 27,177)( 28,176)( 29,175)( 30,174)( 31,173)
( 32,172)( 33,171)( 34,170)( 35,169)( 36,168)( 37,167)( 38,166)( 39,165)
( 40,164)( 41,163)( 42,162)( 43,161)( 44,160)( 45,159)( 46,158)( 47,157)
( 48,156)( 49,155)( 50,154)( 51,153)( 52,152)( 53,151)( 54,150)( 55,149)
( 56,148)( 57,147)( 58,146)( 59,145)( 60,144)( 61,143)( 62,142)( 63,141)
( 64,140)( 65,139)( 66,138)( 67,137)( 68,203)( 69,202)( 70,268)( 71,267)
( 72,266)( 73,265)( 74,264)( 75,263)( 76,262)( 77,261)( 78,260)( 79,259)
( 80,258)( 81,257)( 82,256)( 83,255)( 84,254)( 85,253)( 86,252)( 87,251)
( 88,250)( 89,249)( 90,248)( 91,247)( 92,246)( 93,245)( 94,244)( 95,243)
( 96,242)( 97,241)( 98,240)( 99,239)(100,238)(101,237)(102,236)(103,235)
(104,234)(105,233)(106,232)(107,231)(108,230)(109,229)(110,228)(111,227)
(112,226)(113,225)(114,224)(115,223)(116,222)(117,221)(118,220)(119,219)
(120,218)(121,217)(122,216)(123,215)(124,214)(125,213)(126,212)(127,211)
(128,210)(129,209)(130,208)(131,207)(132,206)(133,205)(134,204)(269,404)
(270,403)(271,469)(272,468)(273,467)(274,466)(275,465)(276,464)(277,463)
(278,462)(279,461)(280,460)(281,459)(282,458)(283,457)(284,456)(285,455)
(286,454)(287,453)(288,452)(289,451)(290,450)(291,449)(292,448)(293,447)
(294,446)(295,445)(296,444)(297,443)(298,442)(299,441)(300,440)(301,439)
(302,438)(303,437)(304,436)(305,435)(306,434)(307,433)(308,432)(309,431)
(310,430)(311,429)(312,428)(313,427)(314,426)(315,425)(316,424)(317,423)
(318,422)(319,421)(320,420)(321,419)(322,418)(323,417)(324,416)(325,415)
(326,414)(327,413)(328,412)(329,411)(330,410)(331,409)(332,408)(333,407)
(334,406)(335,405)(336,471)(337,470)(338,536)(339,535)(340,534)(341,533)
(342,532)(343,531)(344,530)(345,529)(346,528)(347,527)(348,526)(349,525)
(350,524)(351,523)(352,522)(353,521)(354,520)(355,519)(356,518)(357,517)
(358,516)(359,515)(360,514)(361,513)(362,512)(363,511)(364,510)(365,509)
(366,508)(367,507)(368,506)(369,505)(370,504)(371,503)(372,502)(373,501)
(374,500)(375,499)(376,498)(377,497)(378,496)(379,495)(380,494)(381,493)
(382,492)(383,491)(384,490)(385,489)(386,488)(387,487)(388,486)(389,485)
(390,484)(391,483)(392,482)(393,481)(394,480)(395,479)(396,478)(397,477)
(398,476)(399,475)(400,474)(401,473)(402,472);
poly := sub<Sym(536)|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 >;
References : None.
to this polytope