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Polytope of Type {16,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,34}*1088
Also Known As : {16,34|2}. if this polytope has another name.
Group : SmallGroup(1088,968)
Rank : 3
Schlafli Type : {16,34}
Number of vertices, edges, etc : 16, 272, 34
Order of s0s1s2 : 272
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 : {8,34}*544
   4-fold quotients : {4,34}*272
   8-fold quotients : {2,34}*136
   16-fold quotients : {2,17}*68
   17-fold quotients : {16,2}*64
   34-fold quotients : {8,2}*32
   68-fold quotients : {4,2}*16
   136-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)( 41, 58)( 42, 59)
( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)( 49, 66)( 50, 67)
( 51, 68)( 69,103)( 70,104)( 71,105)( 72,106)( 73,107)( 74,108)( 75,109)
( 76,110)( 77,111)( 78,112)( 79,113)( 80,114)( 81,115)( 82,116)( 83,117)
( 84,118)( 85,119)( 86,120)( 87,121)( 88,122)( 89,123)( 90,124)( 91,125)
( 92,126)( 93,127)( 94,128)( 95,129)( 96,130)( 97,131)( 98,132)( 99,133)
(100,134)(101,135)(102,136)(171,188)(172,189)(173,190)(174,191)(175,192)
(176,193)(177,194)(178,195)(179,196)(180,197)(181,198)(182,199)(183,200)
(184,201)(185,202)(186,203)(187,204)(205,239)(206,240)(207,241)(208,242)
(209,243)(210,244)(211,245)(212,246)(213,247)(214,248)(215,249)(216,250)
(217,251)(218,252)(219,253)(220,254)(221,255)(222,256)(223,257)(224,258)
(225,259)(226,260)(227,261)(228,262)(229,263)(230,264)(231,265)(232,266)
(233,267)(234,268)(235,269)(236,270)(237,271)(238,272)(273,341)(274,342)
(275,343)(276,344)(277,345)(278,346)(279,347)(280,348)(281,349)(282,350)
(283,351)(284,352)(285,353)(286,354)(287,355)(288,356)(289,357)(290,358)
(291,359)(292,360)(293,361)(294,362)(295,363)(296,364)(297,365)(298,366)
(299,367)(300,368)(301,369)(302,370)(303,371)(304,372)(305,373)(306,374)
(307,392)(308,393)(309,394)(310,395)(311,396)(312,397)(313,398)(314,399)
(315,400)(316,401)(317,402)(318,403)(319,404)(320,405)(321,406)(322,407)
(323,408)(324,375)(325,376)(326,377)(327,378)(328,379)(329,380)(330,381)
(331,382)(332,383)(333,384)(334,385)(335,386)(336,387)(337,388)(338,389)
(339,390)(340,391)(409,477)(410,478)(411,479)(412,480)(413,481)(414,482)
(415,483)(416,484)(417,485)(418,486)(419,487)(420,488)(421,489)(422,490)
(423,491)(424,492)(425,493)(426,494)(427,495)(428,496)(429,497)(430,498)
(431,499)(432,500)(433,501)(434,502)(435,503)(436,504)(437,505)(438,506)
(439,507)(440,508)(441,509)(442,510)(443,528)(444,529)(445,530)(446,531)
(447,532)(448,533)(449,534)(450,535)(451,536)(452,537)(453,538)(454,539)
(455,540)(456,541)(457,542)(458,543)(459,544)(460,511)(461,512)(462,513)
(463,514)(464,515)(465,516)(466,517)(467,518)(468,519)(469,520)(470,521)
(471,522)(472,523)(473,524)(474,525)(475,526)(476,527);;
s1 := (  1,409)(  2,425)(  3,424)(  4,423)(  5,422)(  6,421)(  7,420)(  8,419)
(  9,418)( 10,417)( 11,416)( 12,415)( 13,414)( 14,413)( 15,412)( 16,411)
( 17,410)( 18,426)( 19,442)( 20,441)( 21,440)( 22,439)( 23,438)( 24,437)
( 25,436)( 26,435)( 27,434)( 28,433)( 29,432)( 30,431)( 31,430)( 32,429)
( 33,428)( 34,427)( 35,460)( 36,476)( 37,475)( 38,474)( 39,473)( 40,472)
( 41,471)( 42,470)( 43,469)( 44,468)( 45,467)( 46,466)( 47,465)( 48,464)
( 49,463)( 50,462)( 51,461)( 52,443)( 53,459)( 54,458)( 55,457)( 56,456)
( 57,455)( 58,454)( 59,453)( 60,452)( 61,451)( 62,450)( 63,449)( 64,448)
( 65,447)( 66,446)( 67,445)( 68,444)( 69,511)( 70,527)( 71,526)( 72,525)
( 73,524)( 74,523)( 75,522)( 76,521)( 77,520)( 78,519)( 79,518)( 80,517)
( 81,516)( 82,515)( 83,514)( 84,513)( 85,512)( 86,528)( 87,544)( 88,543)
( 89,542)( 90,541)( 91,540)( 92,539)( 93,538)( 94,537)( 95,536)( 96,535)
( 97,534)( 98,533)( 99,532)(100,531)(101,530)(102,529)(103,477)(104,493)
(105,492)(106,491)(107,490)(108,489)(109,488)(110,487)(111,486)(112,485)
(113,484)(114,483)(115,482)(116,481)(117,480)(118,479)(119,478)(120,494)
(121,510)(122,509)(123,508)(124,507)(125,506)(126,505)(127,504)(128,503)
(129,502)(130,501)(131,500)(132,499)(133,498)(134,497)(135,496)(136,495)
(137,273)(138,289)(139,288)(140,287)(141,286)(142,285)(143,284)(144,283)
(145,282)(146,281)(147,280)(148,279)(149,278)(150,277)(151,276)(152,275)
(153,274)(154,290)(155,306)(156,305)(157,304)(158,303)(159,302)(160,301)
(161,300)(162,299)(163,298)(164,297)(165,296)(166,295)(167,294)(168,293)
(169,292)(170,291)(171,324)(172,340)(173,339)(174,338)(175,337)(176,336)
(177,335)(178,334)(179,333)(180,332)(181,331)(182,330)(183,329)(184,328)
(185,327)(186,326)(187,325)(188,307)(189,323)(190,322)(191,321)(192,320)
(193,319)(194,318)(195,317)(196,316)(197,315)(198,314)(199,313)(200,312)
(201,311)(202,310)(203,309)(204,308)(205,375)(206,391)(207,390)(208,389)
(209,388)(210,387)(211,386)(212,385)(213,384)(214,383)(215,382)(216,381)
(217,380)(218,379)(219,378)(220,377)(221,376)(222,392)(223,408)(224,407)
(225,406)(226,405)(227,404)(228,403)(229,402)(230,401)(231,400)(232,399)
(233,398)(234,397)(235,396)(236,395)(237,394)(238,393)(239,341)(240,357)
(241,356)(242,355)(243,354)(244,353)(245,352)(246,351)(247,350)(248,349)
(249,348)(250,347)(251,346)(252,345)(253,344)(254,343)(255,342)(256,358)
(257,374)(258,373)(259,372)(260,371)(261,370)(262,369)(263,368)(264,367)
(265,366)(266,365)(267,364)(268,363)(269,362)(270,361)(271,360)(272,359);;
s2 := (  1,138)(  2,137)(  3,153)(  4,152)(  5,151)(  6,150)(  7,149)(  8,148)
(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,141)( 16,140)
( 17,139)( 18,155)( 19,154)( 20,170)( 21,169)( 22,168)( 23,167)( 24,166)
( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)( 32,158)
( 33,157)( 34,156)( 35,172)( 36,171)( 37,187)( 38,186)( 39,185)( 40,184)
( 41,183)( 42,182)( 43,181)( 44,180)( 45,179)( 46,178)( 47,177)( 48,176)
( 49,175)( 50,174)( 51,173)( 52,189)( 53,188)( 54,204)( 55,203)( 56,202)
( 57,201)( 58,200)( 59,199)( 60,198)( 61,197)( 62,196)( 63,195)( 64,194)
( 65,193)( 66,192)( 67,191)( 68,190)( 69,206)( 70,205)( 71,221)( 72,220)
( 73,219)( 74,218)( 75,217)( 76,216)( 77,215)( 78,214)( 79,213)( 80,212)
( 81,211)( 82,210)( 83,209)( 84,208)( 85,207)( 86,223)( 87,222)( 88,238)
( 89,237)( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)( 96,230)
( 97,229)( 98,228)( 99,227)(100,226)(101,225)(102,224)(103,240)(104,239)
(105,255)(106,254)(107,253)(108,252)(109,251)(110,250)(111,249)(112,248)
(113,247)(114,246)(115,245)(116,244)(117,243)(118,242)(119,241)(120,257)
(121,256)(122,272)(123,271)(124,270)(125,269)(126,268)(127,267)(128,266)
(129,265)(130,264)(131,263)(132,262)(133,261)(134,260)(135,259)(136,258)
(273,410)(274,409)(275,425)(276,424)(277,423)(278,422)(279,421)(280,420)
(281,419)(282,418)(283,417)(284,416)(285,415)(286,414)(287,413)(288,412)
(289,411)(290,427)(291,426)(292,442)(293,441)(294,440)(295,439)(296,438)
(297,437)(298,436)(299,435)(300,434)(301,433)(302,432)(303,431)(304,430)
(305,429)(306,428)(307,444)(308,443)(309,459)(310,458)(311,457)(312,456)
(313,455)(314,454)(315,453)(316,452)(317,451)(318,450)(319,449)(320,448)
(321,447)(322,446)(323,445)(324,461)(325,460)(326,476)(327,475)(328,474)
(329,473)(330,472)(331,471)(332,470)(333,469)(334,468)(335,467)(336,466)
(337,465)(338,464)(339,463)(340,462)(341,478)(342,477)(343,493)(344,492)
(345,491)(346,490)(347,489)(348,488)(349,487)(350,486)(351,485)(352,484)
(353,483)(354,482)(355,481)(356,480)(357,479)(358,495)(359,494)(360,510)
(361,509)(362,508)(363,507)(364,506)(365,505)(366,504)(367,503)(368,502)
(369,501)(370,500)(371,499)(372,498)(373,497)(374,496)(375,512)(376,511)
(377,527)(378,526)(379,525)(380,524)(381,523)(382,522)(383,521)(384,520)
(385,519)(386,518)(387,517)(388,516)(389,515)(390,514)(391,513)(392,529)
(393,528)(394,544)(395,543)(396,542)(397,541)(398,540)(399,539)(400,538)
(401,537)(402,536)(403,535)(404,534)(405,533)(406,532)(407,531)(408,530);;
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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(544)!( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)( 41, 58)
( 42, 59)( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)( 49, 66)
( 50, 67)( 51, 68)( 69,103)( 70,104)( 71,105)( 72,106)( 73,107)( 74,108)
( 75,109)( 76,110)( 77,111)( 78,112)( 79,113)( 80,114)( 81,115)( 82,116)
( 83,117)( 84,118)( 85,119)( 86,120)( 87,121)( 88,122)( 89,123)( 90,124)
( 91,125)( 92,126)( 93,127)( 94,128)( 95,129)( 96,130)( 97,131)( 98,132)
( 99,133)(100,134)(101,135)(102,136)(171,188)(172,189)(173,190)(174,191)
(175,192)(176,193)(177,194)(178,195)(179,196)(180,197)(181,198)(182,199)
(183,200)(184,201)(185,202)(186,203)(187,204)(205,239)(206,240)(207,241)
(208,242)(209,243)(210,244)(211,245)(212,246)(213,247)(214,248)(215,249)
(216,250)(217,251)(218,252)(219,253)(220,254)(221,255)(222,256)(223,257)
(224,258)(225,259)(226,260)(227,261)(228,262)(229,263)(230,264)(231,265)
(232,266)(233,267)(234,268)(235,269)(236,270)(237,271)(238,272)(273,341)
(274,342)(275,343)(276,344)(277,345)(278,346)(279,347)(280,348)(281,349)
(282,350)(283,351)(284,352)(285,353)(286,354)(287,355)(288,356)(289,357)
(290,358)(291,359)(292,360)(293,361)(294,362)(295,363)(296,364)(297,365)
(298,366)(299,367)(300,368)(301,369)(302,370)(303,371)(304,372)(305,373)
(306,374)(307,392)(308,393)(309,394)(310,395)(311,396)(312,397)(313,398)
(314,399)(315,400)(316,401)(317,402)(318,403)(319,404)(320,405)(321,406)
(322,407)(323,408)(324,375)(325,376)(326,377)(327,378)(328,379)(329,380)
(330,381)(331,382)(332,383)(333,384)(334,385)(335,386)(336,387)(337,388)
(338,389)(339,390)(340,391)(409,477)(410,478)(411,479)(412,480)(413,481)
(414,482)(415,483)(416,484)(417,485)(418,486)(419,487)(420,488)(421,489)
(422,490)(423,491)(424,492)(425,493)(426,494)(427,495)(428,496)(429,497)
(430,498)(431,499)(432,500)(433,501)(434,502)(435,503)(436,504)(437,505)
(438,506)(439,507)(440,508)(441,509)(442,510)(443,528)(444,529)(445,530)
(446,531)(447,532)(448,533)(449,534)(450,535)(451,536)(452,537)(453,538)
(454,539)(455,540)(456,541)(457,542)(458,543)(459,544)(460,511)(461,512)
(462,513)(463,514)(464,515)(465,516)(466,517)(467,518)(468,519)(469,520)
(470,521)(471,522)(472,523)(473,524)(474,525)(475,526)(476,527);
s1 := Sym(544)!(  1,409)(  2,425)(  3,424)(  4,423)(  5,422)(  6,421)(  7,420)
(  8,419)(  9,418)( 10,417)( 11,416)( 12,415)( 13,414)( 14,413)( 15,412)
( 16,411)( 17,410)( 18,426)( 19,442)( 20,441)( 21,440)( 22,439)( 23,438)
( 24,437)( 25,436)( 26,435)( 27,434)( 28,433)( 29,432)( 30,431)( 31,430)
( 32,429)( 33,428)( 34,427)( 35,460)( 36,476)( 37,475)( 38,474)( 39,473)
( 40,472)( 41,471)( 42,470)( 43,469)( 44,468)( 45,467)( 46,466)( 47,465)
( 48,464)( 49,463)( 50,462)( 51,461)( 52,443)( 53,459)( 54,458)( 55,457)
( 56,456)( 57,455)( 58,454)( 59,453)( 60,452)( 61,451)( 62,450)( 63,449)
( 64,448)( 65,447)( 66,446)( 67,445)( 68,444)( 69,511)( 70,527)( 71,526)
( 72,525)( 73,524)( 74,523)( 75,522)( 76,521)( 77,520)( 78,519)( 79,518)
( 80,517)( 81,516)( 82,515)( 83,514)( 84,513)( 85,512)( 86,528)( 87,544)
( 88,543)( 89,542)( 90,541)( 91,540)( 92,539)( 93,538)( 94,537)( 95,536)
( 96,535)( 97,534)( 98,533)( 99,532)(100,531)(101,530)(102,529)(103,477)
(104,493)(105,492)(106,491)(107,490)(108,489)(109,488)(110,487)(111,486)
(112,485)(113,484)(114,483)(115,482)(116,481)(117,480)(118,479)(119,478)
(120,494)(121,510)(122,509)(123,508)(124,507)(125,506)(126,505)(127,504)
(128,503)(129,502)(130,501)(131,500)(132,499)(133,498)(134,497)(135,496)
(136,495)(137,273)(138,289)(139,288)(140,287)(141,286)(142,285)(143,284)
(144,283)(145,282)(146,281)(147,280)(148,279)(149,278)(150,277)(151,276)
(152,275)(153,274)(154,290)(155,306)(156,305)(157,304)(158,303)(159,302)
(160,301)(161,300)(162,299)(163,298)(164,297)(165,296)(166,295)(167,294)
(168,293)(169,292)(170,291)(171,324)(172,340)(173,339)(174,338)(175,337)
(176,336)(177,335)(178,334)(179,333)(180,332)(181,331)(182,330)(183,329)
(184,328)(185,327)(186,326)(187,325)(188,307)(189,323)(190,322)(191,321)
(192,320)(193,319)(194,318)(195,317)(196,316)(197,315)(198,314)(199,313)
(200,312)(201,311)(202,310)(203,309)(204,308)(205,375)(206,391)(207,390)
(208,389)(209,388)(210,387)(211,386)(212,385)(213,384)(214,383)(215,382)
(216,381)(217,380)(218,379)(219,378)(220,377)(221,376)(222,392)(223,408)
(224,407)(225,406)(226,405)(227,404)(228,403)(229,402)(230,401)(231,400)
(232,399)(233,398)(234,397)(235,396)(236,395)(237,394)(238,393)(239,341)
(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,351)(247,350)
(248,349)(249,348)(250,347)(251,346)(252,345)(253,344)(254,343)(255,342)
(256,358)(257,374)(258,373)(259,372)(260,371)(261,370)(262,369)(263,368)
(264,367)(265,366)(266,365)(267,364)(268,363)(269,362)(270,361)(271,360)
(272,359);
s2 := Sym(544)!(  1,138)(  2,137)(  3,153)(  4,152)(  5,151)(  6,150)(  7,149)
(  8,148)(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,141)
( 16,140)( 17,139)( 18,155)( 19,154)( 20,170)( 21,169)( 22,168)( 23,167)
( 24,166)( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)
( 32,158)( 33,157)( 34,156)( 35,172)( 36,171)( 37,187)( 38,186)( 39,185)
( 40,184)( 41,183)( 42,182)( 43,181)( 44,180)( 45,179)( 46,178)( 47,177)
( 48,176)( 49,175)( 50,174)( 51,173)( 52,189)( 53,188)( 54,204)( 55,203)
( 56,202)( 57,201)( 58,200)( 59,199)( 60,198)( 61,197)( 62,196)( 63,195)
( 64,194)( 65,193)( 66,192)( 67,191)( 68,190)( 69,206)( 70,205)( 71,221)
( 72,220)( 73,219)( 74,218)( 75,217)( 76,216)( 77,215)( 78,214)( 79,213)
( 80,212)( 81,211)( 82,210)( 83,209)( 84,208)( 85,207)( 86,223)( 87,222)
( 88,238)( 89,237)( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)
( 96,230)( 97,229)( 98,228)( 99,227)(100,226)(101,225)(102,224)(103,240)
(104,239)(105,255)(106,254)(107,253)(108,252)(109,251)(110,250)(111,249)
(112,248)(113,247)(114,246)(115,245)(116,244)(117,243)(118,242)(119,241)
(120,257)(121,256)(122,272)(123,271)(124,270)(125,269)(126,268)(127,267)
(128,266)(129,265)(130,264)(131,263)(132,262)(133,261)(134,260)(135,259)
(136,258)(273,410)(274,409)(275,425)(276,424)(277,423)(278,422)(279,421)
(280,420)(281,419)(282,418)(283,417)(284,416)(285,415)(286,414)(287,413)
(288,412)(289,411)(290,427)(291,426)(292,442)(293,441)(294,440)(295,439)
(296,438)(297,437)(298,436)(299,435)(300,434)(301,433)(302,432)(303,431)
(304,430)(305,429)(306,428)(307,444)(308,443)(309,459)(310,458)(311,457)
(312,456)(313,455)(314,454)(315,453)(316,452)(317,451)(318,450)(319,449)
(320,448)(321,447)(322,446)(323,445)(324,461)(325,460)(326,476)(327,475)
(328,474)(329,473)(330,472)(331,471)(332,470)(333,469)(334,468)(335,467)
(336,466)(337,465)(338,464)(339,463)(340,462)(341,478)(342,477)(343,493)
(344,492)(345,491)(346,490)(347,489)(348,488)(349,487)(350,486)(351,485)
(352,484)(353,483)(354,482)(355,481)(356,480)(357,479)(358,495)(359,494)
(360,510)(361,509)(362,508)(363,507)(364,506)(365,505)(366,504)(367,503)
(368,502)(369,501)(370,500)(371,499)(372,498)(373,497)(374,496)(375,512)
(376,511)(377,527)(378,526)(379,525)(380,524)(381,523)(382,522)(383,521)
(384,520)(385,519)(386,518)(387,517)(388,516)(389,515)(390,514)(391,513)
(392,529)(393,528)(394,544)(395,543)(396,542)(397,541)(398,540)(399,539)
(400,538)(401,537)(402,536)(403,535)(404,534)(405,533)(406,532)(407,531)
(408,530);
poly := sub<Sym(544)|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*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 >; 
 
References : None.
to this polytope