Polytope of Type {34,26}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,26}*1768
Also Known As : {34,26|2}. if this polytope has another name.
Group : SmallGroup(1768,49)
Rank : 3
Schlafli Type : {34,26}
Number of vertices, edges, etc : 34, 442, 26
Order of s0s1s2 : 442
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) :
13-fold quotients : {34,2}*136
17-fold quotients : {2,26}*104
26-fold quotients : {17,2}*68
34-fold quotients : {2,13}*52
221-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)( 9, 10)
( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)( 26, 27)
( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 43, 44)
( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)
( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 77, 78)
( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)
(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)
(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)
(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146)
(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)
(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)(179,180)
(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197)
(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)(213,214)
(223,238)(224,237)(225,236)(226,235)(227,234)(228,233)(229,232)(230,231)
(240,255)(241,254)(242,253)(243,252)(244,251)(245,250)(246,249)(247,248)
(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)
(274,289)(275,288)(276,287)(277,286)(278,285)(279,284)(280,283)(281,282)
(291,306)(292,305)(293,304)(294,303)(295,302)(296,301)(297,300)(298,299)
(308,323)(309,322)(310,321)(311,320)(312,319)(313,318)(314,317)(315,316)
(325,340)(326,339)(327,338)(328,337)(329,336)(330,335)(331,334)(332,333)
(342,357)(343,356)(344,355)(345,354)(346,353)(347,352)(348,351)(349,350)
(359,374)(360,373)(361,372)(362,371)(363,370)(364,369)(365,368)(366,367)
(376,391)(377,390)(378,389)(379,388)(380,387)(381,386)(382,385)(383,384)
(393,408)(394,407)(395,406)(396,405)(397,404)(398,403)(399,402)(400,401)
(410,425)(411,424)(412,423)(413,422)(414,421)(415,420)(416,419)(417,418)
(427,442)(428,441)(429,440)(430,439)(431,438)(432,437)(433,436)(434,435);;
s1 := ( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)
( 18,206)( 19,205)( 20,221)( 21,220)( 22,219)( 23,218)( 24,217)( 25,216)
( 26,215)( 27,214)( 28,213)( 29,212)( 30,211)( 31,210)( 32,209)( 33,208)
( 34,207)( 35,189)( 36,188)( 37,204)( 38,203)( 39,202)( 40,201)( 41,200)
( 42,199)( 43,198)( 44,197)( 45,196)( 46,195)( 47,194)( 48,193)( 49,192)
( 50,191)( 51,190)( 52,172)( 53,171)( 54,187)( 55,186)( 56,185)( 57,184)
( 58,183)( 59,182)( 60,181)( 61,180)( 62,179)( 63,178)( 64,177)( 65,176)
( 66,175)( 67,174)( 68,173)( 69,155)( 70,154)( 71,170)( 72,169)( 73,168)
( 74,167)( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)( 81,160)
( 82,159)( 83,158)( 84,157)( 85,156)( 86,138)( 87,137)( 88,153)( 89,152)
( 90,151)( 91,150)( 92,149)( 93,148)( 94,147)( 95,146)( 96,145)( 97,144)
( 98,143)( 99,142)(100,141)(101,140)(102,139)(103,121)(104,120)(105,136)
(106,135)(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)
(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(222,223)(224,238)
(225,237)(226,236)(227,235)(228,234)(229,233)(230,232)(239,427)(240,426)
(241,442)(242,441)(243,440)(244,439)(245,438)(246,437)(247,436)(248,435)
(249,434)(250,433)(251,432)(252,431)(253,430)(254,429)(255,428)(256,410)
(257,409)(258,425)(259,424)(260,423)(261,422)(262,421)(263,420)(264,419)
(265,418)(266,417)(267,416)(268,415)(269,414)(270,413)(271,412)(272,411)
(273,393)(274,392)(275,408)(276,407)(277,406)(278,405)(279,404)(280,403)
(281,402)(282,401)(283,400)(284,399)(285,398)(286,397)(287,396)(288,395)
(289,394)(290,376)(291,375)(292,391)(293,390)(294,389)(295,388)(296,387)
(297,386)(298,385)(299,384)(300,383)(301,382)(302,381)(303,380)(304,379)
(305,378)(306,377)(307,359)(308,358)(309,374)(310,373)(311,372)(312,371)
(313,370)(314,369)(315,368)(316,367)(317,366)(318,365)(319,364)(320,363)
(321,362)(322,361)(323,360)(324,342)(325,341)(326,357)(327,356)(328,355)
(329,354)(330,353)(331,352)(332,351)(333,350)(334,349)(335,348)(336,347)
(337,346)(338,345)(339,344)(340,343);;
s2 := ( 1,239)( 2,240)( 3,241)( 4,242)( 5,243)( 6,244)( 7,245)( 8,246)
( 9,247)( 10,248)( 11,249)( 12,250)( 13,251)( 14,252)( 15,253)( 16,254)
( 17,255)( 18,222)( 19,223)( 20,224)( 21,225)( 22,226)( 23,227)( 24,228)
( 25,229)( 26,230)( 27,231)( 28,232)( 29,233)( 30,234)( 31,235)( 32,236)
( 33,237)( 34,238)( 35,426)( 36,427)( 37,428)( 38,429)( 39,430)( 40,431)
( 41,432)( 42,433)( 43,434)( 44,435)( 45,436)( 46,437)( 47,438)( 48,439)
( 49,440)( 50,441)( 51,442)( 52,409)( 53,410)( 54,411)( 55,412)( 56,413)
( 57,414)( 58,415)( 59,416)( 60,417)( 61,418)( 62,419)( 63,420)( 64,421)
( 65,422)( 66,423)( 67,424)( 68,425)( 69,392)( 70,393)( 71,394)( 72,395)
( 73,396)( 74,397)( 75,398)( 76,399)( 77,400)( 78,401)( 79,402)( 80,403)
( 81,404)( 82,405)( 83,406)( 84,407)( 85,408)( 86,375)( 87,376)( 88,377)
( 89,378)( 90,379)( 91,380)( 92,381)( 93,382)( 94,383)( 95,384)( 96,385)
( 97,386)( 98,387)( 99,388)(100,389)(101,390)(102,391)(103,358)(104,359)
(105,360)(106,361)(107,362)(108,363)(109,364)(110,365)(111,366)(112,367)
(113,368)(114,369)(115,370)(116,371)(117,372)(118,373)(119,374)(120,341)
(121,342)(122,343)(123,344)(124,345)(125,346)(126,347)(127,348)(128,349)
(129,350)(130,351)(131,352)(132,353)(133,354)(134,355)(135,356)(136,357)
(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)(144,331)
(145,332)(146,333)(147,334)(148,335)(149,336)(150,337)(151,338)(152,339)
(153,340)(154,307)(155,308)(156,309)(157,310)(158,311)(159,312)(160,313)
(161,314)(162,315)(163,316)(164,317)(165,318)(166,319)(167,320)(168,321)
(169,322)(170,323)(171,290)(172,291)(173,292)(174,293)(175,294)(176,295)
(177,296)(178,297)(179,298)(180,299)(181,300)(182,301)(183,302)(184,303)
(185,304)(186,305)(187,306)(188,273)(189,274)(190,275)(191,276)(192,277)
(193,278)(194,279)(195,280)(196,281)(197,282)(198,283)(199,284)(200,285)
(201,286)(202,287)(203,288)(204,289)(205,256)(206,257)(207,258)(208,259)
(209,260)(210,261)(211,262)(212,263)(213,264)(214,265)(215,266)(216,267)
(217,268)(218,269)(219,270)(220,271)(221,272);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(442)!( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)
( 9, 10)( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)
( 26, 27)( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)
( 43, 44)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)
( 77, 78)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)
( 94, 95)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)
(111,112)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)
(128,129)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)
(145,146)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)
(179,180)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)
(196,197)(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)
(213,214)(223,238)(224,237)(225,236)(226,235)(227,234)(228,233)(229,232)
(230,231)(240,255)(241,254)(242,253)(243,252)(244,251)(245,250)(246,249)
(247,248)(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)
(264,265)(274,289)(275,288)(276,287)(277,286)(278,285)(279,284)(280,283)
(281,282)(291,306)(292,305)(293,304)(294,303)(295,302)(296,301)(297,300)
(298,299)(308,323)(309,322)(310,321)(311,320)(312,319)(313,318)(314,317)
(315,316)(325,340)(326,339)(327,338)(328,337)(329,336)(330,335)(331,334)
(332,333)(342,357)(343,356)(344,355)(345,354)(346,353)(347,352)(348,351)
(349,350)(359,374)(360,373)(361,372)(362,371)(363,370)(364,369)(365,368)
(366,367)(376,391)(377,390)(378,389)(379,388)(380,387)(381,386)(382,385)
(383,384)(393,408)(394,407)(395,406)(396,405)(397,404)(398,403)(399,402)
(400,401)(410,425)(411,424)(412,423)(413,422)(414,421)(415,420)(416,419)
(417,418)(427,442)(428,441)(429,440)(430,439)(431,438)(432,437)(433,436)
(434,435);
s1 := Sym(442)!( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)
( 9, 11)( 18,206)( 19,205)( 20,221)( 21,220)( 22,219)( 23,218)( 24,217)
( 25,216)( 26,215)( 27,214)( 28,213)( 29,212)( 30,211)( 31,210)( 32,209)
( 33,208)( 34,207)( 35,189)( 36,188)( 37,204)( 38,203)( 39,202)( 40,201)
( 41,200)( 42,199)( 43,198)( 44,197)( 45,196)( 46,195)( 47,194)( 48,193)
( 49,192)( 50,191)( 51,190)( 52,172)( 53,171)( 54,187)( 55,186)( 56,185)
( 57,184)( 58,183)( 59,182)( 60,181)( 61,180)( 62,179)( 63,178)( 64,177)
( 65,176)( 66,175)( 67,174)( 68,173)( 69,155)( 70,154)( 71,170)( 72,169)
( 73,168)( 74,167)( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)
( 81,160)( 82,159)( 83,158)( 84,157)( 85,156)( 86,138)( 87,137)( 88,153)
( 89,152)( 90,151)( 91,150)( 92,149)( 93,148)( 94,147)( 95,146)( 96,145)
( 97,144)( 98,143)( 99,142)(100,141)(101,140)(102,139)(103,121)(104,120)
(105,136)(106,135)(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)
(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(222,223)
(224,238)(225,237)(226,236)(227,235)(228,234)(229,233)(230,232)(239,427)
(240,426)(241,442)(242,441)(243,440)(244,439)(245,438)(246,437)(247,436)
(248,435)(249,434)(250,433)(251,432)(252,431)(253,430)(254,429)(255,428)
(256,410)(257,409)(258,425)(259,424)(260,423)(261,422)(262,421)(263,420)
(264,419)(265,418)(266,417)(267,416)(268,415)(269,414)(270,413)(271,412)
(272,411)(273,393)(274,392)(275,408)(276,407)(277,406)(278,405)(279,404)
(280,403)(281,402)(282,401)(283,400)(284,399)(285,398)(286,397)(287,396)
(288,395)(289,394)(290,376)(291,375)(292,391)(293,390)(294,389)(295,388)
(296,387)(297,386)(298,385)(299,384)(300,383)(301,382)(302,381)(303,380)
(304,379)(305,378)(306,377)(307,359)(308,358)(309,374)(310,373)(311,372)
(312,371)(313,370)(314,369)(315,368)(316,367)(317,366)(318,365)(319,364)
(320,363)(321,362)(322,361)(323,360)(324,342)(325,341)(326,357)(327,356)
(328,355)(329,354)(330,353)(331,352)(332,351)(333,350)(334,349)(335,348)
(336,347)(337,346)(338,345)(339,344)(340,343);
s2 := Sym(442)!( 1,239)( 2,240)( 3,241)( 4,242)( 5,243)( 6,244)( 7,245)
( 8,246)( 9,247)( 10,248)( 11,249)( 12,250)( 13,251)( 14,252)( 15,253)
( 16,254)( 17,255)( 18,222)( 19,223)( 20,224)( 21,225)( 22,226)( 23,227)
( 24,228)( 25,229)( 26,230)( 27,231)( 28,232)( 29,233)( 30,234)( 31,235)
( 32,236)( 33,237)( 34,238)( 35,426)( 36,427)( 37,428)( 38,429)( 39,430)
( 40,431)( 41,432)( 42,433)( 43,434)( 44,435)( 45,436)( 46,437)( 47,438)
( 48,439)( 49,440)( 50,441)( 51,442)( 52,409)( 53,410)( 54,411)( 55,412)
( 56,413)( 57,414)( 58,415)( 59,416)( 60,417)( 61,418)( 62,419)( 63,420)
( 64,421)( 65,422)( 66,423)( 67,424)( 68,425)( 69,392)( 70,393)( 71,394)
( 72,395)( 73,396)( 74,397)( 75,398)( 76,399)( 77,400)( 78,401)( 79,402)
( 80,403)( 81,404)( 82,405)( 83,406)( 84,407)( 85,408)( 86,375)( 87,376)
( 88,377)( 89,378)( 90,379)( 91,380)( 92,381)( 93,382)( 94,383)( 95,384)
( 96,385)( 97,386)( 98,387)( 99,388)(100,389)(101,390)(102,391)(103,358)
(104,359)(105,360)(106,361)(107,362)(108,363)(109,364)(110,365)(111,366)
(112,367)(113,368)(114,369)(115,370)(116,371)(117,372)(118,373)(119,374)
(120,341)(121,342)(122,343)(123,344)(124,345)(125,346)(126,347)(127,348)
(128,349)(129,350)(130,351)(131,352)(132,353)(133,354)(134,355)(135,356)
(136,357)(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)
(144,331)(145,332)(146,333)(147,334)(148,335)(149,336)(150,337)(151,338)
(152,339)(153,340)(154,307)(155,308)(156,309)(157,310)(158,311)(159,312)
(160,313)(161,314)(162,315)(163,316)(164,317)(165,318)(166,319)(167,320)
(168,321)(169,322)(170,323)(171,290)(172,291)(173,292)(174,293)(175,294)
(176,295)(177,296)(178,297)(179,298)(180,299)(181,300)(182,301)(183,302)
(184,303)(185,304)(186,305)(187,306)(188,273)(189,274)(190,275)(191,276)
(192,277)(193,278)(194,279)(195,280)(196,281)(197,282)(198,283)(199,284)
(200,285)(201,286)(202,287)(203,288)(204,289)(205,256)(206,257)(207,258)
(208,259)(209,260)(210,261)(211,262)(212,263)(213,264)(214,265)(215,266)
(216,267)(217,268)(218,269)(219,270)(220,271)(221,272);
poly := sub<Sym(442)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope