Polytope of Type {34,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,28}*1904
Also Known As : {34,28|2}. if this polytope has another name.
Group : SmallGroup(1904,122)
Rank : 3
Schlafli Type : {34,28}
Number of vertices, edges, etc : 34, 476, 28
Order of s₀s₁s₂ : 476
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 : {34,14}*952
   7-fold quotients : {34,4}*272
   14-fold quotients : {34,2}*136
   17-fold quotients : {2,28}*112
   28-fold quotients : {17,2}*68
   34-fold quotients : {2,14}*56
   68-fold quotients : {2,7}*28
   119-fold quotients : {2,4}*16
   238-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)
(444,459)(445,458)(446,457)(447,456)(448,455)(449,454)(450,453)(451,452)
(461,476)(462,475)(463,474)(464,473)(465,472)(466,471)(467,470)(468,469);;
s1 := (  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)
( 18,104)( 19,103)( 20,119)( 21,118)( 22,117)( 23,116)( 24,115)( 25,114)
( 26,113)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)( 33,106)
( 34,105)( 35, 87)( 36, 86)( 37,102)( 38,101)( 39,100)( 40, 99)( 41, 98)
( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)( 49, 90)
( 50, 89)( 51, 88)( 52, 70)( 53, 69)( 54, 85)( 55, 84)( 56, 83)( 57, 82)
( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)
( 66, 73)( 67, 72)( 68, 71)(120,121)(122,136)(123,135)(124,134)(125,133)
(126,132)(127,131)(128,130)(137,223)(138,222)(139,238)(140,237)(141,236)
(142,235)(143,234)(144,233)(145,232)(146,231)(147,230)(148,229)(149,228)
(150,227)(151,226)(152,225)(153,224)(154,206)(155,205)(156,221)(157,220)
(158,219)(159,218)(160,217)(161,216)(162,215)(163,214)(164,213)(165,212)
(166,211)(167,210)(168,209)(169,208)(170,207)(171,189)(172,188)(173,204)
(174,203)(175,202)(176,201)(177,200)(178,199)(179,198)(180,197)(181,196)
(182,195)(183,194)(184,193)(185,192)(186,191)(187,190)(239,359)(240,358)
(241,374)(242,373)(243,372)(244,371)(245,370)(246,369)(247,368)(248,367)
(249,366)(250,365)(251,364)(252,363)(253,362)(254,361)(255,360)(256,461)
(257,460)(258,476)(259,475)(260,474)(261,473)(262,472)(263,471)(264,470)
(265,469)(266,468)(267,467)(268,466)(269,465)(270,464)(271,463)(272,462)
(273,444)(274,443)(275,459)(276,458)(277,457)(278,456)(279,455)(280,454)
(281,453)(282,452)(283,451)(284,450)(285,449)(286,448)(287,447)(288,446)
(289,445)(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)(307,410)(308,409)(309,425)(310,424)(311,423)(312,422)
(313,421)(314,420)(315,419)(316,418)(317,417)(318,416)(319,415)(320,414)
(321,413)(322,412)(323,411)(324,393)(325,392)(326,408)(327,407)(328,406)
(329,405)(330,404)(331,403)(332,402)(333,401)(334,400)(335,399)(336,398)
(337,397)(338,396)(339,395)(340,394)(341,376)(342,375)(343,391)(344,390)
(345,389)(346,388)(347,387)(348,386)(349,385)(350,384)(351,383)(352,382)
(353,381)(354,380)(355,379)(356,378)(357,377);;
s2 := (  1,256)(  2,257)(  3,258)(  4,259)(  5,260)(  6,261)(  7,262)(  8,263)
(  9,264)( 10,265)( 11,266)( 12,267)( 13,268)( 14,269)( 15,270)( 16,271)
( 17,272)( 18,239)( 19,240)( 20,241)( 21,242)( 22,243)( 23,244)( 24,245)
( 25,246)( 26,247)( 27,248)( 28,249)( 29,250)( 30,251)( 31,252)( 32,253)
( 33,254)( 34,255)( 35,341)( 36,342)( 37,343)( 38,344)( 39,345)( 40,346)
( 41,347)( 42,348)( 43,349)( 44,350)( 45,351)( 46,352)( 47,353)( 48,354)
( 49,355)( 50,356)( 51,357)( 52,324)( 53,325)( 54,326)( 55,327)( 56,328)
( 57,329)( 58,330)( 59,331)( 60,332)( 61,333)( 62,334)( 63,335)( 64,336)
( 65,337)( 66,338)( 67,339)( 68,340)( 69,307)( 70,308)( 71,309)( 72,310)
( 73,311)( 74,312)( 75,313)( 76,314)( 77,315)( 78,316)( 79,317)( 80,318)
( 81,319)( 82,320)( 83,321)( 84,322)( 85,323)( 86,290)( 87,291)( 88,292)
( 89,293)( 90,294)( 91,295)( 92,296)( 93,297)( 94,298)( 95,299)( 96,300)
( 97,301)( 98,302)( 99,303)(100,304)(101,305)(102,306)(103,273)(104,274)
(105,275)(106,276)(107,277)(108,278)(109,279)(110,280)(111,281)(112,282)
(113,283)(114,284)(115,285)(116,286)(117,287)(118,288)(119,289)(120,375)
(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)(128,383)
(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)(136,391)
(137,358)(138,359)(139,360)(140,361)(141,362)(142,363)(143,364)(144,365)
(145,366)(146,367)(147,368)(148,369)(149,370)(150,371)(151,372)(152,373)
(153,374)(154,460)(155,461)(156,462)(157,463)(158,464)(159,465)(160,466)
(161,467)(162,468)(163,469)(164,470)(165,471)(166,472)(167,473)(168,474)
(169,475)(170,476)(171,443)(172,444)(173,445)(174,446)(175,447)(176,448)
(177,449)(178,450)(179,451)(180,452)(181,453)(182,454)(183,455)(184,456)
(185,457)(186,458)(187,459)(188,426)(189,427)(190,428)(191,429)(192,430)
(193,431)(194,432)(195,433)(196,434)(197,435)(198,436)(199,437)(200,438)
(201,439)(202,440)(203,441)(204,442)(205,409)(206,410)(207,411)(208,412)
(209,413)(210,414)(211,415)(212,416)(213,417)(214,418)(215,419)(216,420)
(217,421)(218,422)(219,423)(220,424)(221,425)(222,392)(223,393)(224,394)
(225,395)(226,396)(227,397)(228,398)(229,399)(230,400)(231,401)(232,402)
(233,403)(234,404)(235,405)(236,406)(237,407)(238,408);;
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*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(476)!(  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)(444,459)(445,458)(446,457)(447,456)(448,455)(449,454)(450,453)
(451,452)(461,476)(462,475)(463,474)(464,473)(465,472)(466,471)(467,470)
(468,469);
s1 := Sym(476)!(  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)
(  9, 11)( 18,104)( 19,103)( 20,119)( 21,118)( 22,117)( 23,116)( 24,115)
( 25,114)( 26,113)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)
( 33,106)( 34,105)( 35, 87)( 36, 86)( 37,102)( 38,101)( 39,100)( 40, 99)
( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)
( 49, 90)( 50, 89)( 51, 88)( 52, 70)( 53, 69)( 54, 85)( 55, 84)( 56, 83)
( 57, 82)( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 73)( 67, 72)( 68, 71)(120,121)(122,136)(123,135)(124,134)
(125,133)(126,132)(127,131)(128,130)(137,223)(138,222)(139,238)(140,237)
(141,236)(142,235)(143,234)(144,233)(145,232)(146,231)(147,230)(148,229)
(149,228)(150,227)(151,226)(152,225)(153,224)(154,206)(155,205)(156,221)
(157,220)(158,219)(159,218)(160,217)(161,216)(162,215)(163,214)(164,213)
(165,212)(166,211)(167,210)(168,209)(169,208)(170,207)(171,189)(172,188)
(173,204)(174,203)(175,202)(176,201)(177,200)(178,199)(179,198)(180,197)
(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190)(239,359)
(240,358)(241,374)(242,373)(243,372)(244,371)(245,370)(246,369)(247,368)
(248,367)(249,366)(250,365)(251,364)(252,363)(253,362)(254,361)(255,360)
(256,461)(257,460)(258,476)(259,475)(260,474)(261,473)(262,472)(263,471)
(264,470)(265,469)(266,468)(267,467)(268,466)(269,465)(270,464)(271,463)
(272,462)(273,444)(274,443)(275,459)(276,458)(277,457)(278,456)(279,455)
(280,454)(281,453)(282,452)(283,451)(284,450)(285,449)(286,448)(287,447)
(288,446)(289,445)(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)(307,410)(308,409)(309,425)(310,424)(311,423)
(312,422)(313,421)(314,420)(315,419)(316,418)(317,417)(318,416)(319,415)
(320,414)(321,413)(322,412)(323,411)(324,393)(325,392)(326,408)(327,407)
(328,406)(329,405)(330,404)(331,403)(332,402)(333,401)(334,400)(335,399)
(336,398)(337,397)(338,396)(339,395)(340,394)(341,376)(342,375)(343,391)
(344,390)(345,389)(346,388)(347,387)(348,386)(349,385)(350,384)(351,383)
(352,382)(353,381)(354,380)(355,379)(356,378)(357,377);
s2 := Sym(476)!(  1,256)(  2,257)(  3,258)(  4,259)(  5,260)(  6,261)(  7,262)
(  8,263)(  9,264)( 10,265)( 11,266)( 12,267)( 13,268)( 14,269)( 15,270)
( 16,271)( 17,272)( 18,239)( 19,240)( 20,241)( 21,242)( 22,243)( 23,244)
( 24,245)( 25,246)( 26,247)( 27,248)( 28,249)( 29,250)( 30,251)( 31,252)
( 32,253)( 33,254)( 34,255)( 35,341)( 36,342)( 37,343)( 38,344)( 39,345)
( 40,346)( 41,347)( 42,348)( 43,349)( 44,350)( 45,351)( 46,352)( 47,353)
( 48,354)( 49,355)( 50,356)( 51,357)( 52,324)( 53,325)( 54,326)( 55,327)
( 56,328)( 57,329)( 58,330)( 59,331)( 60,332)( 61,333)( 62,334)( 63,335)
( 64,336)( 65,337)( 66,338)( 67,339)( 68,340)( 69,307)( 70,308)( 71,309)
( 72,310)( 73,311)( 74,312)( 75,313)( 76,314)( 77,315)( 78,316)( 79,317)
( 80,318)( 81,319)( 82,320)( 83,321)( 84,322)( 85,323)( 86,290)( 87,291)
( 88,292)( 89,293)( 90,294)( 91,295)( 92,296)( 93,297)( 94,298)( 95,299)
( 96,300)( 97,301)( 98,302)( 99,303)(100,304)(101,305)(102,306)(103,273)
(104,274)(105,275)(106,276)(107,277)(108,278)(109,279)(110,280)(111,281)
(112,282)(113,283)(114,284)(115,285)(116,286)(117,287)(118,288)(119,289)
(120,375)(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)
(128,383)(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)
(136,391)(137,358)(138,359)(139,360)(140,361)(141,362)(142,363)(143,364)
(144,365)(145,366)(146,367)(147,368)(148,369)(149,370)(150,371)(151,372)
(152,373)(153,374)(154,460)(155,461)(156,462)(157,463)(158,464)(159,465)
(160,466)(161,467)(162,468)(163,469)(164,470)(165,471)(166,472)(167,473)
(168,474)(169,475)(170,476)(171,443)(172,444)(173,445)(174,446)(175,447)
(176,448)(177,449)(178,450)(179,451)(180,452)(181,453)(182,454)(183,455)
(184,456)(185,457)(186,458)(187,459)(188,426)(189,427)(190,428)(191,429)
(192,430)(193,431)(194,432)(195,433)(196,434)(197,435)(198,436)(199,437)
(200,438)(201,439)(202,440)(203,441)(204,442)(205,409)(206,410)(207,411)
(208,412)(209,413)(210,414)(211,415)(212,416)(213,417)(214,418)(215,419)
(216,420)(217,421)(218,422)(219,423)(220,424)(221,425)(222,392)(223,393)
(224,394)(225,395)(226,396)(227,397)(228,398)(229,399)(230,400)(231,401)
(232,402)(233,403)(234,404)(235,405)(236,406)(237,407)(238,408);
poly := sub<Sym(476)|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*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