Polytope of Type {28,34}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,34}*1904
Also Known As : {28,34|2}. if this polytope has another name.
Group : SmallGroup(1904,122)
Rank : 3
Schlafli Type : {28,34}
Number of vertices, edges, etc : 28, 476, 34
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 : {14,34}*952
7-fold quotients : {4,34}*272
14-fold quotients : {2,34}*136
17-fold quotients : {28,2}*112
28-fold quotients : {2,17}*68
34-fold quotients : {14,2}*56
68-fold quotients : {7,2}*28
119-fold quotients : {4,2}*16
238-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 18,103)( 19,104)( 20,105)( 21,106)( 22,107)( 23,108)( 24,109)( 25,110)
( 26,111)( 27,112)( 28,113)( 29,114)( 30,115)( 31,116)( 32,117)( 33,118)
( 34,119)( 35, 86)( 36, 87)( 37, 88)( 38, 89)( 39, 90)( 40, 91)( 41, 92)
( 42, 93)( 43, 94)( 44, 95)( 45, 96)( 46, 97)( 47, 98)( 48, 99)( 49,100)
( 50,101)( 51,102)( 52, 69)( 53, 70)( 54, 71)( 55, 72)( 56, 73)( 57, 74)
( 58, 75)( 59, 76)( 60, 77)( 61, 78)( 62, 79)( 63, 80)( 64, 81)( 65, 82)
( 66, 83)( 67, 84)( 68, 85)(137,222)(138,223)(139,224)(140,225)(141,226)
(142,227)(143,228)(144,229)(145,230)(146,231)(147,232)(148,233)(149,234)
(150,235)(151,236)(152,237)(153,238)(154,205)(155,206)(156,207)(157,208)
(158,209)(159,210)(160,211)(161,212)(162,213)(163,214)(164,215)(165,216)
(166,217)(167,218)(168,219)(169,220)(170,221)(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)(239,358)(240,359)
(241,360)(242,361)(243,362)(244,363)(245,364)(246,365)(247,366)(248,367)
(249,368)(250,369)(251,370)(252,371)(253,372)(254,373)(255,374)(256,460)
(257,461)(258,462)(259,463)(260,464)(261,465)(262,466)(263,467)(264,468)
(265,469)(266,470)(267,471)(268,472)(269,473)(270,474)(271,475)(272,476)
(273,443)(274,444)(275,445)(276,446)(277,447)(278,448)(279,449)(280,450)
(281,451)(282,452)(283,453)(284,454)(285,455)(286,456)(287,457)(288,458)
(289,459)(290,426)(291,427)(292,428)(293,429)(294,430)(295,431)(296,432)
(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)(304,440)
(305,441)(306,442)(307,409)(308,410)(309,411)(310,412)(311,413)(312,414)
(313,415)(314,416)(315,417)(316,418)(317,419)(318,420)(319,421)(320,422)
(321,423)(322,424)(323,425)(324,392)(325,393)(326,394)(327,395)(328,396)
(329,397)(330,398)(331,399)(332,400)(333,401)(334,402)(335,403)(336,404)
(337,405)(338,406)(339,407)(340,408)(341,375)(342,376)(343,377)(344,378)
(345,379)(346,380)(347,381)(348,382)(349,383)(350,384)(351,385)(352,386)
(353,387)(354,388)(355,389)(356,390)(357,391);;
s1 := ( 1,256)( 2,272)( 3,271)( 4,270)( 5,269)( 6,268)( 7,267)( 8,266)
( 9,265)( 10,264)( 11,263)( 12,262)( 13,261)( 14,260)( 15,259)( 16,258)
( 17,257)( 18,239)( 19,255)( 20,254)( 21,253)( 22,252)( 23,251)( 24,250)
( 25,249)( 26,248)( 27,247)( 28,246)( 29,245)( 30,244)( 31,243)( 32,242)
( 33,241)( 34,240)( 35,341)( 36,357)( 37,356)( 38,355)( 39,354)( 40,353)
( 41,352)( 42,351)( 43,350)( 44,349)( 45,348)( 46,347)( 47,346)( 48,345)
( 49,344)( 50,343)( 51,342)( 52,324)( 53,340)( 54,339)( 55,338)( 56,337)
( 57,336)( 58,335)( 59,334)( 60,333)( 61,332)( 62,331)( 63,330)( 64,329)
( 65,328)( 66,327)( 67,326)( 68,325)( 69,307)( 70,323)( 71,322)( 72,321)
( 73,320)( 74,319)( 75,318)( 76,317)( 77,316)( 78,315)( 79,314)( 80,313)
( 81,312)( 82,311)( 83,310)( 84,309)( 85,308)( 86,290)( 87,306)( 88,305)
( 89,304)( 90,303)( 91,302)( 92,301)( 93,300)( 94,299)( 95,298)( 96,297)
( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,273)(104,289)
(105,288)(106,287)(107,286)(108,285)(109,284)(110,283)(111,282)(112,281)
(113,280)(114,279)(115,278)(116,277)(117,276)(118,275)(119,274)(120,375)
(121,391)(122,390)(123,389)(124,388)(125,387)(126,386)(127,385)(128,384)
(129,383)(130,382)(131,381)(132,380)(133,379)(134,378)(135,377)(136,376)
(137,358)(138,374)(139,373)(140,372)(141,371)(142,370)(143,369)(144,368)
(145,367)(146,366)(147,365)(148,364)(149,363)(150,362)(151,361)(152,360)
(153,359)(154,460)(155,476)(156,475)(157,474)(158,473)(159,472)(160,471)
(161,470)(162,469)(163,468)(164,467)(165,466)(166,465)(167,464)(168,463)
(169,462)(170,461)(171,443)(172,459)(173,458)(174,457)(175,456)(176,455)
(177,454)(178,453)(179,452)(180,451)(181,450)(182,449)(183,448)(184,447)
(185,446)(186,445)(187,444)(188,426)(189,442)(190,441)(191,440)(192,439)
(193,438)(194,437)(195,436)(196,435)(197,434)(198,433)(199,432)(200,431)
(201,430)(202,429)(203,428)(204,427)(205,409)(206,425)(207,424)(208,423)
(209,422)(210,421)(211,420)(212,419)(213,418)(214,417)(215,416)(216,415)
(217,414)(218,413)(219,412)(220,411)(221,410)(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);;
s2 := ( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)
( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)
( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)
( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)
( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)
(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)(111,113)
(120,121)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130)
(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)
(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)
(171,172)(173,187)(174,186)(175,185)(176,184)(177,183)(178,182)(179,181)
(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)
(205,206)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)(213,215)
(222,223)(224,238)(225,237)(226,236)(227,235)(228,234)(229,233)(230,232)
(239,240)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)
(256,257)(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)(264,266)
(273,274)(275,289)(276,288)(277,287)(278,286)(279,285)(280,284)(281,283)
(290,291)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)(298,300)
(307,308)(309,323)(310,322)(311,321)(312,320)(313,319)(314,318)(315,317)
(324,325)(326,340)(327,339)(328,338)(329,337)(330,336)(331,335)(332,334)
(341,342)(343,357)(344,356)(345,355)(346,354)(347,353)(348,352)(349,351)
(358,359)(360,374)(361,373)(362,372)(363,371)(364,370)(365,369)(366,368)
(375,376)(377,391)(378,390)(379,389)(380,388)(381,387)(382,386)(383,385)
(392,393)(394,408)(395,407)(396,406)(397,405)(398,404)(399,403)(400,402)
(409,410)(411,425)(412,424)(413,423)(414,422)(415,421)(416,420)(417,419)
(426,427)(428,442)(429,441)(430,440)(431,439)(432,438)(433,437)(434,436)
(443,444)(445,459)(446,458)(447,457)(448,456)(449,455)(450,454)(451,453)
(460,461)(462,476)(463,475)(464,474)(465,473)(466,472)(467,471)(468,470);;
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*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(476)!( 18,103)( 19,104)( 20,105)( 21,106)( 22,107)( 23,108)( 24,109)
( 25,110)( 26,111)( 27,112)( 28,113)( 29,114)( 30,115)( 31,116)( 32,117)
( 33,118)( 34,119)( 35, 86)( 36, 87)( 37, 88)( 38, 89)( 39, 90)( 40, 91)
( 41, 92)( 42, 93)( 43, 94)( 44, 95)( 45, 96)( 46, 97)( 47, 98)( 48, 99)
( 49,100)( 50,101)( 51,102)( 52, 69)( 53, 70)( 54, 71)( 55, 72)( 56, 73)
( 57, 74)( 58, 75)( 59, 76)( 60, 77)( 61, 78)( 62, 79)( 63, 80)( 64, 81)
( 65, 82)( 66, 83)( 67, 84)( 68, 85)(137,222)(138,223)(139,224)(140,225)
(141,226)(142,227)(143,228)(144,229)(145,230)(146,231)(147,232)(148,233)
(149,234)(150,235)(151,236)(152,237)(153,238)(154,205)(155,206)(156,207)
(157,208)(158,209)(159,210)(160,211)(161,212)(162,213)(163,214)(164,215)
(165,216)(166,217)(167,218)(168,219)(169,220)(170,221)(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)(239,358)
(240,359)(241,360)(242,361)(243,362)(244,363)(245,364)(246,365)(247,366)
(248,367)(249,368)(250,369)(251,370)(252,371)(253,372)(254,373)(255,374)
(256,460)(257,461)(258,462)(259,463)(260,464)(261,465)(262,466)(263,467)
(264,468)(265,469)(266,470)(267,471)(268,472)(269,473)(270,474)(271,475)
(272,476)(273,443)(274,444)(275,445)(276,446)(277,447)(278,448)(279,449)
(280,450)(281,451)(282,452)(283,453)(284,454)(285,455)(286,456)(287,457)
(288,458)(289,459)(290,426)(291,427)(292,428)(293,429)(294,430)(295,431)
(296,432)(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)
(304,440)(305,441)(306,442)(307,409)(308,410)(309,411)(310,412)(311,413)
(312,414)(313,415)(314,416)(315,417)(316,418)(317,419)(318,420)(319,421)
(320,422)(321,423)(322,424)(323,425)(324,392)(325,393)(326,394)(327,395)
(328,396)(329,397)(330,398)(331,399)(332,400)(333,401)(334,402)(335,403)
(336,404)(337,405)(338,406)(339,407)(340,408)(341,375)(342,376)(343,377)
(344,378)(345,379)(346,380)(347,381)(348,382)(349,383)(350,384)(351,385)
(352,386)(353,387)(354,388)(355,389)(356,390)(357,391);
s1 := Sym(476)!( 1,256)( 2,272)( 3,271)( 4,270)( 5,269)( 6,268)( 7,267)
( 8,266)( 9,265)( 10,264)( 11,263)( 12,262)( 13,261)( 14,260)( 15,259)
( 16,258)( 17,257)( 18,239)( 19,255)( 20,254)( 21,253)( 22,252)( 23,251)
( 24,250)( 25,249)( 26,248)( 27,247)( 28,246)( 29,245)( 30,244)( 31,243)
( 32,242)( 33,241)( 34,240)( 35,341)( 36,357)( 37,356)( 38,355)( 39,354)
( 40,353)( 41,352)( 42,351)( 43,350)( 44,349)( 45,348)( 46,347)( 47,346)
( 48,345)( 49,344)( 50,343)( 51,342)( 52,324)( 53,340)( 54,339)( 55,338)
( 56,337)( 57,336)( 58,335)( 59,334)( 60,333)( 61,332)( 62,331)( 63,330)
( 64,329)( 65,328)( 66,327)( 67,326)( 68,325)( 69,307)( 70,323)( 71,322)
( 72,321)( 73,320)( 74,319)( 75,318)( 76,317)( 77,316)( 78,315)( 79,314)
( 80,313)( 81,312)( 82,311)( 83,310)( 84,309)( 85,308)( 86,290)( 87,306)
( 88,305)( 89,304)( 90,303)( 91,302)( 92,301)( 93,300)( 94,299)( 95,298)
( 96,297)( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,273)
(104,289)(105,288)(106,287)(107,286)(108,285)(109,284)(110,283)(111,282)
(112,281)(113,280)(114,279)(115,278)(116,277)(117,276)(118,275)(119,274)
(120,375)(121,391)(122,390)(123,389)(124,388)(125,387)(126,386)(127,385)
(128,384)(129,383)(130,382)(131,381)(132,380)(133,379)(134,378)(135,377)
(136,376)(137,358)(138,374)(139,373)(140,372)(141,371)(142,370)(143,369)
(144,368)(145,367)(146,366)(147,365)(148,364)(149,363)(150,362)(151,361)
(152,360)(153,359)(154,460)(155,476)(156,475)(157,474)(158,473)(159,472)
(160,471)(161,470)(162,469)(163,468)(164,467)(165,466)(166,465)(167,464)
(168,463)(169,462)(170,461)(171,443)(172,459)(173,458)(174,457)(175,456)
(176,455)(177,454)(178,453)(179,452)(180,451)(181,450)(182,449)(183,448)
(184,447)(185,446)(186,445)(187,444)(188,426)(189,442)(190,441)(191,440)
(192,439)(193,438)(194,437)(195,436)(196,435)(197,434)(198,433)(199,432)
(200,431)(201,430)(202,429)(203,428)(204,427)(205,409)(206,425)(207,424)
(208,423)(209,422)(210,421)(211,420)(212,419)(213,418)(214,417)(215,416)
(216,415)(217,414)(218,413)(219,412)(220,411)(221,410)(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);
s2 := Sym(476)!( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)
( 9, 11)( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)
( 26, 28)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 45)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)
( 60, 62)( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)
( 94, 96)(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)
(111,113)(120,121)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)
(128,130)(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)
(145,147)(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)
(162,164)(171,172)(173,187)(174,186)(175,185)(176,184)(177,183)(178,182)
(179,181)(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)
(196,198)(205,206)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)
(213,215)(222,223)(224,238)(225,237)(226,236)(227,235)(228,234)(229,233)
(230,232)(239,240)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)
(247,249)(256,257)(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)
(264,266)(273,274)(275,289)(276,288)(277,287)(278,286)(279,285)(280,284)
(281,283)(290,291)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)
(298,300)(307,308)(309,323)(310,322)(311,321)(312,320)(313,319)(314,318)
(315,317)(324,325)(326,340)(327,339)(328,338)(329,337)(330,336)(331,335)
(332,334)(341,342)(343,357)(344,356)(345,355)(346,354)(347,353)(348,352)
(349,351)(358,359)(360,374)(361,373)(362,372)(363,371)(364,370)(365,369)
(366,368)(375,376)(377,391)(378,390)(379,389)(380,388)(381,387)(382,386)
(383,385)(392,393)(394,408)(395,407)(396,406)(397,405)(398,404)(399,403)
(400,402)(409,410)(411,425)(412,424)(413,423)(414,422)(415,421)(416,420)
(417,419)(426,427)(428,442)(429,441)(430,440)(431,439)(432,438)(433,437)
(434,436)(443,444)(445,459)(446,458)(447,457)(448,456)(449,455)(450,454)
(451,453)(460,461)(462,476)(463,475)(464,474)(465,473)(466,472)(467,471)
(468,470);
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,
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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