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