Polytope of Type {2,4,117}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,117}*1872
if this polytope has a name.
Group : SmallGroup(1872,542)
Rank : 4
Schlafli Type : {2,4,117}
Number of vertices, edges, etc : 2, 4, 234, 117
Order of s0s1s2s3 : 234
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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) :
3-fold quotients : {2,4,39}*624
13-fold quotients : {2,4,9}*144
39-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)
( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)
( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)
(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)
(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)
(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)
(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)(176,178)
(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194)
(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)(208,210)
(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)(224,226)
(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)(240,242)
(243,245)(244,246)(247,249)(248,250)(251,253)(252,254)(255,257)(256,258)
(259,261)(260,262)(263,265)(264,266)(267,269)(268,270)(271,273)(272,274)
(275,277)(276,278)(279,281)(280,282)(283,285)(284,286)(287,289)(288,290)
(291,293)(292,294)(295,297)(296,298)(299,301)(300,302)(303,305)(304,306)
(307,309)(308,310)(311,313)(312,314)(315,317)(316,318)(319,321)(320,322)
(323,325)(324,326)(327,329)(328,330)(331,333)(332,334)(335,337)(336,338)
(339,341)(340,342)(343,345)(344,346)(347,349)(348,350)(351,353)(352,354)
(355,357)(356,358)(359,361)(360,362)(363,365)(364,366)(367,369)(368,370)
(371,373)(372,374)(375,377)(376,378)(379,381)(380,382)(383,385)(384,386)
(387,389)(388,390)(391,393)(392,394)(395,397)(396,398)(399,401)(400,402)
(403,405)(404,406)(407,409)(408,410)(411,413)(412,414)(415,417)(416,418)
(419,421)(420,422)(423,425)(424,426)(427,429)(428,430)(431,433)(432,434)
(435,437)(436,438)(439,441)(440,442)(443,445)(444,446)(447,449)(448,450)
(451,453)(452,454)(455,457)(456,458)(459,461)(460,462)(463,465)(464,466)
(467,469)(468,470);;
s2 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15,147)( 16,149)( 17,148)
( 18,150)( 19,155)( 20,157)( 21,156)( 22,158)( 23,151)( 24,153)( 25,152)
( 26,154)( 27,135)( 28,137)( 29,136)( 30,138)( 31,143)( 32,145)( 33,144)
( 34,146)( 35,139)( 36,141)( 37,140)( 38,142)( 39,123)( 40,125)( 41,124)
( 42,126)( 43,131)( 44,133)( 45,132)( 46,134)( 47,127)( 48,129)( 49,128)
( 50,130)( 51,111)( 52,113)( 53,112)( 54,114)( 55,119)( 56,121)( 57,120)
( 58,122)( 59,115)( 60,117)( 61,116)( 62,118)( 63, 99)( 64,101)( 65,100)
( 66,102)( 67,107)( 68,109)( 69,108)( 70,110)( 71,103)( 72,105)( 73,104)
( 74,106)( 75, 87)( 76, 89)( 77, 88)( 78, 90)( 79, 95)( 80, 97)( 81, 96)
( 82, 98)( 83, 91)( 84, 93)( 85, 92)( 86, 94)(159,319)(160,321)(161,320)
(162,322)(163,315)(164,317)(165,316)(166,318)(167,323)(168,325)(169,324)
(170,326)(171,463)(172,465)(173,464)(174,466)(175,459)(176,461)(177,460)
(178,462)(179,467)(180,469)(181,468)(182,470)(183,451)(184,453)(185,452)
(186,454)(187,447)(188,449)(189,448)(190,450)(191,455)(192,457)(193,456)
(194,458)(195,439)(196,441)(197,440)(198,442)(199,435)(200,437)(201,436)
(202,438)(203,443)(204,445)(205,444)(206,446)(207,427)(208,429)(209,428)
(210,430)(211,423)(212,425)(213,424)(214,426)(215,431)(216,433)(217,432)
(218,434)(219,415)(220,417)(221,416)(222,418)(223,411)(224,413)(225,412)
(226,414)(227,419)(228,421)(229,420)(230,422)(231,403)(232,405)(233,404)
(234,406)(235,399)(236,401)(237,400)(238,402)(239,407)(240,409)(241,408)
(242,410)(243,391)(244,393)(245,392)(246,394)(247,387)(248,389)(249,388)
(250,390)(251,395)(252,397)(253,396)(254,398)(255,379)(256,381)(257,380)
(258,382)(259,375)(260,377)(261,376)(262,378)(263,383)(264,385)(265,384)
(266,386)(267,367)(268,369)(269,368)(270,370)(271,363)(272,365)(273,364)
(274,366)(275,371)(276,373)(277,372)(278,374)(279,355)(280,357)(281,356)
(282,358)(283,351)(284,353)(285,352)(286,354)(287,359)(288,361)(289,360)
(290,362)(291,343)(292,345)(293,344)(294,346)(295,339)(296,341)(297,340)
(298,342)(299,347)(300,349)(301,348)(302,350)(303,331)(304,333)(305,332)
(306,334)(307,327)(308,329)(309,328)(310,330)(311,335)(312,337)(313,336)
(314,338);;
s3 := ( 3,327)( 4,330)( 5,329)( 6,328)( 7,335)( 8,338)( 9,337)( 10,336)
( 11,331)( 12,334)( 13,333)( 14,332)( 15,315)( 16,318)( 17,317)( 18,316)
( 19,323)( 20,326)( 21,325)( 22,324)( 23,319)( 24,322)( 25,321)( 26,320)
( 27,459)( 28,462)( 29,461)( 30,460)( 31,467)( 32,470)( 33,469)( 34,468)
( 35,463)( 36,466)( 37,465)( 38,464)( 39,447)( 40,450)( 41,449)( 42,448)
( 43,455)( 44,458)( 45,457)( 46,456)( 47,451)( 48,454)( 49,453)( 50,452)
( 51,435)( 52,438)( 53,437)( 54,436)( 55,443)( 56,446)( 57,445)( 58,444)
( 59,439)( 60,442)( 61,441)( 62,440)( 63,423)( 64,426)( 65,425)( 66,424)
( 67,431)( 68,434)( 69,433)( 70,432)( 71,427)( 72,430)( 73,429)( 74,428)
( 75,411)( 76,414)( 77,413)( 78,412)( 79,419)( 80,422)( 81,421)( 82,420)
( 83,415)( 84,418)( 85,417)( 86,416)( 87,399)( 88,402)( 89,401)( 90,400)
( 91,407)( 92,410)( 93,409)( 94,408)( 95,403)( 96,406)( 97,405)( 98,404)
( 99,387)(100,390)(101,389)(102,388)(103,395)(104,398)(105,397)(106,396)
(107,391)(108,394)(109,393)(110,392)(111,375)(112,378)(113,377)(114,376)
(115,383)(116,386)(117,385)(118,384)(119,379)(120,382)(121,381)(122,380)
(123,363)(124,366)(125,365)(126,364)(127,371)(128,374)(129,373)(130,372)
(131,367)(132,370)(133,369)(134,368)(135,351)(136,354)(137,353)(138,352)
(139,359)(140,362)(141,361)(142,360)(143,355)(144,358)(145,357)(146,356)
(147,339)(148,342)(149,341)(150,340)(151,347)(152,350)(153,349)(154,348)
(155,343)(156,346)(157,345)(158,344)(159,171)(160,174)(161,173)(162,172)
(163,179)(164,182)(165,181)(166,180)(167,175)(168,178)(169,177)(170,176)
(183,303)(184,306)(185,305)(186,304)(187,311)(188,314)(189,313)(190,312)
(191,307)(192,310)(193,309)(194,308)(195,291)(196,294)(197,293)(198,292)
(199,299)(200,302)(201,301)(202,300)(203,295)(204,298)(205,297)(206,296)
(207,279)(208,282)(209,281)(210,280)(211,287)(212,290)(213,289)(214,288)
(215,283)(216,286)(217,285)(218,284)(219,267)(220,270)(221,269)(222,268)
(223,275)(224,278)(225,277)(226,276)(227,271)(228,274)(229,273)(230,272)
(231,255)(232,258)(233,257)(234,256)(235,263)(236,266)(237,265)(238,264)
(239,259)(240,262)(241,261)(242,260)(244,246)(247,251)(248,254)(249,253)
(250,252);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(470)!(1,2);
s1 := Sym(470)!( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)
( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)
(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)
(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)
(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)
(160,162)(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)
(176,178)(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)
(192,194)(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)
(208,210)(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)
(224,226)(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)
(240,242)(243,245)(244,246)(247,249)(248,250)(251,253)(252,254)(255,257)
(256,258)(259,261)(260,262)(263,265)(264,266)(267,269)(268,270)(271,273)
(272,274)(275,277)(276,278)(279,281)(280,282)(283,285)(284,286)(287,289)
(288,290)(291,293)(292,294)(295,297)(296,298)(299,301)(300,302)(303,305)
(304,306)(307,309)(308,310)(311,313)(312,314)(315,317)(316,318)(319,321)
(320,322)(323,325)(324,326)(327,329)(328,330)(331,333)(332,334)(335,337)
(336,338)(339,341)(340,342)(343,345)(344,346)(347,349)(348,350)(351,353)
(352,354)(355,357)(356,358)(359,361)(360,362)(363,365)(364,366)(367,369)
(368,370)(371,373)(372,374)(375,377)(376,378)(379,381)(380,382)(383,385)
(384,386)(387,389)(388,390)(391,393)(392,394)(395,397)(396,398)(399,401)
(400,402)(403,405)(404,406)(407,409)(408,410)(411,413)(412,414)(415,417)
(416,418)(419,421)(420,422)(423,425)(424,426)(427,429)(428,430)(431,433)
(432,434)(435,437)(436,438)(439,441)(440,442)(443,445)(444,446)(447,449)
(448,450)(451,453)(452,454)(455,457)(456,458)(459,461)(460,462)(463,465)
(464,466)(467,469)(468,470);
s2 := Sym(470)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15,147)( 16,149)
( 17,148)( 18,150)( 19,155)( 20,157)( 21,156)( 22,158)( 23,151)( 24,153)
( 25,152)( 26,154)( 27,135)( 28,137)( 29,136)( 30,138)( 31,143)( 32,145)
( 33,144)( 34,146)( 35,139)( 36,141)( 37,140)( 38,142)( 39,123)( 40,125)
( 41,124)( 42,126)( 43,131)( 44,133)( 45,132)( 46,134)( 47,127)( 48,129)
( 49,128)( 50,130)( 51,111)( 52,113)( 53,112)( 54,114)( 55,119)( 56,121)
( 57,120)( 58,122)( 59,115)( 60,117)( 61,116)( 62,118)( 63, 99)( 64,101)
( 65,100)( 66,102)( 67,107)( 68,109)( 69,108)( 70,110)( 71,103)( 72,105)
( 73,104)( 74,106)( 75, 87)( 76, 89)( 77, 88)( 78, 90)( 79, 95)( 80, 97)
( 81, 96)( 82, 98)( 83, 91)( 84, 93)( 85, 92)( 86, 94)(159,319)(160,321)
(161,320)(162,322)(163,315)(164,317)(165,316)(166,318)(167,323)(168,325)
(169,324)(170,326)(171,463)(172,465)(173,464)(174,466)(175,459)(176,461)
(177,460)(178,462)(179,467)(180,469)(181,468)(182,470)(183,451)(184,453)
(185,452)(186,454)(187,447)(188,449)(189,448)(190,450)(191,455)(192,457)
(193,456)(194,458)(195,439)(196,441)(197,440)(198,442)(199,435)(200,437)
(201,436)(202,438)(203,443)(204,445)(205,444)(206,446)(207,427)(208,429)
(209,428)(210,430)(211,423)(212,425)(213,424)(214,426)(215,431)(216,433)
(217,432)(218,434)(219,415)(220,417)(221,416)(222,418)(223,411)(224,413)
(225,412)(226,414)(227,419)(228,421)(229,420)(230,422)(231,403)(232,405)
(233,404)(234,406)(235,399)(236,401)(237,400)(238,402)(239,407)(240,409)
(241,408)(242,410)(243,391)(244,393)(245,392)(246,394)(247,387)(248,389)
(249,388)(250,390)(251,395)(252,397)(253,396)(254,398)(255,379)(256,381)
(257,380)(258,382)(259,375)(260,377)(261,376)(262,378)(263,383)(264,385)
(265,384)(266,386)(267,367)(268,369)(269,368)(270,370)(271,363)(272,365)
(273,364)(274,366)(275,371)(276,373)(277,372)(278,374)(279,355)(280,357)
(281,356)(282,358)(283,351)(284,353)(285,352)(286,354)(287,359)(288,361)
(289,360)(290,362)(291,343)(292,345)(293,344)(294,346)(295,339)(296,341)
(297,340)(298,342)(299,347)(300,349)(301,348)(302,350)(303,331)(304,333)
(305,332)(306,334)(307,327)(308,329)(309,328)(310,330)(311,335)(312,337)
(313,336)(314,338);
s3 := Sym(470)!( 3,327)( 4,330)( 5,329)( 6,328)( 7,335)( 8,338)( 9,337)
( 10,336)( 11,331)( 12,334)( 13,333)( 14,332)( 15,315)( 16,318)( 17,317)
( 18,316)( 19,323)( 20,326)( 21,325)( 22,324)( 23,319)( 24,322)( 25,321)
( 26,320)( 27,459)( 28,462)( 29,461)( 30,460)( 31,467)( 32,470)( 33,469)
( 34,468)( 35,463)( 36,466)( 37,465)( 38,464)( 39,447)( 40,450)( 41,449)
( 42,448)( 43,455)( 44,458)( 45,457)( 46,456)( 47,451)( 48,454)( 49,453)
( 50,452)( 51,435)( 52,438)( 53,437)( 54,436)( 55,443)( 56,446)( 57,445)
( 58,444)( 59,439)( 60,442)( 61,441)( 62,440)( 63,423)( 64,426)( 65,425)
( 66,424)( 67,431)( 68,434)( 69,433)( 70,432)( 71,427)( 72,430)( 73,429)
( 74,428)( 75,411)( 76,414)( 77,413)( 78,412)( 79,419)( 80,422)( 81,421)
( 82,420)( 83,415)( 84,418)( 85,417)( 86,416)( 87,399)( 88,402)( 89,401)
( 90,400)( 91,407)( 92,410)( 93,409)( 94,408)( 95,403)( 96,406)( 97,405)
( 98,404)( 99,387)(100,390)(101,389)(102,388)(103,395)(104,398)(105,397)
(106,396)(107,391)(108,394)(109,393)(110,392)(111,375)(112,378)(113,377)
(114,376)(115,383)(116,386)(117,385)(118,384)(119,379)(120,382)(121,381)
(122,380)(123,363)(124,366)(125,365)(126,364)(127,371)(128,374)(129,373)
(130,372)(131,367)(132,370)(133,369)(134,368)(135,351)(136,354)(137,353)
(138,352)(139,359)(140,362)(141,361)(142,360)(143,355)(144,358)(145,357)
(146,356)(147,339)(148,342)(149,341)(150,340)(151,347)(152,350)(153,349)
(154,348)(155,343)(156,346)(157,345)(158,344)(159,171)(160,174)(161,173)
(162,172)(163,179)(164,182)(165,181)(166,180)(167,175)(168,178)(169,177)
(170,176)(183,303)(184,306)(185,305)(186,304)(187,311)(188,314)(189,313)
(190,312)(191,307)(192,310)(193,309)(194,308)(195,291)(196,294)(197,293)
(198,292)(199,299)(200,302)(201,301)(202,300)(203,295)(204,298)(205,297)
(206,296)(207,279)(208,282)(209,281)(210,280)(211,287)(212,290)(213,289)
(214,288)(215,283)(216,286)(217,285)(218,284)(219,267)(220,270)(221,269)
(222,268)(223,275)(224,278)(225,277)(226,276)(227,271)(228,274)(229,273)
(230,272)(231,255)(232,258)(233,257)(234,256)(235,263)(236,266)(237,265)
(238,264)(239,259)(240,262)(241,261)(242,260)(244,246)(247,251)(248,254)
(249,253)(250,252);
poly := sub<Sym(470)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope