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