Polytope of Type {2,114,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,114,4}*1824b
if this polytope has a name.
Group : SmallGroup(1824,1247)
Rank : 4
Schlafli Type : {2,114,4}
Number of vertices, edges, etc : 2, 114, 228, 4
Order of s0s1s2s3 : 114
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) :
2-fold quotients : {2,57,4}*912
19-fold quotients : {2,6,4}*96c
38-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, 75)( 8, 77)( 9, 76)( 10, 78)( 11, 71)( 12, 73)( 13, 72)
( 14, 74)( 15, 67)( 16, 69)( 17, 68)( 18, 70)( 19, 63)( 20, 65)( 21, 64)
( 22, 66)( 23, 59)( 24, 61)( 25, 60)( 26, 62)( 27, 55)( 28, 57)( 29, 56)
( 30, 58)( 31, 51)( 32, 53)( 33, 52)( 34, 54)( 35, 47)( 36, 49)( 37, 48)
( 38, 50)( 39, 43)( 40, 45)( 41, 44)( 42, 46)( 79,155)( 80,157)( 81,156)
( 82,158)( 83,227)( 84,229)( 85,228)( 86,230)( 87,223)( 88,225)( 89,224)
( 90,226)( 91,219)( 92,221)( 93,220)( 94,222)( 95,215)( 96,217)( 97,216)
( 98,218)( 99,211)(100,213)(101,212)(102,214)(103,207)(104,209)(105,208)
(106,210)(107,203)(108,205)(109,204)(110,206)(111,199)(112,201)(113,200)
(114,202)(115,195)(116,197)(117,196)(118,198)(119,191)(120,193)(121,192)
(122,194)(123,187)(124,189)(125,188)(126,190)(127,183)(128,185)(129,184)
(130,186)(131,179)(132,181)(133,180)(134,182)(135,175)(136,177)(137,176)
(138,178)(139,171)(140,173)(141,172)(142,174)(143,167)(144,169)(145,168)
(146,170)(147,163)(148,165)(149,164)(150,166)(151,159)(152,161)(153,160)
(154,162)(232,233)(235,303)(236,305)(237,304)(238,306)(239,299)(240,301)
(241,300)(242,302)(243,295)(244,297)(245,296)(246,298)(247,291)(248,293)
(249,292)(250,294)(251,287)(252,289)(253,288)(254,290)(255,283)(256,285)
(257,284)(258,286)(259,279)(260,281)(261,280)(262,282)(263,275)(264,277)
(265,276)(266,278)(267,271)(268,273)(269,272)(270,274)(307,383)(308,385)
(309,384)(310,386)(311,455)(312,457)(313,456)(314,458)(315,451)(316,453)
(317,452)(318,454)(319,447)(320,449)(321,448)(322,450)(323,443)(324,445)
(325,444)(326,446)(327,439)(328,441)(329,440)(330,442)(331,435)(332,437)
(333,436)(334,438)(335,431)(336,433)(337,432)(338,434)(339,427)(340,429)
(341,428)(342,430)(343,423)(344,425)(345,424)(346,426)(347,419)(348,421)
(349,420)(350,422)(351,415)(352,417)(353,416)(354,418)(355,411)(356,413)
(357,412)(358,414)(359,407)(360,409)(361,408)(362,410)(363,403)(364,405)
(365,404)(366,406)(367,399)(368,401)(369,400)(370,402)(371,395)(372,397)
(373,396)(374,398)(375,391)(376,393)(377,392)(378,394)(379,387)(380,389)
(381,388)(382,390);;
s2 := ( 3,311)( 4,312)( 5,314)( 6,313)( 7,307)( 8,308)( 9,310)( 10,309)
( 11,379)( 12,380)( 13,382)( 14,381)( 15,375)( 16,376)( 17,378)( 18,377)
( 19,371)( 20,372)( 21,374)( 22,373)( 23,367)( 24,368)( 25,370)( 26,369)
( 27,363)( 28,364)( 29,366)( 30,365)( 31,359)( 32,360)( 33,362)( 34,361)
( 35,355)( 36,356)( 37,358)( 38,357)( 39,351)( 40,352)( 41,354)( 42,353)
( 43,347)( 44,348)( 45,350)( 46,349)( 47,343)( 48,344)( 49,346)( 50,345)
( 51,339)( 52,340)( 53,342)( 54,341)( 55,335)( 56,336)( 57,338)( 58,337)
( 59,331)( 60,332)( 61,334)( 62,333)( 63,327)( 64,328)( 65,330)( 66,329)
( 67,323)( 68,324)( 69,326)( 70,325)( 71,319)( 72,320)( 73,322)( 74,321)
( 75,315)( 76,316)( 77,318)( 78,317)( 79,235)( 80,236)( 81,238)( 82,237)
( 83,231)( 84,232)( 85,234)( 86,233)( 87,303)( 88,304)( 89,306)( 90,305)
( 91,299)( 92,300)( 93,302)( 94,301)( 95,295)( 96,296)( 97,298)( 98,297)
( 99,291)(100,292)(101,294)(102,293)(103,287)(104,288)(105,290)(106,289)
(107,283)(108,284)(109,286)(110,285)(111,279)(112,280)(113,282)(114,281)
(115,275)(116,276)(117,278)(118,277)(119,271)(120,272)(121,274)(122,273)
(123,267)(124,268)(125,270)(126,269)(127,263)(128,264)(129,266)(130,265)
(131,259)(132,260)(133,262)(134,261)(135,255)(136,256)(137,258)(138,257)
(139,251)(140,252)(141,254)(142,253)(143,247)(144,248)(145,250)(146,249)
(147,243)(148,244)(149,246)(150,245)(151,239)(152,240)(153,242)(154,241)
(155,387)(156,388)(157,390)(158,389)(159,383)(160,384)(161,386)(162,385)
(163,455)(164,456)(165,458)(166,457)(167,451)(168,452)(169,454)(170,453)
(171,447)(172,448)(173,450)(174,449)(175,443)(176,444)(177,446)(178,445)
(179,439)(180,440)(181,442)(182,441)(183,435)(184,436)(185,438)(186,437)
(187,431)(188,432)(189,434)(190,433)(191,427)(192,428)(193,430)(194,429)
(195,423)(196,424)(197,426)(198,425)(199,419)(200,420)(201,422)(202,421)
(203,415)(204,416)(205,418)(206,417)(207,411)(208,412)(209,414)(210,413)
(211,407)(212,408)(213,410)(214,409)(215,403)(216,404)(217,406)(218,405)
(219,399)(220,400)(221,402)(222,401)(223,395)(224,396)(225,398)(226,397)
(227,391)(228,392)(229,394)(230,393);;
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);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(458)!(1,2);
s1 := Sym(458)!( 4, 5)( 7, 75)( 8, 77)( 9, 76)( 10, 78)( 11, 71)( 12, 73)
( 13, 72)( 14, 74)( 15, 67)( 16, 69)( 17, 68)( 18, 70)( 19, 63)( 20, 65)
( 21, 64)( 22, 66)( 23, 59)( 24, 61)( 25, 60)( 26, 62)( 27, 55)( 28, 57)
( 29, 56)( 30, 58)( 31, 51)( 32, 53)( 33, 52)( 34, 54)( 35, 47)( 36, 49)
( 37, 48)( 38, 50)( 39, 43)( 40, 45)( 41, 44)( 42, 46)( 79,155)( 80,157)
( 81,156)( 82,158)( 83,227)( 84,229)( 85,228)( 86,230)( 87,223)( 88,225)
( 89,224)( 90,226)( 91,219)( 92,221)( 93,220)( 94,222)( 95,215)( 96,217)
( 97,216)( 98,218)( 99,211)(100,213)(101,212)(102,214)(103,207)(104,209)
(105,208)(106,210)(107,203)(108,205)(109,204)(110,206)(111,199)(112,201)
(113,200)(114,202)(115,195)(116,197)(117,196)(118,198)(119,191)(120,193)
(121,192)(122,194)(123,187)(124,189)(125,188)(126,190)(127,183)(128,185)
(129,184)(130,186)(131,179)(132,181)(133,180)(134,182)(135,175)(136,177)
(137,176)(138,178)(139,171)(140,173)(141,172)(142,174)(143,167)(144,169)
(145,168)(146,170)(147,163)(148,165)(149,164)(150,166)(151,159)(152,161)
(153,160)(154,162)(232,233)(235,303)(236,305)(237,304)(238,306)(239,299)
(240,301)(241,300)(242,302)(243,295)(244,297)(245,296)(246,298)(247,291)
(248,293)(249,292)(250,294)(251,287)(252,289)(253,288)(254,290)(255,283)
(256,285)(257,284)(258,286)(259,279)(260,281)(261,280)(262,282)(263,275)
(264,277)(265,276)(266,278)(267,271)(268,273)(269,272)(270,274)(307,383)
(308,385)(309,384)(310,386)(311,455)(312,457)(313,456)(314,458)(315,451)
(316,453)(317,452)(318,454)(319,447)(320,449)(321,448)(322,450)(323,443)
(324,445)(325,444)(326,446)(327,439)(328,441)(329,440)(330,442)(331,435)
(332,437)(333,436)(334,438)(335,431)(336,433)(337,432)(338,434)(339,427)
(340,429)(341,428)(342,430)(343,423)(344,425)(345,424)(346,426)(347,419)
(348,421)(349,420)(350,422)(351,415)(352,417)(353,416)(354,418)(355,411)
(356,413)(357,412)(358,414)(359,407)(360,409)(361,408)(362,410)(363,403)
(364,405)(365,404)(366,406)(367,399)(368,401)(369,400)(370,402)(371,395)
(372,397)(373,396)(374,398)(375,391)(376,393)(377,392)(378,394)(379,387)
(380,389)(381,388)(382,390);
s2 := Sym(458)!( 3,311)( 4,312)( 5,314)( 6,313)( 7,307)( 8,308)( 9,310)
( 10,309)( 11,379)( 12,380)( 13,382)( 14,381)( 15,375)( 16,376)( 17,378)
( 18,377)( 19,371)( 20,372)( 21,374)( 22,373)( 23,367)( 24,368)( 25,370)
( 26,369)( 27,363)( 28,364)( 29,366)( 30,365)( 31,359)( 32,360)( 33,362)
( 34,361)( 35,355)( 36,356)( 37,358)( 38,357)( 39,351)( 40,352)( 41,354)
( 42,353)( 43,347)( 44,348)( 45,350)( 46,349)( 47,343)( 48,344)( 49,346)
( 50,345)( 51,339)( 52,340)( 53,342)( 54,341)( 55,335)( 56,336)( 57,338)
( 58,337)( 59,331)( 60,332)( 61,334)( 62,333)( 63,327)( 64,328)( 65,330)
( 66,329)( 67,323)( 68,324)( 69,326)( 70,325)( 71,319)( 72,320)( 73,322)
( 74,321)( 75,315)( 76,316)( 77,318)( 78,317)( 79,235)( 80,236)( 81,238)
( 82,237)( 83,231)( 84,232)( 85,234)( 86,233)( 87,303)( 88,304)( 89,306)
( 90,305)( 91,299)( 92,300)( 93,302)( 94,301)( 95,295)( 96,296)( 97,298)
( 98,297)( 99,291)(100,292)(101,294)(102,293)(103,287)(104,288)(105,290)
(106,289)(107,283)(108,284)(109,286)(110,285)(111,279)(112,280)(113,282)
(114,281)(115,275)(116,276)(117,278)(118,277)(119,271)(120,272)(121,274)
(122,273)(123,267)(124,268)(125,270)(126,269)(127,263)(128,264)(129,266)
(130,265)(131,259)(132,260)(133,262)(134,261)(135,255)(136,256)(137,258)
(138,257)(139,251)(140,252)(141,254)(142,253)(143,247)(144,248)(145,250)
(146,249)(147,243)(148,244)(149,246)(150,245)(151,239)(152,240)(153,242)
(154,241)(155,387)(156,388)(157,390)(158,389)(159,383)(160,384)(161,386)
(162,385)(163,455)(164,456)(165,458)(166,457)(167,451)(168,452)(169,454)
(170,453)(171,447)(172,448)(173,450)(174,449)(175,443)(176,444)(177,446)
(178,445)(179,439)(180,440)(181,442)(182,441)(183,435)(184,436)(185,438)
(186,437)(187,431)(188,432)(189,434)(190,433)(191,427)(192,428)(193,430)
(194,429)(195,423)(196,424)(197,426)(198,425)(199,419)(200,420)(201,422)
(202,421)(203,415)(204,416)(205,418)(206,417)(207,411)(208,412)(209,414)
(210,413)(211,407)(212,408)(213,410)(214,409)(215,403)(216,404)(217,406)
(218,405)(219,399)(220,400)(221,402)(222,401)(223,395)(224,396)(225,398)
(226,397)(227,391)(228,392)(229,394)(230,393);
s3 := Sym(458)!( 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);
poly := sub<Sym(458)|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 >;
to this polytope