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