Polytope of Type {2,4,57}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,57}*1824
if this polytope has a name.
Group : SmallGroup(1824,1247)
Rank : 4
Schlafli Type : {2,4,57}
Number of vertices, edges, etc : 2, 8, 228, 114
Order of s0s1s2s3 : 114
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
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
4-fold quotients : {2,2,57}*456
12-fold quotients : {2,2,19}*152
19-fold quotients : {2,4,3}*96
38-fold quotients : {2,4,3}*48
76-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,233)( 4,234)( 5,231)( 6,232)( 7,237)( 8,238)( 9,235)( 10,236)
( 11,241)( 12,242)( 13,239)( 14,240)( 15,245)( 16,246)( 17,243)( 18,244)
( 19,249)( 20,250)( 21,247)( 22,248)( 23,253)( 24,254)( 25,251)( 26,252)
( 27,257)( 28,258)( 29,255)( 30,256)( 31,261)( 32,262)( 33,259)( 34,260)
( 35,265)( 36,266)( 37,263)( 38,264)( 39,269)( 40,270)( 41,267)( 42,268)
( 43,273)( 44,274)( 45,271)( 46,272)( 47,277)( 48,278)( 49,275)( 50,276)
( 51,281)( 52,282)( 53,279)( 54,280)( 55,285)( 56,286)( 57,283)( 58,284)
( 59,289)( 60,290)( 61,287)( 62,288)( 63,293)( 64,294)( 65,291)( 66,292)
( 67,297)( 68,298)( 69,295)( 70,296)( 71,301)( 72,302)( 73,299)( 74,300)
( 75,305)( 76,306)( 77,303)( 78,304)( 79,309)( 80,310)( 81,307)( 82,308)
( 83,313)( 84,314)( 85,311)( 86,312)( 87,317)( 88,318)( 89,315)( 90,316)
( 91,321)( 92,322)( 93,319)( 94,320)( 95,325)( 96,326)( 97,323)( 98,324)
( 99,329)(100,330)(101,327)(102,328)(103,333)(104,334)(105,331)(106,332)
(107,337)(108,338)(109,335)(110,336)(111,341)(112,342)(113,339)(114,340)
(115,345)(116,346)(117,343)(118,344)(119,349)(120,350)(121,347)(122,348)
(123,353)(124,354)(125,351)(126,352)(127,357)(128,358)(129,355)(130,356)
(131,361)(132,362)(133,359)(134,360)(135,365)(136,366)(137,363)(138,364)
(139,369)(140,370)(141,367)(142,368)(143,373)(144,374)(145,371)(146,372)
(147,377)(148,378)(149,375)(150,376)(151,381)(152,382)(153,379)(154,380)
(155,385)(156,386)(157,383)(158,384)(159,389)(160,390)(161,387)(162,388)
(163,393)(164,394)(165,391)(166,392)(167,397)(168,398)(169,395)(170,396)
(171,401)(172,402)(173,399)(174,400)(175,405)(176,406)(177,403)(178,404)
(179,409)(180,410)(181,407)(182,408)(183,413)(184,414)(185,411)(186,412)
(187,417)(188,418)(189,415)(190,416)(191,421)(192,422)(193,419)(194,420)
(195,425)(196,426)(197,423)(198,424)(199,429)(200,430)(201,427)(202,428)
(203,433)(204,434)(205,431)(206,432)(207,437)(208,438)(209,435)(210,436)
(211,441)(212,442)(213,439)(214,440)(215,445)(216,446)(217,443)(218,444)
(219,449)(220,450)(221,447)(222,448)(223,453)(224,454)(225,451)(226,452)
(227,457)(228,458)(229,455)(230,456);;
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 := ( 3,159)( 4,162)( 5,161)( 6,160)( 7,155)( 8,158)( 9,157)( 10,156)
( 11,227)( 12,230)( 13,229)( 14,228)( 15,223)( 16,226)( 17,225)( 18,224)
( 19,219)( 20,222)( 21,221)( 22,220)( 23,215)( 24,218)( 25,217)( 26,216)
( 27,211)( 28,214)( 29,213)( 30,212)( 31,207)( 32,210)( 33,209)( 34,208)
( 35,203)( 36,206)( 37,205)( 38,204)( 39,199)( 40,202)( 41,201)( 42,200)
( 43,195)( 44,198)( 45,197)( 46,196)( 47,191)( 48,194)( 49,193)( 50,192)
( 51,187)( 52,190)( 53,189)( 54,188)( 55,183)( 56,186)( 57,185)( 58,184)
( 59,179)( 60,182)( 61,181)( 62,180)( 63,175)( 64,178)( 65,177)( 66,176)
( 67,171)( 68,174)( 69,173)( 70,172)( 71,167)( 72,170)( 73,169)( 74,168)
( 75,163)( 76,166)( 77,165)( 78,164)( 79, 83)( 80, 86)( 81, 85)( 82, 84)
( 87,151)( 88,154)( 89,153)( 90,152)( 91,147)( 92,150)( 93,149)( 94,148)
( 95,143)( 96,146)( 97,145)( 98,144)( 99,139)(100,142)(101,141)(102,140)
(103,135)(104,138)(105,137)(106,136)(107,131)(108,134)(109,133)(110,132)
(111,127)(112,130)(113,129)(114,128)(115,123)(116,126)(117,125)(118,124)
(120,122)(231,387)(232,390)(233,389)(234,388)(235,383)(236,386)(237,385)
(238,384)(239,455)(240,458)(241,457)(242,456)(243,451)(244,454)(245,453)
(246,452)(247,447)(248,450)(249,449)(250,448)(251,443)(252,446)(253,445)
(254,444)(255,439)(256,442)(257,441)(258,440)(259,435)(260,438)(261,437)
(262,436)(263,431)(264,434)(265,433)(266,432)(267,427)(268,430)(269,429)
(270,428)(271,423)(272,426)(273,425)(274,424)(275,419)(276,422)(277,421)
(278,420)(279,415)(280,418)(281,417)(282,416)(283,411)(284,414)(285,413)
(286,412)(287,407)(288,410)(289,409)(290,408)(291,403)(292,406)(293,405)
(294,404)(295,399)(296,402)(297,401)(298,400)(299,395)(300,398)(301,397)
(302,396)(303,391)(304,394)(305,393)(306,392)(307,311)(308,314)(309,313)
(310,312)(315,379)(316,382)(317,381)(318,380)(319,375)(320,378)(321,377)
(322,376)(323,371)(324,374)(325,373)(326,372)(327,367)(328,370)(329,369)
(330,368)(331,363)(332,366)(333,365)(334,364)(335,359)(336,362)(337,361)
(338,360)(339,355)(340,358)(341,357)(342,356)(343,351)(344,354)(345,353)
(346,352)(348,350);;
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*s3*s2*s1*s2*s3*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(458)!(1,2);
s1 := Sym(458)!( 3,233)( 4,234)( 5,231)( 6,232)( 7,237)( 8,238)( 9,235)
( 10,236)( 11,241)( 12,242)( 13,239)( 14,240)( 15,245)( 16,246)( 17,243)
( 18,244)( 19,249)( 20,250)( 21,247)( 22,248)( 23,253)( 24,254)( 25,251)
( 26,252)( 27,257)( 28,258)( 29,255)( 30,256)( 31,261)( 32,262)( 33,259)
( 34,260)( 35,265)( 36,266)( 37,263)( 38,264)( 39,269)( 40,270)( 41,267)
( 42,268)( 43,273)( 44,274)( 45,271)( 46,272)( 47,277)( 48,278)( 49,275)
( 50,276)( 51,281)( 52,282)( 53,279)( 54,280)( 55,285)( 56,286)( 57,283)
( 58,284)( 59,289)( 60,290)( 61,287)( 62,288)( 63,293)( 64,294)( 65,291)
( 66,292)( 67,297)( 68,298)( 69,295)( 70,296)( 71,301)( 72,302)( 73,299)
( 74,300)( 75,305)( 76,306)( 77,303)( 78,304)( 79,309)( 80,310)( 81,307)
( 82,308)( 83,313)( 84,314)( 85,311)( 86,312)( 87,317)( 88,318)( 89,315)
( 90,316)( 91,321)( 92,322)( 93,319)( 94,320)( 95,325)( 96,326)( 97,323)
( 98,324)( 99,329)(100,330)(101,327)(102,328)(103,333)(104,334)(105,331)
(106,332)(107,337)(108,338)(109,335)(110,336)(111,341)(112,342)(113,339)
(114,340)(115,345)(116,346)(117,343)(118,344)(119,349)(120,350)(121,347)
(122,348)(123,353)(124,354)(125,351)(126,352)(127,357)(128,358)(129,355)
(130,356)(131,361)(132,362)(133,359)(134,360)(135,365)(136,366)(137,363)
(138,364)(139,369)(140,370)(141,367)(142,368)(143,373)(144,374)(145,371)
(146,372)(147,377)(148,378)(149,375)(150,376)(151,381)(152,382)(153,379)
(154,380)(155,385)(156,386)(157,383)(158,384)(159,389)(160,390)(161,387)
(162,388)(163,393)(164,394)(165,391)(166,392)(167,397)(168,398)(169,395)
(170,396)(171,401)(172,402)(173,399)(174,400)(175,405)(176,406)(177,403)
(178,404)(179,409)(180,410)(181,407)(182,408)(183,413)(184,414)(185,411)
(186,412)(187,417)(188,418)(189,415)(190,416)(191,421)(192,422)(193,419)
(194,420)(195,425)(196,426)(197,423)(198,424)(199,429)(200,430)(201,427)
(202,428)(203,433)(204,434)(205,431)(206,432)(207,437)(208,438)(209,435)
(210,436)(211,441)(212,442)(213,439)(214,440)(215,445)(216,446)(217,443)
(218,444)(219,449)(220,450)(221,447)(222,448)(223,453)(224,454)(225,451)
(226,452)(227,457)(228,458)(229,455)(230,456);
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)!( 3,159)( 4,162)( 5,161)( 6,160)( 7,155)( 8,158)( 9,157)
( 10,156)( 11,227)( 12,230)( 13,229)( 14,228)( 15,223)( 16,226)( 17,225)
( 18,224)( 19,219)( 20,222)( 21,221)( 22,220)( 23,215)( 24,218)( 25,217)
( 26,216)( 27,211)( 28,214)( 29,213)( 30,212)( 31,207)( 32,210)( 33,209)
( 34,208)( 35,203)( 36,206)( 37,205)( 38,204)( 39,199)( 40,202)( 41,201)
( 42,200)( 43,195)( 44,198)( 45,197)( 46,196)( 47,191)( 48,194)( 49,193)
( 50,192)( 51,187)( 52,190)( 53,189)( 54,188)( 55,183)( 56,186)( 57,185)
( 58,184)( 59,179)( 60,182)( 61,181)( 62,180)( 63,175)( 64,178)( 65,177)
( 66,176)( 67,171)( 68,174)( 69,173)( 70,172)( 71,167)( 72,170)( 73,169)
( 74,168)( 75,163)( 76,166)( 77,165)( 78,164)( 79, 83)( 80, 86)( 81, 85)
( 82, 84)( 87,151)( 88,154)( 89,153)( 90,152)( 91,147)( 92,150)( 93,149)
( 94,148)( 95,143)( 96,146)( 97,145)( 98,144)( 99,139)(100,142)(101,141)
(102,140)(103,135)(104,138)(105,137)(106,136)(107,131)(108,134)(109,133)
(110,132)(111,127)(112,130)(113,129)(114,128)(115,123)(116,126)(117,125)
(118,124)(120,122)(231,387)(232,390)(233,389)(234,388)(235,383)(236,386)
(237,385)(238,384)(239,455)(240,458)(241,457)(242,456)(243,451)(244,454)
(245,453)(246,452)(247,447)(248,450)(249,449)(250,448)(251,443)(252,446)
(253,445)(254,444)(255,439)(256,442)(257,441)(258,440)(259,435)(260,438)
(261,437)(262,436)(263,431)(264,434)(265,433)(266,432)(267,427)(268,430)
(269,429)(270,428)(271,423)(272,426)(273,425)(274,424)(275,419)(276,422)
(277,421)(278,420)(279,415)(280,418)(281,417)(282,416)(283,411)(284,414)
(285,413)(286,412)(287,407)(288,410)(289,409)(290,408)(291,403)(292,406)
(293,405)(294,404)(295,399)(296,402)(297,401)(298,400)(299,395)(300,398)
(301,397)(302,396)(303,391)(304,394)(305,393)(306,392)(307,311)(308,314)
(309,313)(310,312)(315,379)(316,382)(317,381)(318,380)(319,375)(320,378)
(321,377)(322,376)(323,371)(324,374)(325,373)(326,372)(327,367)(328,370)
(329,369)(330,368)(331,363)(332,366)(333,365)(334,364)(335,359)(336,362)
(337,361)(338,360)(339,355)(340,358)(341,357)(342,356)(343,351)(344,354)
(345,353)(346,352)(348,350);
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*s3*s2*s1*s2*s3*s2*s3*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 >;
to this polytope