Polytope of Type {228,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {228,4}*1824a
Also Known As : {228,4|2}. if this polytope has another name.
Group : SmallGroup(1824,948)
Rank : 3
Schlafli Type : {228,4}
Number of vertices, edges, etc : 228, 456, 4
Order of s₀s₁s₂ : 228
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {228,2}*912, {114,4}*912a
   3-fold quotients : {76,4}*608
   4-fold quotients : {114,2}*456
   6-fold quotients : {76,2}*304, {38,4}*304
   8-fold quotients : {57,2}*228
   12-fold quotients : {38,2}*152
   19-fold quotients : {12,4}*96a
   24-fold quotients : {19,2}*76
   38-fold quotients : {12,2}*48, {6,4}*48a
   57-fold quotients : {4,4}*32
   76-fold quotients : {6,2}*24
   114-fold quotients : {2,4}*16, {4,2}*16
   152-fold quotients : {3,2}*12
   228-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope