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