Polytope of Type {114,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {114,4}*912b
if this polytope has a name.
Group : SmallGroup(912,209)
Rank : 3
Schlafli Type : {114,4}
Number of vertices, edges, etc : 114, 228, 4
Order of s0s1s2 : 114
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {114,4,2} of size 1824
Vertex Figure Of :
   {2,114,4} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {57,4}*456
   19-fold quotients : {6,4}*48c
   38-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {228,4}*1824b, {228,4}*1824c, {114,4}*1824
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);;
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, 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(456)!(  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(456)!(  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(456)!(  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);
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, 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 >;
References : None.
to this polytope