Polytope of Type {114,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {114,4}*912c
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 : 57
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
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}*48b
38-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {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 := ( 1,232)( 2,231)( 3,230)( 4,229)( 5,236)( 6,235)( 7,234)( 8,233)
( 9,240)( 10,239)( 11,238)( 12,237)( 13,244)( 14,243)( 15,242)( 16,241)
( 17,248)( 18,247)( 19,246)( 20,245)( 21,252)( 22,251)( 23,250)( 24,249)
( 25,256)( 26,255)( 27,254)( 28,253)( 29,260)( 30,259)( 31,258)( 32,257)
( 33,264)( 34,263)( 35,262)( 36,261)( 37,268)( 38,267)( 39,266)( 40,265)
( 41,272)( 42,271)( 43,270)( 44,269)( 45,276)( 46,275)( 47,274)( 48,273)
( 49,280)( 50,279)( 51,278)( 52,277)( 53,284)( 54,283)( 55,282)( 56,281)
( 57,288)( 58,287)( 59,286)( 60,285)( 61,292)( 62,291)( 63,290)( 64,289)
( 65,296)( 66,295)( 67,294)( 68,293)( 69,300)( 70,299)( 71,298)( 72,297)
( 73,304)( 74,303)( 75,302)( 76,301)( 77,308)( 78,307)( 79,306)( 80,305)
( 81,312)( 82,311)( 83,310)( 84,309)( 85,316)( 86,315)( 87,314)( 88,313)
( 89,320)( 90,319)( 91,318)( 92,317)( 93,324)( 94,323)( 95,322)( 96,321)
( 97,328)( 98,327)( 99,326)(100,325)(101,332)(102,331)(103,330)(104,329)
(105,336)(106,335)(107,334)(108,333)(109,340)(110,339)(111,338)(112,337)
(113,344)(114,343)(115,342)(116,341)(117,348)(118,347)(119,346)(120,345)
(121,352)(122,351)(123,350)(124,349)(125,356)(126,355)(127,354)(128,353)
(129,360)(130,359)(131,358)(132,357)(133,364)(134,363)(135,362)(136,361)
(137,368)(138,367)(139,366)(140,365)(141,372)(142,371)(143,370)(144,369)
(145,376)(146,375)(147,374)(148,373)(149,380)(150,379)(151,378)(152,377)
(153,384)(154,383)(155,382)(156,381)(157,388)(158,387)(159,386)(160,385)
(161,392)(162,391)(163,390)(164,389)(165,396)(166,395)(167,394)(168,393)
(169,400)(170,399)(171,398)(172,397)(173,404)(174,403)(175,402)(176,401)
(177,408)(178,407)(179,406)(180,405)(181,412)(182,411)(183,410)(184,409)
(185,416)(186,415)(187,414)(188,413)(189,420)(190,419)(191,418)(192,417)
(193,424)(194,423)(195,422)(196,421)(197,428)(198,427)(199,426)(200,425)
(201,432)(202,431)(203,430)(204,429)(205,436)(206,435)(207,434)(208,433)
(209,440)(210,439)(211,438)(212,437)(213,444)(214,443)(215,442)(216,441)
(217,448)(218,447)(219,446)(220,445)(221,452)(222,451)(223,450)(224,449)
(225,456)(226,455)(227,454)(228,453);;
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,
s0*s1*s2*s1*s0*s1*s0*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*s2*s1*s0*s2*s1*s0*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 ];;
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)!( 1,232)( 2,231)( 3,230)( 4,229)( 5,236)( 6,235)( 7,234)
( 8,233)( 9,240)( 10,239)( 11,238)( 12,237)( 13,244)( 14,243)( 15,242)
( 16,241)( 17,248)( 18,247)( 19,246)( 20,245)( 21,252)( 22,251)( 23,250)
( 24,249)( 25,256)( 26,255)( 27,254)( 28,253)( 29,260)( 30,259)( 31,258)
( 32,257)( 33,264)( 34,263)( 35,262)( 36,261)( 37,268)( 38,267)( 39,266)
( 40,265)( 41,272)( 42,271)( 43,270)( 44,269)( 45,276)( 46,275)( 47,274)
( 48,273)( 49,280)( 50,279)( 51,278)( 52,277)( 53,284)( 54,283)( 55,282)
( 56,281)( 57,288)( 58,287)( 59,286)( 60,285)( 61,292)( 62,291)( 63,290)
( 64,289)( 65,296)( 66,295)( 67,294)( 68,293)( 69,300)( 70,299)( 71,298)
( 72,297)( 73,304)( 74,303)( 75,302)( 76,301)( 77,308)( 78,307)( 79,306)
( 80,305)( 81,312)( 82,311)( 83,310)( 84,309)( 85,316)( 86,315)( 87,314)
( 88,313)( 89,320)( 90,319)( 91,318)( 92,317)( 93,324)( 94,323)( 95,322)
( 96,321)( 97,328)( 98,327)( 99,326)(100,325)(101,332)(102,331)(103,330)
(104,329)(105,336)(106,335)(107,334)(108,333)(109,340)(110,339)(111,338)
(112,337)(113,344)(114,343)(115,342)(116,341)(117,348)(118,347)(119,346)
(120,345)(121,352)(122,351)(123,350)(124,349)(125,356)(126,355)(127,354)
(128,353)(129,360)(130,359)(131,358)(132,357)(133,364)(134,363)(135,362)
(136,361)(137,368)(138,367)(139,366)(140,365)(141,372)(142,371)(143,370)
(144,369)(145,376)(146,375)(147,374)(148,373)(149,380)(150,379)(151,378)
(152,377)(153,384)(154,383)(155,382)(156,381)(157,388)(158,387)(159,386)
(160,385)(161,392)(162,391)(163,390)(164,389)(165,396)(166,395)(167,394)
(168,393)(169,400)(170,399)(171,398)(172,397)(173,404)(174,403)(175,402)
(176,401)(177,408)(178,407)(179,406)(180,405)(181,412)(182,411)(183,410)
(184,409)(185,416)(186,415)(187,414)(188,413)(189,420)(190,419)(191,418)
(192,417)(193,424)(194,423)(195,422)(196,421)(197,428)(198,427)(199,426)
(200,425)(201,432)(202,431)(203,430)(204,429)(205,436)(206,435)(207,434)
(208,433)(209,440)(210,439)(211,438)(212,437)(213,444)(214,443)(215,442)
(216,441)(217,448)(218,447)(219,446)(220,445)(221,452)(222,451)(223,450)
(224,449)(225,456)(226,455)(227,454)(228,453);
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,
s0*s1*s2*s1*s0*s1*s0*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*s2*s1*s0*s2*s1*s0*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 >;
References : None.
to this polytope