Polytope of Type {50,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,18}*1800
Also Known As : {50,18|2}. if this polytope has another name.
Group : SmallGroup(1800,45)
Rank : 3
Schlafli Type : {50,18}
Number of vertices, edges, etc : 50, 450, 18
Order of s0s1s2 : 450
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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) :
3-fold quotients : {50,6}*600
5-fold quotients : {10,18}*360
9-fold quotients : {50,2}*200
15-fold quotients : {10,6}*120
18-fold quotients : {25,2}*100
25-fold quotients : {2,18}*72
45-fold quotients : {10,2}*40
50-fold quotients : {2,9}*36
75-fold quotients : {2,6}*24
90-fold quotients : {5,2}*20
150-fold quotients : {2,3}*12
225-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 16, 62)( 17, 61)
( 18, 65)( 19, 64)( 20, 63)( 21, 67)( 22, 66)( 23, 70)( 24, 69)( 25, 68)
( 26, 72)( 27, 71)( 28, 75)( 29, 74)( 30, 73)( 31, 47)( 32, 46)( 33, 50)
( 34, 49)( 35, 48)( 36, 52)( 37, 51)( 38, 55)( 39, 54)( 40, 53)( 41, 57)
( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 77, 80)( 78, 79)( 82, 85)( 83, 84)
( 87, 90)( 88, 89)( 91,137)( 92,136)( 93,140)( 94,139)( 95,138)( 96,142)
( 97,141)( 98,145)( 99,144)(100,143)(101,147)(102,146)(103,150)(104,149)
(105,148)(106,122)(107,121)(108,125)(109,124)(110,123)(111,127)(112,126)
(113,130)(114,129)(115,128)(116,132)(117,131)(118,135)(119,134)(120,133)
(152,155)(153,154)(157,160)(158,159)(162,165)(163,164)(166,212)(167,211)
(168,215)(169,214)(170,213)(171,217)(172,216)(173,220)(174,219)(175,218)
(176,222)(177,221)(178,225)(179,224)(180,223)(181,197)(182,196)(183,200)
(184,199)(185,198)(186,202)(187,201)(188,205)(189,204)(190,203)(191,207)
(192,206)(193,210)(194,209)(195,208)(227,230)(228,229)(232,235)(233,234)
(237,240)(238,239)(241,287)(242,286)(243,290)(244,289)(245,288)(246,292)
(247,291)(248,295)(249,294)(250,293)(251,297)(252,296)(253,300)(254,299)
(255,298)(256,272)(257,271)(258,275)(259,274)(260,273)(261,277)(262,276)
(263,280)(264,279)(265,278)(266,282)(267,281)(268,285)(269,284)(270,283)
(302,305)(303,304)(307,310)(308,309)(312,315)(313,314)(316,362)(317,361)
(318,365)(319,364)(320,363)(321,367)(322,366)(323,370)(324,369)(325,368)
(326,372)(327,371)(328,375)(329,374)(330,373)(331,347)(332,346)(333,350)
(334,349)(335,348)(336,352)(337,351)(338,355)(339,354)(340,353)(341,357)
(342,356)(343,360)(344,359)(345,358)(377,380)(378,379)(382,385)(383,384)
(387,390)(388,389)(391,437)(392,436)(393,440)(394,439)(395,438)(396,442)
(397,441)(398,445)(399,444)(400,443)(401,447)(402,446)(403,450)(404,449)
(405,448)(406,422)(407,421)(408,425)(409,424)(410,423)(411,427)(412,426)
(413,430)(414,429)(415,428)(416,432)(417,431)(418,435)(419,434)(420,433);;
s1 := ( 1, 16)( 2, 20)( 3, 19)( 4, 18)( 5, 17)( 6, 26)( 7, 30)( 8, 29)
( 9, 28)( 10, 27)( 11, 21)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 31, 62)
( 32, 61)( 33, 65)( 34, 64)( 35, 63)( 36, 72)( 37, 71)( 38, 75)( 39, 74)
( 40, 73)( 41, 67)( 42, 66)( 43, 70)( 44, 69)( 45, 68)( 46, 47)( 48, 50)
( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 76,171)( 77,175)( 78,174)
( 79,173)( 80,172)( 81,166)( 82,170)( 83,169)( 84,168)( 85,167)( 86,176)
( 87,180)( 88,179)( 89,178)( 90,177)( 91,156)( 92,160)( 93,159)( 94,158)
( 95,157)( 96,151)( 97,155)( 98,154)( 99,153)(100,152)(101,161)(102,165)
(103,164)(104,163)(105,162)(106,217)(107,216)(108,220)(109,219)(110,218)
(111,212)(112,211)(113,215)(114,214)(115,213)(116,222)(117,221)(118,225)
(119,224)(120,223)(121,202)(122,201)(123,205)(124,204)(125,203)(126,197)
(127,196)(128,200)(129,199)(130,198)(131,207)(132,206)(133,210)(134,209)
(135,208)(136,187)(137,186)(138,190)(139,189)(140,188)(141,182)(142,181)
(143,185)(144,184)(145,183)(146,192)(147,191)(148,195)(149,194)(150,193)
(226,241)(227,245)(228,244)(229,243)(230,242)(231,251)(232,255)(233,254)
(234,253)(235,252)(236,246)(237,250)(238,249)(239,248)(240,247)(256,287)
(257,286)(258,290)(259,289)(260,288)(261,297)(262,296)(263,300)(264,299)
(265,298)(266,292)(267,291)(268,295)(269,294)(270,293)(271,272)(273,275)
(276,282)(277,281)(278,285)(279,284)(280,283)(301,396)(302,400)(303,399)
(304,398)(305,397)(306,391)(307,395)(308,394)(309,393)(310,392)(311,401)
(312,405)(313,404)(314,403)(315,402)(316,381)(317,385)(318,384)(319,383)
(320,382)(321,376)(322,380)(323,379)(324,378)(325,377)(326,386)(327,390)
(328,389)(329,388)(330,387)(331,442)(332,441)(333,445)(334,444)(335,443)
(336,437)(337,436)(338,440)(339,439)(340,438)(341,447)(342,446)(343,450)
(344,449)(345,448)(346,427)(347,426)(348,430)(349,429)(350,428)(351,422)
(352,421)(353,425)(354,424)(355,423)(356,432)(357,431)(358,435)(359,434)
(360,433)(361,412)(362,411)(363,415)(364,414)(365,413)(366,407)(367,406)
(368,410)(369,409)(370,408)(371,417)(372,416)(373,420)(374,419)(375,418);;
s2 := ( 1,301)( 2,302)( 3,303)( 4,304)( 5,305)( 6,311)( 7,312)( 8,313)
( 9,314)( 10,315)( 11,306)( 12,307)( 13,308)( 14,309)( 15,310)( 16,316)
( 17,317)( 18,318)( 19,319)( 20,320)( 21,326)( 22,327)( 23,328)( 24,329)
( 25,330)( 26,321)( 27,322)( 28,323)( 29,324)( 30,325)( 31,331)( 32,332)
( 33,333)( 34,334)( 35,335)( 36,341)( 37,342)( 38,343)( 39,344)( 40,345)
( 41,336)( 42,337)( 43,338)( 44,339)( 45,340)( 46,346)( 47,347)( 48,348)
( 49,349)( 50,350)( 51,356)( 52,357)( 53,358)( 54,359)( 55,360)( 56,351)
( 57,352)( 58,353)( 59,354)( 60,355)( 61,361)( 62,362)( 63,363)( 64,364)
( 65,365)( 66,371)( 67,372)( 68,373)( 69,374)( 70,375)( 71,366)( 72,367)
( 73,368)( 74,369)( 75,370)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)
( 81,236)( 82,237)( 83,238)( 84,239)( 85,240)( 86,231)( 87,232)( 88,233)
( 89,234)( 90,235)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,251)
( 97,252)( 98,253)( 99,254)(100,255)(101,246)(102,247)(103,248)(104,249)
(105,250)(106,256)(107,257)(108,258)(109,259)(110,260)(111,266)(112,267)
(113,268)(114,269)(115,270)(116,261)(117,262)(118,263)(119,264)(120,265)
(121,271)(122,272)(123,273)(124,274)(125,275)(126,281)(127,282)(128,283)
(129,284)(130,285)(131,276)(132,277)(133,278)(134,279)(135,280)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,296)(142,297)(143,298)(144,299)
(145,300)(146,291)(147,292)(148,293)(149,294)(150,295)(151,381)(152,382)
(153,383)(154,384)(155,385)(156,376)(157,377)(158,378)(159,379)(160,380)
(161,386)(162,387)(163,388)(164,389)(165,390)(166,396)(167,397)(168,398)
(169,399)(170,400)(171,391)(172,392)(173,393)(174,394)(175,395)(176,401)
(177,402)(178,403)(179,404)(180,405)(181,411)(182,412)(183,413)(184,414)
(185,415)(186,406)(187,407)(188,408)(189,409)(190,410)(191,416)(192,417)
(193,418)(194,419)(195,420)(196,426)(197,427)(198,428)(199,429)(200,430)
(201,421)(202,422)(203,423)(204,424)(205,425)(206,431)(207,432)(208,433)
(209,434)(210,435)(211,441)(212,442)(213,443)(214,444)(215,445)(216,436)
(217,437)(218,438)(219,439)(220,440)(221,446)(222,447)(223,448)(224,449)
(225,450);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(450)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 16, 62)
( 17, 61)( 18, 65)( 19, 64)( 20, 63)( 21, 67)( 22, 66)( 23, 70)( 24, 69)
( 25, 68)( 26, 72)( 27, 71)( 28, 75)( 29, 74)( 30, 73)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 52)( 37, 51)( 38, 55)( 39, 54)( 40, 53)
( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 77, 80)( 78, 79)( 82, 85)
( 83, 84)( 87, 90)( 88, 89)( 91,137)( 92,136)( 93,140)( 94,139)( 95,138)
( 96,142)( 97,141)( 98,145)( 99,144)(100,143)(101,147)(102,146)(103,150)
(104,149)(105,148)(106,122)(107,121)(108,125)(109,124)(110,123)(111,127)
(112,126)(113,130)(114,129)(115,128)(116,132)(117,131)(118,135)(119,134)
(120,133)(152,155)(153,154)(157,160)(158,159)(162,165)(163,164)(166,212)
(167,211)(168,215)(169,214)(170,213)(171,217)(172,216)(173,220)(174,219)
(175,218)(176,222)(177,221)(178,225)(179,224)(180,223)(181,197)(182,196)
(183,200)(184,199)(185,198)(186,202)(187,201)(188,205)(189,204)(190,203)
(191,207)(192,206)(193,210)(194,209)(195,208)(227,230)(228,229)(232,235)
(233,234)(237,240)(238,239)(241,287)(242,286)(243,290)(244,289)(245,288)
(246,292)(247,291)(248,295)(249,294)(250,293)(251,297)(252,296)(253,300)
(254,299)(255,298)(256,272)(257,271)(258,275)(259,274)(260,273)(261,277)
(262,276)(263,280)(264,279)(265,278)(266,282)(267,281)(268,285)(269,284)
(270,283)(302,305)(303,304)(307,310)(308,309)(312,315)(313,314)(316,362)
(317,361)(318,365)(319,364)(320,363)(321,367)(322,366)(323,370)(324,369)
(325,368)(326,372)(327,371)(328,375)(329,374)(330,373)(331,347)(332,346)
(333,350)(334,349)(335,348)(336,352)(337,351)(338,355)(339,354)(340,353)
(341,357)(342,356)(343,360)(344,359)(345,358)(377,380)(378,379)(382,385)
(383,384)(387,390)(388,389)(391,437)(392,436)(393,440)(394,439)(395,438)
(396,442)(397,441)(398,445)(399,444)(400,443)(401,447)(402,446)(403,450)
(404,449)(405,448)(406,422)(407,421)(408,425)(409,424)(410,423)(411,427)
(412,426)(413,430)(414,429)(415,428)(416,432)(417,431)(418,435)(419,434)
(420,433);
s1 := Sym(450)!( 1, 16)( 2, 20)( 3, 19)( 4, 18)( 5, 17)( 6, 26)( 7, 30)
( 8, 29)( 9, 28)( 10, 27)( 11, 21)( 12, 25)( 13, 24)( 14, 23)( 15, 22)
( 31, 62)( 32, 61)( 33, 65)( 34, 64)( 35, 63)( 36, 72)( 37, 71)( 38, 75)
( 39, 74)( 40, 73)( 41, 67)( 42, 66)( 43, 70)( 44, 69)( 45, 68)( 46, 47)
( 48, 50)( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 76,171)( 77,175)
( 78,174)( 79,173)( 80,172)( 81,166)( 82,170)( 83,169)( 84,168)( 85,167)
( 86,176)( 87,180)( 88,179)( 89,178)( 90,177)( 91,156)( 92,160)( 93,159)
( 94,158)( 95,157)( 96,151)( 97,155)( 98,154)( 99,153)(100,152)(101,161)
(102,165)(103,164)(104,163)(105,162)(106,217)(107,216)(108,220)(109,219)
(110,218)(111,212)(112,211)(113,215)(114,214)(115,213)(116,222)(117,221)
(118,225)(119,224)(120,223)(121,202)(122,201)(123,205)(124,204)(125,203)
(126,197)(127,196)(128,200)(129,199)(130,198)(131,207)(132,206)(133,210)
(134,209)(135,208)(136,187)(137,186)(138,190)(139,189)(140,188)(141,182)
(142,181)(143,185)(144,184)(145,183)(146,192)(147,191)(148,195)(149,194)
(150,193)(226,241)(227,245)(228,244)(229,243)(230,242)(231,251)(232,255)
(233,254)(234,253)(235,252)(236,246)(237,250)(238,249)(239,248)(240,247)
(256,287)(257,286)(258,290)(259,289)(260,288)(261,297)(262,296)(263,300)
(264,299)(265,298)(266,292)(267,291)(268,295)(269,294)(270,293)(271,272)
(273,275)(276,282)(277,281)(278,285)(279,284)(280,283)(301,396)(302,400)
(303,399)(304,398)(305,397)(306,391)(307,395)(308,394)(309,393)(310,392)
(311,401)(312,405)(313,404)(314,403)(315,402)(316,381)(317,385)(318,384)
(319,383)(320,382)(321,376)(322,380)(323,379)(324,378)(325,377)(326,386)
(327,390)(328,389)(329,388)(330,387)(331,442)(332,441)(333,445)(334,444)
(335,443)(336,437)(337,436)(338,440)(339,439)(340,438)(341,447)(342,446)
(343,450)(344,449)(345,448)(346,427)(347,426)(348,430)(349,429)(350,428)
(351,422)(352,421)(353,425)(354,424)(355,423)(356,432)(357,431)(358,435)
(359,434)(360,433)(361,412)(362,411)(363,415)(364,414)(365,413)(366,407)
(367,406)(368,410)(369,409)(370,408)(371,417)(372,416)(373,420)(374,419)
(375,418);
s2 := Sym(450)!( 1,301)( 2,302)( 3,303)( 4,304)( 5,305)( 6,311)( 7,312)
( 8,313)( 9,314)( 10,315)( 11,306)( 12,307)( 13,308)( 14,309)( 15,310)
( 16,316)( 17,317)( 18,318)( 19,319)( 20,320)( 21,326)( 22,327)( 23,328)
( 24,329)( 25,330)( 26,321)( 27,322)( 28,323)( 29,324)( 30,325)( 31,331)
( 32,332)( 33,333)( 34,334)( 35,335)( 36,341)( 37,342)( 38,343)( 39,344)
( 40,345)( 41,336)( 42,337)( 43,338)( 44,339)( 45,340)( 46,346)( 47,347)
( 48,348)( 49,349)( 50,350)( 51,356)( 52,357)( 53,358)( 54,359)( 55,360)
( 56,351)( 57,352)( 58,353)( 59,354)( 60,355)( 61,361)( 62,362)( 63,363)
( 64,364)( 65,365)( 66,371)( 67,372)( 68,373)( 69,374)( 70,375)( 71,366)
( 72,367)( 73,368)( 74,369)( 75,370)( 76,226)( 77,227)( 78,228)( 79,229)
( 80,230)( 81,236)( 82,237)( 83,238)( 84,239)( 85,240)( 86,231)( 87,232)
( 88,233)( 89,234)( 90,235)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)
( 96,251)( 97,252)( 98,253)( 99,254)(100,255)(101,246)(102,247)(103,248)
(104,249)(105,250)(106,256)(107,257)(108,258)(109,259)(110,260)(111,266)
(112,267)(113,268)(114,269)(115,270)(116,261)(117,262)(118,263)(119,264)
(120,265)(121,271)(122,272)(123,273)(124,274)(125,275)(126,281)(127,282)
(128,283)(129,284)(130,285)(131,276)(132,277)(133,278)(134,279)(135,280)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,296)(142,297)(143,298)
(144,299)(145,300)(146,291)(147,292)(148,293)(149,294)(150,295)(151,381)
(152,382)(153,383)(154,384)(155,385)(156,376)(157,377)(158,378)(159,379)
(160,380)(161,386)(162,387)(163,388)(164,389)(165,390)(166,396)(167,397)
(168,398)(169,399)(170,400)(171,391)(172,392)(173,393)(174,394)(175,395)
(176,401)(177,402)(178,403)(179,404)(180,405)(181,411)(182,412)(183,413)
(184,414)(185,415)(186,406)(187,407)(188,408)(189,409)(190,410)(191,416)
(192,417)(193,418)(194,419)(195,420)(196,426)(197,427)(198,428)(199,429)
(200,430)(201,421)(202,422)(203,423)(204,424)(205,425)(206,431)(207,432)
(208,433)(209,434)(210,435)(211,441)(212,442)(213,443)(214,444)(215,445)
(216,436)(217,437)(218,438)(219,439)(220,440)(221,446)(222,447)(223,448)
(224,449)(225,450);
poly := sub<Sym(450)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope