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