Polytope of Type {18,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,10}*1800b
if this polytope has a name.
Group : SmallGroup(1800,276)
Rank : 3
Schlafli Type : {18,10}
Number of vertices, edges, etc : 90, 450, 50
Order of s0s1s2 : 18
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {9,10}*900
3-fold quotients : {6,10}*600b
6-fold quotients : {3,10}*300
25-fold quotients : {18,2}*72
50-fold quotients : {9,2}*36
75-fold quotients : {6,2}*24
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 := ( 2, 5)( 3, 4)( 6, 7)( 8, 10)( 11, 13)( 14, 15)( 16, 19)( 17, 18)
( 21, 25)( 22, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)( 31, 57)
( 32, 56)( 33, 60)( 34, 59)( 35, 58)( 36, 63)( 37, 62)( 38, 61)( 39, 65)
( 40, 64)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 75)( 47, 74)
( 48, 73)( 49, 72)( 50, 71)( 76,201)( 77,205)( 78,204)( 79,203)( 80,202)
( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,213)( 87,212)( 88,211)
( 89,215)( 90,214)( 91,219)( 92,218)( 93,217)( 94,216)( 95,220)( 96,225)
( 97,224)( 98,223)( 99,222)(100,221)(101,176)(102,180)(103,179)(104,178)
(105,177)(106,182)(107,181)(108,185)(109,184)(110,183)(111,188)(112,187)
(113,186)(114,190)(115,189)(116,194)(117,193)(118,192)(119,191)(120,195)
(121,200)(122,199)(123,198)(124,197)(125,196)(126,151)(127,155)(128,154)
(129,153)(130,152)(131,157)(132,156)(133,160)(134,159)(135,158)(136,163)
(137,162)(138,161)(139,165)(140,164)(141,169)(142,168)(143,167)(144,166)
(145,170)(146,175)(147,174)(148,173)(149,172)(150,171)(227,230)(228,229)
(231,232)(233,235)(236,238)(239,240)(241,244)(242,243)(246,250)(247,249)
(251,276)(252,280)(253,279)(254,278)(255,277)(256,282)(257,281)(258,285)
(259,284)(260,283)(261,288)(262,287)(263,286)(264,290)(265,289)(266,294)
(267,293)(268,292)(269,291)(270,295)(271,300)(272,299)(273,298)(274,297)
(275,296)(301,426)(302,430)(303,429)(304,428)(305,427)(306,432)(307,431)
(308,435)(309,434)(310,433)(311,438)(312,437)(313,436)(314,440)(315,439)
(316,444)(317,443)(318,442)(319,441)(320,445)(321,450)(322,449)(323,448)
(324,447)(325,446)(326,401)(327,405)(328,404)(329,403)(330,402)(331,407)
(332,406)(333,410)(334,409)(335,408)(336,413)(337,412)(338,411)(339,415)
(340,414)(341,419)(342,418)(343,417)(344,416)(345,420)(346,425)(347,424)
(348,423)(349,422)(350,421)(351,376)(352,380)(353,379)(354,378)(355,377)
(356,382)(357,381)(358,385)(359,384)(360,383)(361,388)(362,387)(363,386)
(364,390)(365,389)(366,394)(367,393)(368,392)(369,391)(370,395)(371,400)
(372,399)(373,398)(374,397)(375,396);;
s1 := ( 1,301)( 2,307)( 3,313)( 4,319)( 5,325)( 6,321)( 7,302)( 8,308)
( 9,314)( 10,320)( 11,316)( 12,322)( 13,303)( 14,309)( 15,315)( 16,311)
( 17,317)( 18,323)( 19,304)( 20,310)( 21,306)( 22,312)( 23,318)( 24,324)
( 25,305)( 26,351)( 27,357)( 28,363)( 29,369)( 30,375)( 31,371)( 32,352)
( 33,358)( 34,364)( 35,370)( 36,366)( 37,372)( 38,353)( 39,359)( 40,365)
( 41,361)( 42,367)( 43,373)( 44,354)( 45,360)( 46,356)( 47,362)( 48,368)
( 49,374)( 50,355)( 51,326)( 52,332)( 53,338)( 54,344)( 55,350)( 56,346)
( 57,327)( 58,333)( 59,339)( 60,345)( 61,341)( 62,347)( 63,328)( 64,334)
( 65,340)( 66,336)( 67,342)( 68,348)( 69,329)( 70,335)( 71,331)( 72,337)
( 73,343)( 74,349)( 75,330)( 76,226)( 77,232)( 78,238)( 79,244)( 80,250)
( 81,246)( 82,227)( 83,233)( 84,239)( 85,245)( 86,241)( 87,247)( 88,228)
( 89,234)( 90,240)( 91,236)( 92,242)( 93,248)( 94,229)( 95,235)( 96,231)
( 97,237)( 98,243)( 99,249)(100,230)(101,276)(102,282)(103,288)(104,294)
(105,300)(106,296)(107,277)(108,283)(109,289)(110,295)(111,291)(112,297)
(113,278)(114,284)(115,290)(116,286)(117,292)(118,298)(119,279)(120,285)
(121,281)(122,287)(123,293)(124,299)(125,280)(126,251)(127,257)(128,263)
(129,269)(130,275)(131,271)(132,252)(133,258)(134,264)(135,270)(136,266)
(137,272)(138,253)(139,259)(140,265)(141,261)(142,267)(143,273)(144,254)
(145,260)(146,256)(147,262)(148,268)(149,274)(150,255)(151,426)(152,432)
(153,438)(154,444)(155,450)(156,446)(157,427)(158,433)(159,439)(160,445)
(161,441)(162,447)(163,428)(164,434)(165,440)(166,436)(167,442)(168,448)
(169,429)(170,435)(171,431)(172,437)(173,443)(174,449)(175,430)(176,401)
(177,407)(178,413)(179,419)(180,425)(181,421)(182,402)(183,408)(184,414)
(185,420)(186,416)(187,422)(188,403)(189,409)(190,415)(191,411)(192,417)
(193,423)(194,404)(195,410)(196,406)(197,412)(198,418)(199,424)(200,405)
(201,376)(202,382)(203,388)(204,394)(205,400)(206,396)(207,377)(208,383)
(209,389)(210,395)(211,391)(212,397)(213,378)(214,384)(215,390)(216,386)
(217,392)(218,398)(219,379)(220,385)(221,381)(222,387)(223,393)(224,399)
(225,380);;
s2 := ( 1, 12)( 2, 11)( 3, 15)( 4, 14)( 5, 13)( 6, 7)( 8, 10)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 37)( 27, 36)( 28, 40)( 29, 39)
( 30, 38)( 31, 32)( 33, 35)( 41, 47)( 42, 46)( 43, 50)( 44, 49)( 45, 48)
( 51, 62)( 52, 61)( 53, 65)( 54, 64)( 55, 63)( 56, 57)( 58, 60)( 66, 72)
( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 87)( 77, 86)( 78, 90)( 79, 89)
( 80, 88)( 81, 82)( 83, 85)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)
(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)(116,122)
(117,121)(118,125)(119,124)(120,123)(126,137)(127,136)(128,140)(129,139)
(130,138)(131,132)(133,135)(141,147)(142,146)(143,150)(144,149)(145,148)
(151,162)(152,161)(153,165)(154,164)(155,163)(156,157)(158,160)(166,172)
(167,171)(168,175)(169,174)(170,173)(176,187)(177,186)(178,190)(179,189)
(180,188)(181,182)(183,185)(191,197)(192,196)(193,200)(194,199)(195,198)
(201,212)(202,211)(203,215)(204,214)(205,213)(206,207)(208,210)(216,222)
(217,221)(218,225)(219,224)(220,223)(226,237)(227,236)(228,240)(229,239)
(230,238)(231,232)(233,235)(241,247)(242,246)(243,250)(244,249)(245,248)
(251,262)(252,261)(253,265)(254,264)(255,263)(256,257)(258,260)(266,272)
(267,271)(268,275)(269,274)(270,273)(276,287)(277,286)(278,290)(279,289)
(280,288)(281,282)(283,285)(291,297)(292,296)(293,300)(294,299)(295,298)
(301,312)(302,311)(303,315)(304,314)(305,313)(306,307)(308,310)(316,322)
(317,321)(318,325)(319,324)(320,323)(326,337)(327,336)(328,340)(329,339)
(330,338)(331,332)(333,335)(341,347)(342,346)(343,350)(344,349)(345,348)
(351,362)(352,361)(353,365)(354,364)(355,363)(356,357)(358,360)(366,372)
(367,371)(368,375)(369,374)(370,373)(376,387)(377,386)(378,390)(379,389)
(380,388)(381,382)(383,385)(391,397)(392,396)(393,400)(394,399)(395,398)
(401,412)(402,411)(403,415)(404,414)(405,413)(406,407)(408,410)(416,422)
(417,421)(418,425)(419,424)(420,423)(426,437)(427,436)(428,440)(429,439)
(430,438)(431,432)(433,435)(441,447)(442,446)(443,450)(444,449)(445,448);;
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*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1,
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(450)!( 2, 5)( 3, 4)( 6, 7)( 8, 10)( 11, 13)( 14, 15)( 16, 19)
( 17, 18)( 21, 25)( 22, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)
( 31, 57)( 32, 56)( 33, 60)( 34, 59)( 35, 58)( 36, 63)( 37, 62)( 38, 61)
( 39, 65)( 40, 64)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 75)
( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 76,201)( 77,205)( 78,204)( 79,203)
( 80,202)( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,213)( 87,212)
( 88,211)( 89,215)( 90,214)( 91,219)( 92,218)( 93,217)( 94,216)( 95,220)
( 96,225)( 97,224)( 98,223)( 99,222)(100,221)(101,176)(102,180)(103,179)
(104,178)(105,177)(106,182)(107,181)(108,185)(109,184)(110,183)(111,188)
(112,187)(113,186)(114,190)(115,189)(116,194)(117,193)(118,192)(119,191)
(120,195)(121,200)(122,199)(123,198)(124,197)(125,196)(126,151)(127,155)
(128,154)(129,153)(130,152)(131,157)(132,156)(133,160)(134,159)(135,158)
(136,163)(137,162)(138,161)(139,165)(140,164)(141,169)(142,168)(143,167)
(144,166)(145,170)(146,175)(147,174)(148,173)(149,172)(150,171)(227,230)
(228,229)(231,232)(233,235)(236,238)(239,240)(241,244)(242,243)(246,250)
(247,249)(251,276)(252,280)(253,279)(254,278)(255,277)(256,282)(257,281)
(258,285)(259,284)(260,283)(261,288)(262,287)(263,286)(264,290)(265,289)
(266,294)(267,293)(268,292)(269,291)(270,295)(271,300)(272,299)(273,298)
(274,297)(275,296)(301,426)(302,430)(303,429)(304,428)(305,427)(306,432)
(307,431)(308,435)(309,434)(310,433)(311,438)(312,437)(313,436)(314,440)
(315,439)(316,444)(317,443)(318,442)(319,441)(320,445)(321,450)(322,449)
(323,448)(324,447)(325,446)(326,401)(327,405)(328,404)(329,403)(330,402)
(331,407)(332,406)(333,410)(334,409)(335,408)(336,413)(337,412)(338,411)
(339,415)(340,414)(341,419)(342,418)(343,417)(344,416)(345,420)(346,425)
(347,424)(348,423)(349,422)(350,421)(351,376)(352,380)(353,379)(354,378)
(355,377)(356,382)(357,381)(358,385)(359,384)(360,383)(361,388)(362,387)
(363,386)(364,390)(365,389)(366,394)(367,393)(368,392)(369,391)(370,395)
(371,400)(372,399)(373,398)(374,397)(375,396);
s1 := Sym(450)!( 1,301)( 2,307)( 3,313)( 4,319)( 5,325)( 6,321)( 7,302)
( 8,308)( 9,314)( 10,320)( 11,316)( 12,322)( 13,303)( 14,309)( 15,315)
( 16,311)( 17,317)( 18,323)( 19,304)( 20,310)( 21,306)( 22,312)( 23,318)
( 24,324)( 25,305)( 26,351)( 27,357)( 28,363)( 29,369)( 30,375)( 31,371)
( 32,352)( 33,358)( 34,364)( 35,370)( 36,366)( 37,372)( 38,353)( 39,359)
( 40,365)( 41,361)( 42,367)( 43,373)( 44,354)( 45,360)( 46,356)( 47,362)
( 48,368)( 49,374)( 50,355)( 51,326)( 52,332)( 53,338)( 54,344)( 55,350)
( 56,346)( 57,327)( 58,333)( 59,339)( 60,345)( 61,341)( 62,347)( 63,328)
( 64,334)( 65,340)( 66,336)( 67,342)( 68,348)( 69,329)( 70,335)( 71,331)
( 72,337)( 73,343)( 74,349)( 75,330)( 76,226)( 77,232)( 78,238)( 79,244)
( 80,250)( 81,246)( 82,227)( 83,233)( 84,239)( 85,245)( 86,241)( 87,247)
( 88,228)( 89,234)( 90,240)( 91,236)( 92,242)( 93,248)( 94,229)( 95,235)
( 96,231)( 97,237)( 98,243)( 99,249)(100,230)(101,276)(102,282)(103,288)
(104,294)(105,300)(106,296)(107,277)(108,283)(109,289)(110,295)(111,291)
(112,297)(113,278)(114,284)(115,290)(116,286)(117,292)(118,298)(119,279)
(120,285)(121,281)(122,287)(123,293)(124,299)(125,280)(126,251)(127,257)
(128,263)(129,269)(130,275)(131,271)(132,252)(133,258)(134,264)(135,270)
(136,266)(137,272)(138,253)(139,259)(140,265)(141,261)(142,267)(143,273)
(144,254)(145,260)(146,256)(147,262)(148,268)(149,274)(150,255)(151,426)
(152,432)(153,438)(154,444)(155,450)(156,446)(157,427)(158,433)(159,439)
(160,445)(161,441)(162,447)(163,428)(164,434)(165,440)(166,436)(167,442)
(168,448)(169,429)(170,435)(171,431)(172,437)(173,443)(174,449)(175,430)
(176,401)(177,407)(178,413)(179,419)(180,425)(181,421)(182,402)(183,408)
(184,414)(185,420)(186,416)(187,422)(188,403)(189,409)(190,415)(191,411)
(192,417)(193,423)(194,404)(195,410)(196,406)(197,412)(198,418)(199,424)
(200,405)(201,376)(202,382)(203,388)(204,394)(205,400)(206,396)(207,377)
(208,383)(209,389)(210,395)(211,391)(212,397)(213,378)(214,384)(215,390)
(216,386)(217,392)(218,398)(219,379)(220,385)(221,381)(222,387)(223,393)
(224,399)(225,380);
s2 := Sym(450)!( 1, 12)( 2, 11)( 3, 15)( 4, 14)( 5, 13)( 6, 7)( 8, 10)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 37)( 27, 36)( 28, 40)
( 29, 39)( 30, 38)( 31, 32)( 33, 35)( 41, 47)( 42, 46)( 43, 50)( 44, 49)
( 45, 48)( 51, 62)( 52, 61)( 53, 65)( 54, 64)( 55, 63)( 56, 57)( 58, 60)
( 66, 72)( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 87)( 77, 86)( 78, 90)
( 79, 89)( 80, 88)( 81, 82)( 83, 85)( 91, 97)( 92, 96)( 93,100)( 94, 99)
( 95, 98)(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)
(116,122)(117,121)(118,125)(119,124)(120,123)(126,137)(127,136)(128,140)
(129,139)(130,138)(131,132)(133,135)(141,147)(142,146)(143,150)(144,149)
(145,148)(151,162)(152,161)(153,165)(154,164)(155,163)(156,157)(158,160)
(166,172)(167,171)(168,175)(169,174)(170,173)(176,187)(177,186)(178,190)
(179,189)(180,188)(181,182)(183,185)(191,197)(192,196)(193,200)(194,199)
(195,198)(201,212)(202,211)(203,215)(204,214)(205,213)(206,207)(208,210)
(216,222)(217,221)(218,225)(219,224)(220,223)(226,237)(227,236)(228,240)
(229,239)(230,238)(231,232)(233,235)(241,247)(242,246)(243,250)(244,249)
(245,248)(251,262)(252,261)(253,265)(254,264)(255,263)(256,257)(258,260)
(266,272)(267,271)(268,275)(269,274)(270,273)(276,287)(277,286)(278,290)
(279,289)(280,288)(281,282)(283,285)(291,297)(292,296)(293,300)(294,299)
(295,298)(301,312)(302,311)(303,315)(304,314)(305,313)(306,307)(308,310)
(316,322)(317,321)(318,325)(319,324)(320,323)(326,337)(327,336)(328,340)
(329,339)(330,338)(331,332)(333,335)(341,347)(342,346)(343,350)(344,349)
(345,348)(351,362)(352,361)(353,365)(354,364)(355,363)(356,357)(358,360)
(366,372)(367,371)(368,375)(369,374)(370,373)(376,387)(377,386)(378,390)
(379,389)(380,388)(381,382)(383,385)(391,397)(392,396)(393,400)(394,399)
(395,398)(401,412)(402,411)(403,415)(404,414)(405,413)(406,407)(408,410)
(416,422)(417,421)(418,425)(419,424)(420,423)(426,437)(427,436)(428,440)
(429,439)(430,438)(431,432)(433,435)(441,447)(442,446)(443,450)(444,449)
(445,448);
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*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1,
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 >;
References : None.
to this polytope