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