Polytope of Type {10,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,18}*1800b
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 : {10,18}*900
3-fold quotients : {10,6}*600a
6-fold quotients : {10,6}*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)( 2,325)( 3,319)( 4,313)( 5,307)( 6,306)( 7,305)( 8,324)
( 9,318)( 10,312)( 11,311)( 12,310)( 13,304)( 14,323)( 15,317)( 16,316)
( 17,315)( 18,309)( 19,303)( 20,322)( 21,321)( 22,320)( 23,314)( 24,308)
( 25,302)( 26,351)( 27,375)( 28,369)( 29,363)( 30,357)( 31,356)( 32,355)
( 33,374)( 34,368)( 35,362)( 36,361)( 37,360)( 38,354)( 39,373)( 40,367)
( 41,366)( 42,365)( 43,359)( 44,353)( 45,372)( 46,371)( 47,370)( 48,364)
( 49,358)( 50,352)( 51,326)( 52,350)( 53,344)( 54,338)( 55,332)( 56,331)
( 57,330)( 58,349)( 59,343)( 60,337)( 61,336)( 62,335)( 63,329)( 64,348)
( 65,342)( 66,341)( 67,340)( 68,334)( 69,328)( 70,347)( 71,346)( 72,345)
( 73,339)( 74,333)( 75,327)( 76,226)( 77,250)( 78,244)( 79,238)( 80,232)
( 81,231)( 82,230)( 83,249)( 84,243)( 85,237)( 86,236)( 87,235)( 88,229)
( 89,248)( 90,242)( 91,241)( 92,240)( 93,234)( 94,228)( 95,247)( 96,246)
( 97,245)( 98,239)( 99,233)(100,227)(101,276)(102,300)(103,294)(104,288)
(105,282)(106,281)(107,280)(108,299)(109,293)(110,287)(111,286)(112,285)
(113,279)(114,298)(115,292)(116,291)(117,290)(118,284)(119,278)(120,297)
(121,296)(122,295)(123,289)(124,283)(125,277)(126,251)(127,275)(128,269)
(129,263)(130,257)(131,256)(132,255)(133,274)(134,268)(135,262)(136,261)
(137,260)(138,254)(139,273)(140,267)(141,266)(142,265)(143,259)(144,253)
(145,272)(146,271)(147,270)(148,264)(149,258)(150,252)(151,426)(152,450)
(153,444)(154,438)(155,432)(156,431)(157,430)(158,449)(159,443)(160,437)
(161,436)(162,435)(163,429)(164,448)(165,442)(166,441)(167,440)(168,434)
(169,428)(170,447)(171,446)(172,445)(173,439)(174,433)(175,427)(176,401)
(177,425)(178,419)(179,413)(180,407)(181,406)(182,405)(183,424)(184,418)
(185,412)(186,411)(187,410)(188,404)(189,423)(190,417)(191,416)(192,415)
(193,409)(194,403)(195,422)(196,421)(197,420)(198,414)(199,408)(200,402)
(201,376)(202,400)(203,394)(204,388)(205,382)(206,381)(207,380)(208,399)
(209,393)(210,387)(211,386)(212,385)(213,379)(214,398)(215,392)(216,391)
(217,390)(218,384)(219,378)(220,397)(221,396)(222,395)(223,389)(224,383)
(225,377);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*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)( 2,325)( 3,319)( 4,313)( 5,307)( 6,306)( 7,305)
( 8,324)( 9,318)( 10,312)( 11,311)( 12,310)( 13,304)( 14,323)( 15,317)
( 16,316)( 17,315)( 18,309)( 19,303)( 20,322)( 21,321)( 22,320)( 23,314)
( 24,308)( 25,302)( 26,351)( 27,375)( 28,369)( 29,363)( 30,357)( 31,356)
( 32,355)( 33,374)( 34,368)( 35,362)( 36,361)( 37,360)( 38,354)( 39,373)
( 40,367)( 41,366)( 42,365)( 43,359)( 44,353)( 45,372)( 46,371)( 47,370)
( 48,364)( 49,358)( 50,352)( 51,326)( 52,350)( 53,344)( 54,338)( 55,332)
( 56,331)( 57,330)( 58,349)( 59,343)( 60,337)( 61,336)( 62,335)( 63,329)
( 64,348)( 65,342)( 66,341)( 67,340)( 68,334)( 69,328)( 70,347)( 71,346)
( 72,345)( 73,339)( 74,333)( 75,327)( 76,226)( 77,250)( 78,244)( 79,238)
( 80,232)( 81,231)( 82,230)( 83,249)( 84,243)( 85,237)( 86,236)( 87,235)
( 88,229)( 89,248)( 90,242)( 91,241)( 92,240)( 93,234)( 94,228)( 95,247)
( 96,246)( 97,245)( 98,239)( 99,233)(100,227)(101,276)(102,300)(103,294)
(104,288)(105,282)(106,281)(107,280)(108,299)(109,293)(110,287)(111,286)
(112,285)(113,279)(114,298)(115,292)(116,291)(117,290)(118,284)(119,278)
(120,297)(121,296)(122,295)(123,289)(124,283)(125,277)(126,251)(127,275)
(128,269)(129,263)(130,257)(131,256)(132,255)(133,274)(134,268)(135,262)
(136,261)(137,260)(138,254)(139,273)(140,267)(141,266)(142,265)(143,259)
(144,253)(145,272)(146,271)(147,270)(148,264)(149,258)(150,252)(151,426)
(152,450)(153,444)(154,438)(155,432)(156,431)(157,430)(158,449)(159,443)
(160,437)(161,436)(162,435)(163,429)(164,448)(165,442)(166,441)(167,440)
(168,434)(169,428)(170,447)(171,446)(172,445)(173,439)(174,433)(175,427)
(176,401)(177,425)(178,419)(179,413)(180,407)(181,406)(182,405)(183,424)
(184,418)(185,412)(186,411)(187,410)(188,404)(189,423)(190,417)(191,416)
(192,415)(193,409)(194,403)(195,422)(196,421)(197,420)(198,414)(199,408)
(200,402)(201,376)(202,400)(203,394)(204,388)(205,382)(206,381)(207,380)
(208,399)(209,393)(210,387)(211,386)(212,385)(213,379)(214,398)(215,392)
(216,391)(217,390)(218,384)(219,378)(220,397)(221,396)(222,395)(223,389)
(224,383)(225,377);
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*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