Polytope of Type {6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*1800d
if this polytope has a name.
Group : SmallGroup(1800,586)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 150, 450, 150
Order of s0s1s2 : 30
Order of s0s1s2s1 : 6
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 : {3,6}*900
3-fold quotients : {6,6}*600b
6-fold quotients : {3,6}*300
25-fold quotients : {6,6}*72c
50-fold quotients : {3,6}*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)( 76,151)( 77,155)( 78,154)( 79,153)( 80,152)
( 81,157)( 82,156)( 83,160)( 84,159)( 85,158)( 86,163)( 87,162)( 88,161)
( 89,165)( 90,164)( 91,169)( 92,168)( 93,167)( 94,166)( 95,170)( 96,175)
( 97,174)( 98,173)( 99,172)(100,171)(101,201)(102,205)(103,204)(104,203)
(105,202)(106,207)(107,206)(108,210)(109,209)(110,208)(111,213)(112,212)
(113,211)(114,215)(115,214)(116,219)(117,218)(118,217)(119,216)(120,220)
(121,225)(122,224)(123,223)(124,222)(125,221)(126,176)(127,180)(128,179)
(129,178)(130,177)(131,182)(132,181)(133,185)(134,184)(135,183)(136,188)
(137,187)(138,186)(139,190)(140,189)(141,194)(142,193)(143,192)(144,191)
(145,195)(146,200)(147,199)(148,198)(149,197)(150,196)(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)(301,376)(302,380)(303,379)(304,378)(305,377)(306,382)(307,381)
(308,385)(309,384)(310,383)(311,388)(312,387)(313,386)(314,390)(315,389)
(316,394)(317,393)(318,392)(319,391)(320,395)(321,400)(322,399)(323,398)
(324,397)(325,396)(326,426)(327,430)(328,429)(329,428)(330,427)(331,432)
(332,431)(333,435)(334,434)(335,433)(336,438)(337,437)(338,436)(339,440)
(340,439)(341,444)(342,443)(343,442)(344,441)(345,445)(346,450)(347,449)
(348,448)(349,447)(350,446)(351,401)(352,405)(353,404)(354,403)(355,402)
(356,407)(357,406)(358,410)(359,409)(360,408)(361,413)(362,412)(363,411)
(364,415)(365,414)(366,419)(367,418)(368,417)(369,416)(370,420)(371,425)
(372,424)(373,423)(374,422)(375,421);;
s1 := ( 1,326)( 2,332)( 3,338)( 4,344)( 5,350)( 6,346)( 7,327)( 8,333)
( 9,339)( 10,345)( 11,341)( 12,347)( 13,328)( 14,334)( 15,340)( 16,336)
( 17,342)( 18,348)( 19,329)( 20,335)( 21,331)( 22,337)( 23,343)( 24,349)
( 25,330)( 26,301)( 27,307)( 28,313)( 29,319)( 30,325)( 31,321)( 32,302)
( 33,308)( 34,314)( 35,320)( 36,316)( 37,322)( 38,303)( 39,309)( 40,315)
( 41,311)( 42,317)( 43,323)( 44,304)( 45,310)( 46,306)( 47,312)( 48,318)
( 49,324)( 50,305)( 51,351)( 52,357)( 53,363)( 54,369)( 55,375)( 56,371)
( 57,352)( 58,358)( 59,364)( 60,370)( 61,366)( 62,372)( 63,353)( 64,359)
( 65,365)( 66,361)( 67,367)( 68,373)( 69,354)( 70,360)( 71,356)( 72,362)
( 73,368)( 74,374)( 75,355)( 76,251)( 77,257)( 78,263)( 79,269)( 80,275)
( 81,271)( 82,252)( 83,258)( 84,264)( 85,270)( 86,266)( 87,272)( 88,253)
( 89,259)( 90,265)( 91,261)( 92,267)( 93,273)( 94,254)( 95,260)( 96,256)
( 97,262)( 98,268)( 99,274)(100,255)(101,226)(102,232)(103,238)(104,244)
(105,250)(106,246)(107,227)(108,233)(109,239)(110,245)(111,241)(112,247)
(113,228)(114,234)(115,240)(116,236)(117,242)(118,248)(119,229)(120,235)
(121,231)(122,237)(123,243)(124,249)(125,230)(126,276)(127,282)(128,288)
(129,294)(130,300)(131,296)(132,277)(133,283)(134,289)(135,295)(136,291)
(137,297)(138,278)(139,284)(140,290)(141,286)(142,292)(143,298)(144,279)
(145,285)(146,281)(147,287)(148,293)(149,299)(150,280)(151,401)(152,407)
(153,413)(154,419)(155,425)(156,421)(157,402)(158,408)(159,414)(160,420)
(161,416)(162,422)(163,403)(164,409)(165,415)(166,411)(167,417)(168,423)
(169,404)(170,410)(171,406)(172,412)(173,418)(174,424)(175,405)(176,376)
(177,382)(178,388)(179,394)(180,400)(181,396)(182,377)(183,383)(184,389)
(185,395)(186,391)(187,397)(188,378)(189,384)(190,390)(191,386)(192,392)
(193,398)(194,379)(195,385)(196,381)(197,387)(198,393)(199,399)(200,380)
(201,426)(202,432)(203,438)(204,444)(205,450)(206,446)(207,427)(208,433)
(209,439)(210,445)(211,441)(212,447)(213,428)(214,434)(215,440)(216,436)
(217,442)(218,448)(219,429)(220,435)(221,431)(222,437)(223,443)(224,449)
(225,430);;
s2 := ( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 11)( 16, 24)( 17, 25)( 18, 21)
( 19, 22)( 20, 23)( 26, 37)( 27, 38)( 28, 39)( 29, 40)( 30, 36)( 41, 49)
( 42, 50)( 43, 46)( 44, 47)( 45, 48)( 51, 62)( 52, 63)( 53, 64)( 54, 65)
( 55, 61)( 66, 74)( 67, 75)( 68, 71)( 69, 72)( 70, 73)( 76,162)( 77,163)
( 78,164)( 79,165)( 80,161)( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)
( 86,155)( 87,151)( 88,152)( 89,153)( 90,154)( 91,174)( 92,175)( 93,171)
( 94,172)( 95,173)( 96,168)( 97,169)( 98,170)( 99,166)(100,167)(101,187)
(102,188)(103,189)(104,190)(105,186)(106,181)(107,182)(108,183)(109,184)
(110,185)(111,180)(112,176)(113,177)(114,178)(115,179)(116,199)(117,200)
(118,196)(119,197)(120,198)(121,193)(122,194)(123,195)(124,191)(125,192)
(126,212)(127,213)(128,214)(129,215)(130,211)(131,206)(132,207)(133,208)
(134,209)(135,210)(136,205)(137,201)(138,202)(139,203)(140,204)(141,224)
(142,225)(143,221)(144,222)(145,223)(146,218)(147,219)(148,220)(149,216)
(150,217)(226,237)(227,238)(228,239)(229,240)(230,236)(241,249)(242,250)
(243,246)(244,247)(245,248)(251,262)(252,263)(253,264)(254,265)(255,261)
(266,274)(267,275)(268,271)(269,272)(270,273)(276,287)(277,288)(278,289)
(279,290)(280,286)(291,299)(292,300)(293,296)(294,297)(295,298)(301,387)
(302,388)(303,389)(304,390)(305,386)(306,381)(307,382)(308,383)(309,384)
(310,385)(311,380)(312,376)(313,377)(314,378)(315,379)(316,399)(317,400)
(318,396)(319,397)(320,398)(321,393)(322,394)(323,395)(324,391)(325,392)
(326,412)(327,413)(328,414)(329,415)(330,411)(331,406)(332,407)(333,408)
(334,409)(335,410)(336,405)(337,401)(338,402)(339,403)(340,404)(341,424)
(342,425)(343,421)(344,422)(345,423)(346,418)(347,419)(348,420)(349,416)
(350,417)(351,437)(352,438)(353,439)(354,440)(355,436)(356,431)(357,432)
(358,433)(359,434)(360,435)(361,430)(362,426)(363,427)(364,428)(365,429)
(366,449)(367,450)(368,446)(369,447)(370,448)(371,443)(372,444)(373,445)
(374,441)(375,442);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*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)( 76,151)( 77,155)( 78,154)( 79,153)
( 80,152)( 81,157)( 82,156)( 83,160)( 84,159)( 85,158)( 86,163)( 87,162)
( 88,161)( 89,165)( 90,164)( 91,169)( 92,168)( 93,167)( 94,166)( 95,170)
( 96,175)( 97,174)( 98,173)( 99,172)(100,171)(101,201)(102,205)(103,204)
(104,203)(105,202)(106,207)(107,206)(108,210)(109,209)(110,208)(111,213)
(112,212)(113,211)(114,215)(115,214)(116,219)(117,218)(118,217)(119,216)
(120,220)(121,225)(122,224)(123,223)(124,222)(125,221)(126,176)(127,180)
(128,179)(129,178)(130,177)(131,182)(132,181)(133,185)(134,184)(135,183)
(136,188)(137,187)(138,186)(139,190)(140,189)(141,194)(142,193)(143,192)
(144,191)(145,195)(146,200)(147,199)(148,198)(149,197)(150,196)(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)(301,376)(302,380)(303,379)(304,378)(305,377)(306,382)
(307,381)(308,385)(309,384)(310,383)(311,388)(312,387)(313,386)(314,390)
(315,389)(316,394)(317,393)(318,392)(319,391)(320,395)(321,400)(322,399)
(323,398)(324,397)(325,396)(326,426)(327,430)(328,429)(329,428)(330,427)
(331,432)(332,431)(333,435)(334,434)(335,433)(336,438)(337,437)(338,436)
(339,440)(340,439)(341,444)(342,443)(343,442)(344,441)(345,445)(346,450)
(347,449)(348,448)(349,447)(350,446)(351,401)(352,405)(353,404)(354,403)
(355,402)(356,407)(357,406)(358,410)(359,409)(360,408)(361,413)(362,412)
(363,411)(364,415)(365,414)(366,419)(367,418)(368,417)(369,416)(370,420)
(371,425)(372,424)(373,423)(374,422)(375,421);
s1 := Sym(450)!( 1,326)( 2,332)( 3,338)( 4,344)( 5,350)( 6,346)( 7,327)
( 8,333)( 9,339)( 10,345)( 11,341)( 12,347)( 13,328)( 14,334)( 15,340)
( 16,336)( 17,342)( 18,348)( 19,329)( 20,335)( 21,331)( 22,337)( 23,343)
( 24,349)( 25,330)( 26,301)( 27,307)( 28,313)( 29,319)( 30,325)( 31,321)
( 32,302)( 33,308)( 34,314)( 35,320)( 36,316)( 37,322)( 38,303)( 39,309)
( 40,315)( 41,311)( 42,317)( 43,323)( 44,304)( 45,310)( 46,306)( 47,312)
( 48,318)( 49,324)( 50,305)( 51,351)( 52,357)( 53,363)( 54,369)( 55,375)
( 56,371)( 57,352)( 58,358)( 59,364)( 60,370)( 61,366)( 62,372)( 63,353)
( 64,359)( 65,365)( 66,361)( 67,367)( 68,373)( 69,354)( 70,360)( 71,356)
( 72,362)( 73,368)( 74,374)( 75,355)( 76,251)( 77,257)( 78,263)( 79,269)
( 80,275)( 81,271)( 82,252)( 83,258)( 84,264)( 85,270)( 86,266)( 87,272)
( 88,253)( 89,259)( 90,265)( 91,261)( 92,267)( 93,273)( 94,254)( 95,260)
( 96,256)( 97,262)( 98,268)( 99,274)(100,255)(101,226)(102,232)(103,238)
(104,244)(105,250)(106,246)(107,227)(108,233)(109,239)(110,245)(111,241)
(112,247)(113,228)(114,234)(115,240)(116,236)(117,242)(118,248)(119,229)
(120,235)(121,231)(122,237)(123,243)(124,249)(125,230)(126,276)(127,282)
(128,288)(129,294)(130,300)(131,296)(132,277)(133,283)(134,289)(135,295)
(136,291)(137,297)(138,278)(139,284)(140,290)(141,286)(142,292)(143,298)
(144,279)(145,285)(146,281)(147,287)(148,293)(149,299)(150,280)(151,401)
(152,407)(153,413)(154,419)(155,425)(156,421)(157,402)(158,408)(159,414)
(160,420)(161,416)(162,422)(163,403)(164,409)(165,415)(166,411)(167,417)
(168,423)(169,404)(170,410)(171,406)(172,412)(173,418)(174,424)(175,405)
(176,376)(177,382)(178,388)(179,394)(180,400)(181,396)(182,377)(183,383)
(184,389)(185,395)(186,391)(187,397)(188,378)(189,384)(190,390)(191,386)
(192,392)(193,398)(194,379)(195,385)(196,381)(197,387)(198,393)(199,399)
(200,380)(201,426)(202,432)(203,438)(204,444)(205,450)(206,446)(207,427)
(208,433)(209,439)(210,445)(211,441)(212,447)(213,428)(214,434)(215,440)
(216,436)(217,442)(218,448)(219,429)(220,435)(221,431)(222,437)(223,443)
(224,449)(225,430);
s2 := Sym(450)!( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 11)( 16, 24)( 17, 25)
( 18, 21)( 19, 22)( 20, 23)( 26, 37)( 27, 38)( 28, 39)( 29, 40)( 30, 36)
( 41, 49)( 42, 50)( 43, 46)( 44, 47)( 45, 48)( 51, 62)( 52, 63)( 53, 64)
( 54, 65)( 55, 61)( 66, 74)( 67, 75)( 68, 71)( 69, 72)( 70, 73)( 76,162)
( 77,163)( 78,164)( 79,165)( 80,161)( 81,156)( 82,157)( 83,158)( 84,159)
( 85,160)( 86,155)( 87,151)( 88,152)( 89,153)( 90,154)( 91,174)( 92,175)
( 93,171)( 94,172)( 95,173)( 96,168)( 97,169)( 98,170)( 99,166)(100,167)
(101,187)(102,188)(103,189)(104,190)(105,186)(106,181)(107,182)(108,183)
(109,184)(110,185)(111,180)(112,176)(113,177)(114,178)(115,179)(116,199)
(117,200)(118,196)(119,197)(120,198)(121,193)(122,194)(123,195)(124,191)
(125,192)(126,212)(127,213)(128,214)(129,215)(130,211)(131,206)(132,207)
(133,208)(134,209)(135,210)(136,205)(137,201)(138,202)(139,203)(140,204)
(141,224)(142,225)(143,221)(144,222)(145,223)(146,218)(147,219)(148,220)
(149,216)(150,217)(226,237)(227,238)(228,239)(229,240)(230,236)(241,249)
(242,250)(243,246)(244,247)(245,248)(251,262)(252,263)(253,264)(254,265)
(255,261)(266,274)(267,275)(268,271)(269,272)(270,273)(276,287)(277,288)
(278,289)(279,290)(280,286)(291,299)(292,300)(293,296)(294,297)(295,298)
(301,387)(302,388)(303,389)(304,390)(305,386)(306,381)(307,382)(308,383)
(309,384)(310,385)(311,380)(312,376)(313,377)(314,378)(315,379)(316,399)
(317,400)(318,396)(319,397)(320,398)(321,393)(322,394)(323,395)(324,391)
(325,392)(326,412)(327,413)(328,414)(329,415)(330,411)(331,406)(332,407)
(333,408)(334,409)(335,410)(336,405)(337,401)(338,402)(339,403)(340,404)
(341,424)(342,425)(343,421)(344,422)(345,423)(346,418)(347,419)(348,420)
(349,416)(350,417)(351,437)(352,438)(353,439)(354,440)(355,436)(356,431)
(357,432)(358,433)(359,434)(360,435)(361,430)(362,426)(363,427)(364,428)
(365,429)(366,449)(367,450)(368,446)(369,447)(370,448)(371,443)(372,444)
(373,445)(374,441)(375,442);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope