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