Polytope of Type {6,154}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,154}*1848
Also Known As : {6,154|2}. if this polytope has another name.
Group : SmallGroup(1848,150)
Rank : 3
Schlafli Type : {6,154}
Number of vertices, edges, etc : 6, 462, 154
Order of s0s1s2 : 462
Order of s0s1s2s1 : 2
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) :
3-fold quotients : {2,154}*616
6-fold quotients : {2,77}*308
7-fold quotients : {6,22}*264
11-fold quotients : {6,14}*168
21-fold quotients : {2,22}*88
33-fold quotients : {2,14}*56
42-fold quotients : {2,11}*44
66-fold quotients : {2,7}*28
77-fold quotients : {6,2}*24
154-fold quotients : {3,2}*12
231-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 78,155)( 79,156)( 80,157)( 81,158)( 82,159)( 83,160)( 84,161)( 85,162)
( 86,163)( 87,164)( 88,165)( 89,166)( 90,167)( 91,168)( 92,169)( 93,170)
( 94,171)( 95,172)( 96,173)( 97,174)( 98,175)( 99,176)(100,177)(101,178)
(102,179)(103,180)(104,181)(105,182)(106,183)(107,184)(108,185)(109,186)
(110,187)(111,188)(112,189)(113,190)(114,191)(115,192)(116,193)(117,194)
(118,195)(119,196)(120,197)(121,198)(122,199)(123,200)(124,201)(125,202)
(126,203)(127,204)(128,205)(129,206)(130,207)(131,208)(132,209)(133,210)
(134,211)(135,212)(136,213)(137,214)(138,215)(139,216)(140,217)(141,218)
(142,219)(143,220)(144,221)(145,222)(146,223)(147,224)(148,225)(149,226)
(150,227)(151,228)(152,229)(153,230)(154,231)(309,386)(310,387)(311,388)
(312,389)(313,390)(314,391)(315,392)(316,393)(317,394)(318,395)(319,396)
(320,397)(321,398)(322,399)(323,400)(324,401)(325,402)(326,403)(327,404)
(328,405)(329,406)(330,407)(331,408)(332,409)(333,410)(334,411)(335,412)
(336,413)(337,414)(338,415)(339,416)(340,417)(341,418)(342,419)(343,420)
(344,421)(345,422)(346,423)(347,424)(348,425)(349,426)(350,427)(351,428)
(352,429)(353,430)(354,431)(355,432)(356,433)(357,434)(358,435)(359,436)
(360,437)(361,438)(362,439)(363,440)(364,441)(365,442)(366,443)(367,444)
(368,445)(369,446)(370,447)(371,448)(372,449)(373,450)(374,451)(375,452)
(376,453)(377,454)(378,455)(379,456)(380,457)(381,458)(382,459)(383,460)
(384,461)(385,462);;
s1 := ( 1, 78)( 2, 88)( 3, 87)( 4, 86)( 5, 85)( 6, 84)( 7, 83)( 8, 82)
( 9, 81)( 10, 80)( 11, 79)( 12,144)( 13,154)( 14,153)( 15,152)( 16,151)
( 17,150)( 18,149)( 19,148)( 20,147)( 21,146)( 22,145)( 23,133)( 24,143)
( 25,142)( 26,141)( 27,140)( 28,139)( 29,138)( 30,137)( 31,136)( 32,135)
( 33,134)( 34,122)( 35,132)( 36,131)( 37,130)( 38,129)( 39,128)( 40,127)
( 41,126)( 42,125)( 43,124)( 44,123)( 45,111)( 46,121)( 47,120)( 48,119)
( 49,118)( 50,117)( 51,116)( 52,115)( 53,114)( 54,113)( 55,112)( 56,100)
( 57,110)( 58,109)( 59,108)( 60,107)( 61,106)( 62,105)( 63,104)( 64,103)
( 65,102)( 66,101)( 67, 89)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)
( 73, 94)( 74, 93)( 75, 92)( 76, 91)( 77, 90)(156,165)(157,164)(158,163)
(159,162)(160,161)(166,221)(167,231)(168,230)(169,229)(170,228)(171,227)
(172,226)(173,225)(174,224)(175,223)(176,222)(177,210)(178,220)(179,219)
(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)(186,212)(187,211)
(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)(194,204)(195,203)
(196,202)(197,201)(198,200)(232,309)(233,319)(234,318)(235,317)(236,316)
(237,315)(238,314)(239,313)(240,312)(241,311)(242,310)(243,375)(244,385)
(245,384)(246,383)(247,382)(248,381)(249,380)(250,379)(251,378)(252,377)
(253,376)(254,364)(255,374)(256,373)(257,372)(258,371)(259,370)(260,369)
(261,368)(262,367)(263,366)(264,365)(265,353)(266,363)(267,362)(268,361)
(269,360)(270,359)(271,358)(272,357)(273,356)(274,355)(275,354)(276,342)
(277,352)(278,351)(279,350)(280,349)(281,348)(282,347)(283,346)(284,345)
(285,344)(286,343)(287,331)(288,341)(289,340)(290,339)(291,338)(292,337)
(293,336)(294,335)(295,334)(296,333)(297,332)(298,320)(299,330)(300,329)
(301,328)(302,327)(303,326)(304,325)(305,324)(306,323)(307,322)(308,321)
(387,396)(388,395)(389,394)(390,393)(391,392)(397,452)(398,462)(399,461)
(400,460)(401,459)(402,458)(403,457)(404,456)(405,455)(406,454)(407,453)
(408,441)(409,451)(410,450)(411,449)(412,448)(413,447)(414,446)(415,445)
(416,444)(417,443)(418,442)(419,430)(420,440)(421,439)(422,438)(423,437)
(424,436)(425,435)(426,434)(427,433)(428,432)(429,431);;
s2 := ( 1,244)( 2,243)( 3,253)( 4,252)( 5,251)( 6,250)( 7,249)( 8,248)
( 9,247)( 10,246)( 11,245)( 12,233)( 13,232)( 14,242)( 15,241)( 16,240)
( 17,239)( 18,238)( 19,237)( 20,236)( 21,235)( 22,234)( 23,299)( 24,298)
( 25,308)( 26,307)( 27,306)( 28,305)( 29,304)( 30,303)( 31,302)( 32,301)
( 33,300)( 34,288)( 35,287)( 36,297)( 37,296)( 38,295)( 39,294)( 40,293)
( 41,292)( 42,291)( 43,290)( 44,289)( 45,277)( 46,276)( 47,286)( 48,285)
( 49,284)( 50,283)( 51,282)( 52,281)( 53,280)( 54,279)( 55,278)( 56,266)
( 57,265)( 58,275)( 59,274)( 60,273)( 61,272)( 62,271)( 63,270)( 64,269)
( 65,268)( 66,267)( 67,255)( 68,254)( 69,264)( 70,263)( 71,262)( 72,261)
( 73,260)( 74,259)( 75,258)( 76,257)( 77,256)( 78,321)( 79,320)( 80,330)
( 81,329)( 82,328)( 83,327)( 84,326)( 85,325)( 86,324)( 87,323)( 88,322)
( 89,310)( 90,309)( 91,319)( 92,318)( 93,317)( 94,316)( 95,315)( 96,314)
( 97,313)( 98,312)( 99,311)(100,376)(101,375)(102,385)(103,384)(104,383)
(105,382)(106,381)(107,380)(108,379)(109,378)(110,377)(111,365)(112,364)
(113,374)(114,373)(115,372)(116,371)(117,370)(118,369)(119,368)(120,367)
(121,366)(122,354)(123,353)(124,363)(125,362)(126,361)(127,360)(128,359)
(129,358)(130,357)(131,356)(132,355)(133,343)(134,342)(135,352)(136,351)
(137,350)(138,349)(139,348)(140,347)(141,346)(142,345)(143,344)(144,332)
(145,331)(146,341)(147,340)(148,339)(149,338)(150,337)(151,336)(152,335)
(153,334)(154,333)(155,398)(156,397)(157,407)(158,406)(159,405)(160,404)
(161,403)(162,402)(163,401)(164,400)(165,399)(166,387)(167,386)(168,396)
(169,395)(170,394)(171,393)(172,392)(173,391)(174,390)(175,389)(176,388)
(177,453)(178,452)(179,462)(180,461)(181,460)(182,459)(183,458)(184,457)
(185,456)(186,455)(187,454)(188,442)(189,441)(190,451)(191,450)(192,449)
(193,448)(194,447)(195,446)(196,445)(197,444)(198,443)(199,431)(200,430)
(201,440)(202,439)(203,438)(204,437)(205,436)(206,435)(207,434)(208,433)
(209,432)(210,420)(211,419)(212,429)(213,428)(214,427)(215,426)(216,425)
(217,424)(218,423)(219,422)(220,421)(221,409)(222,408)(223,418)(224,417)
(225,416)(226,415)(227,414)(228,413)(229,412)(230,411)(231,410);;
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*s2*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(462)!( 78,155)( 79,156)( 80,157)( 81,158)( 82,159)( 83,160)( 84,161)
( 85,162)( 86,163)( 87,164)( 88,165)( 89,166)( 90,167)( 91,168)( 92,169)
( 93,170)( 94,171)( 95,172)( 96,173)( 97,174)( 98,175)( 99,176)(100,177)
(101,178)(102,179)(103,180)(104,181)(105,182)(106,183)(107,184)(108,185)
(109,186)(110,187)(111,188)(112,189)(113,190)(114,191)(115,192)(116,193)
(117,194)(118,195)(119,196)(120,197)(121,198)(122,199)(123,200)(124,201)
(125,202)(126,203)(127,204)(128,205)(129,206)(130,207)(131,208)(132,209)
(133,210)(134,211)(135,212)(136,213)(137,214)(138,215)(139,216)(140,217)
(141,218)(142,219)(143,220)(144,221)(145,222)(146,223)(147,224)(148,225)
(149,226)(150,227)(151,228)(152,229)(153,230)(154,231)(309,386)(310,387)
(311,388)(312,389)(313,390)(314,391)(315,392)(316,393)(317,394)(318,395)
(319,396)(320,397)(321,398)(322,399)(323,400)(324,401)(325,402)(326,403)
(327,404)(328,405)(329,406)(330,407)(331,408)(332,409)(333,410)(334,411)
(335,412)(336,413)(337,414)(338,415)(339,416)(340,417)(341,418)(342,419)
(343,420)(344,421)(345,422)(346,423)(347,424)(348,425)(349,426)(350,427)
(351,428)(352,429)(353,430)(354,431)(355,432)(356,433)(357,434)(358,435)
(359,436)(360,437)(361,438)(362,439)(363,440)(364,441)(365,442)(366,443)
(367,444)(368,445)(369,446)(370,447)(371,448)(372,449)(373,450)(374,451)
(375,452)(376,453)(377,454)(378,455)(379,456)(380,457)(381,458)(382,459)
(383,460)(384,461)(385,462);
s1 := Sym(462)!( 1, 78)( 2, 88)( 3, 87)( 4, 86)( 5, 85)( 6, 84)( 7, 83)
( 8, 82)( 9, 81)( 10, 80)( 11, 79)( 12,144)( 13,154)( 14,153)( 15,152)
( 16,151)( 17,150)( 18,149)( 19,148)( 20,147)( 21,146)( 22,145)( 23,133)
( 24,143)( 25,142)( 26,141)( 27,140)( 28,139)( 29,138)( 30,137)( 31,136)
( 32,135)( 33,134)( 34,122)( 35,132)( 36,131)( 37,130)( 38,129)( 39,128)
( 40,127)( 41,126)( 42,125)( 43,124)( 44,123)( 45,111)( 46,121)( 47,120)
( 48,119)( 49,118)( 50,117)( 51,116)( 52,115)( 53,114)( 54,113)( 55,112)
( 56,100)( 57,110)( 58,109)( 59,108)( 60,107)( 61,106)( 62,105)( 63,104)
( 64,103)( 65,102)( 66,101)( 67, 89)( 68, 99)( 69, 98)( 70, 97)( 71, 96)
( 72, 95)( 73, 94)( 74, 93)( 75, 92)( 76, 91)( 77, 90)(156,165)(157,164)
(158,163)(159,162)(160,161)(166,221)(167,231)(168,230)(169,229)(170,228)
(171,227)(172,226)(173,225)(174,224)(175,223)(176,222)(177,210)(178,220)
(179,219)(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)(186,212)
(187,211)(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)(194,204)
(195,203)(196,202)(197,201)(198,200)(232,309)(233,319)(234,318)(235,317)
(236,316)(237,315)(238,314)(239,313)(240,312)(241,311)(242,310)(243,375)
(244,385)(245,384)(246,383)(247,382)(248,381)(249,380)(250,379)(251,378)
(252,377)(253,376)(254,364)(255,374)(256,373)(257,372)(258,371)(259,370)
(260,369)(261,368)(262,367)(263,366)(264,365)(265,353)(266,363)(267,362)
(268,361)(269,360)(270,359)(271,358)(272,357)(273,356)(274,355)(275,354)
(276,342)(277,352)(278,351)(279,350)(280,349)(281,348)(282,347)(283,346)
(284,345)(285,344)(286,343)(287,331)(288,341)(289,340)(290,339)(291,338)
(292,337)(293,336)(294,335)(295,334)(296,333)(297,332)(298,320)(299,330)
(300,329)(301,328)(302,327)(303,326)(304,325)(305,324)(306,323)(307,322)
(308,321)(387,396)(388,395)(389,394)(390,393)(391,392)(397,452)(398,462)
(399,461)(400,460)(401,459)(402,458)(403,457)(404,456)(405,455)(406,454)
(407,453)(408,441)(409,451)(410,450)(411,449)(412,448)(413,447)(414,446)
(415,445)(416,444)(417,443)(418,442)(419,430)(420,440)(421,439)(422,438)
(423,437)(424,436)(425,435)(426,434)(427,433)(428,432)(429,431);
s2 := Sym(462)!( 1,244)( 2,243)( 3,253)( 4,252)( 5,251)( 6,250)( 7,249)
( 8,248)( 9,247)( 10,246)( 11,245)( 12,233)( 13,232)( 14,242)( 15,241)
( 16,240)( 17,239)( 18,238)( 19,237)( 20,236)( 21,235)( 22,234)( 23,299)
( 24,298)( 25,308)( 26,307)( 27,306)( 28,305)( 29,304)( 30,303)( 31,302)
( 32,301)( 33,300)( 34,288)( 35,287)( 36,297)( 37,296)( 38,295)( 39,294)
( 40,293)( 41,292)( 42,291)( 43,290)( 44,289)( 45,277)( 46,276)( 47,286)
( 48,285)( 49,284)( 50,283)( 51,282)( 52,281)( 53,280)( 54,279)( 55,278)
( 56,266)( 57,265)( 58,275)( 59,274)( 60,273)( 61,272)( 62,271)( 63,270)
( 64,269)( 65,268)( 66,267)( 67,255)( 68,254)( 69,264)( 70,263)( 71,262)
( 72,261)( 73,260)( 74,259)( 75,258)( 76,257)( 77,256)( 78,321)( 79,320)
( 80,330)( 81,329)( 82,328)( 83,327)( 84,326)( 85,325)( 86,324)( 87,323)
( 88,322)( 89,310)( 90,309)( 91,319)( 92,318)( 93,317)( 94,316)( 95,315)
( 96,314)( 97,313)( 98,312)( 99,311)(100,376)(101,375)(102,385)(103,384)
(104,383)(105,382)(106,381)(107,380)(108,379)(109,378)(110,377)(111,365)
(112,364)(113,374)(114,373)(115,372)(116,371)(117,370)(118,369)(119,368)
(120,367)(121,366)(122,354)(123,353)(124,363)(125,362)(126,361)(127,360)
(128,359)(129,358)(130,357)(131,356)(132,355)(133,343)(134,342)(135,352)
(136,351)(137,350)(138,349)(139,348)(140,347)(141,346)(142,345)(143,344)
(144,332)(145,331)(146,341)(147,340)(148,339)(149,338)(150,337)(151,336)
(152,335)(153,334)(154,333)(155,398)(156,397)(157,407)(158,406)(159,405)
(160,404)(161,403)(162,402)(163,401)(164,400)(165,399)(166,387)(167,386)
(168,396)(169,395)(170,394)(171,393)(172,392)(173,391)(174,390)(175,389)
(176,388)(177,453)(178,452)(179,462)(180,461)(181,460)(182,459)(183,458)
(184,457)(185,456)(186,455)(187,454)(188,442)(189,441)(190,451)(191,450)
(192,449)(193,448)(194,447)(195,446)(196,445)(197,444)(198,443)(199,431)
(200,430)(201,440)(202,439)(203,438)(204,437)(205,436)(206,435)(207,434)
(208,433)(209,432)(210,420)(211,419)(212,429)(213,428)(214,427)(215,426)
(216,425)(217,424)(218,423)(219,422)(220,421)(221,409)(222,408)(223,418)
(224,417)(225,416)(226,415)(227,414)(228,413)(229,412)(230,411)(231,410);
poly := sub<Sym(462)|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*s2*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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope