Polytope of Type {6,158}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,158}*1896
Also Known As : {6,158|2}. if this polytope has another name.
Group : SmallGroup(1896,47)
Rank : 3
Schlafli Type : {6,158}
Number of vertices, edges, etc : 6, 474, 158
Order of s0s1s2 : 474
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 : {2,158}*632
6-fold quotients : {2,79}*316
79-fold quotients : {6,2}*24
158-fold quotients : {3,2}*12
237-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 80,159)( 81,160)( 82,161)( 83,162)( 84,163)( 85,164)( 86,165)( 87,166)
( 88,167)( 89,168)( 90,169)( 91,170)( 92,171)( 93,172)( 94,173)( 95,174)
( 96,175)( 97,176)( 98,177)( 99,178)(100,179)(101,180)(102,181)(103,182)
(104,183)(105,184)(106,185)(107,186)(108,187)(109,188)(110,189)(111,190)
(112,191)(113,192)(114,193)(115,194)(116,195)(117,196)(118,197)(119,198)
(120,199)(121,200)(122,201)(123,202)(124,203)(125,204)(126,205)(127,206)
(128,207)(129,208)(130,209)(131,210)(132,211)(133,212)(134,213)(135,214)
(136,215)(137,216)(138,217)(139,218)(140,219)(141,220)(142,221)(143,222)
(144,223)(145,224)(146,225)(147,226)(148,227)(149,228)(150,229)(151,230)
(152,231)(153,232)(154,233)(155,234)(156,235)(157,236)(158,237)(317,396)
(318,397)(319,398)(320,399)(321,400)(322,401)(323,402)(324,403)(325,404)
(326,405)(327,406)(328,407)(329,408)(330,409)(331,410)(332,411)(333,412)
(334,413)(335,414)(336,415)(337,416)(338,417)(339,418)(340,419)(341,420)
(342,421)(343,422)(344,423)(345,424)(346,425)(347,426)(348,427)(349,428)
(350,429)(351,430)(352,431)(353,432)(354,433)(355,434)(356,435)(357,436)
(358,437)(359,438)(360,439)(361,440)(362,441)(363,442)(364,443)(365,444)
(366,445)(367,446)(368,447)(369,448)(370,449)(371,450)(372,451)(373,452)
(374,453)(375,454)(376,455)(377,456)(378,457)(379,458)(380,459)(381,460)
(382,461)(383,462)(384,463)(385,464)(386,465)(387,466)(388,467)(389,468)
(390,469)(391,470)(392,471)(393,472)(394,473)(395,474);;
s1 := ( 1, 80)( 2,158)( 3,157)( 4,156)( 5,155)( 6,154)( 7,153)( 8,152)
( 9,151)( 10,150)( 11,149)( 12,148)( 13,147)( 14,146)( 15,145)( 16,144)
( 17,143)( 18,142)( 19,141)( 20,140)( 21,139)( 22,138)( 23,137)( 24,136)
( 25,135)( 26,134)( 27,133)( 28,132)( 29,131)( 30,130)( 31,129)( 32,128)
( 33,127)( 34,126)( 35,125)( 36,124)( 37,123)( 38,122)( 39,121)( 40,120)
( 41,119)( 42,118)( 43,117)( 44,116)( 45,115)( 46,114)( 47,113)( 48,112)
( 49,111)( 50,110)( 51,109)( 52,108)( 53,107)( 54,106)( 55,105)( 56,104)
( 57,103)( 58,102)( 59,101)( 60,100)( 61, 99)( 62, 98)( 63, 97)( 64, 96)
( 65, 95)( 66, 94)( 67, 93)( 68, 92)( 69, 91)( 70, 90)( 71, 89)( 72, 88)
( 73, 87)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81)(160,237)
(161,236)(162,235)(163,234)(164,233)(165,232)(166,231)(167,230)(168,229)
(169,228)(170,227)(171,226)(172,225)(173,224)(174,223)(175,222)(176,221)
(177,220)(178,219)(179,218)(180,217)(181,216)(182,215)(183,214)(184,213)
(185,212)(186,211)(187,210)(188,209)(189,208)(190,207)(191,206)(192,205)
(193,204)(194,203)(195,202)(196,201)(197,200)(198,199)(238,317)(239,395)
(240,394)(241,393)(242,392)(243,391)(244,390)(245,389)(246,388)(247,387)
(248,386)(249,385)(250,384)(251,383)(252,382)(253,381)(254,380)(255,379)
(256,378)(257,377)(258,376)(259,375)(260,374)(261,373)(262,372)(263,371)
(264,370)(265,369)(266,368)(267,367)(268,366)(269,365)(270,364)(271,363)
(272,362)(273,361)(274,360)(275,359)(276,358)(277,357)(278,356)(279,355)
(280,354)(281,353)(282,352)(283,351)(284,350)(285,349)(286,348)(287,347)
(288,346)(289,345)(290,344)(291,343)(292,342)(293,341)(294,340)(295,339)
(296,338)(297,337)(298,336)(299,335)(300,334)(301,333)(302,332)(303,331)
(304,330)(305,329)(306,328)(307,327)(308,326)(309,325)(310,324)(311,323)
(312,322)(313,321)(314,320)(315,319)(316,318)(397,474)(398,473)(399,472)
(400,471)(401,470)(402,469)(403,468)(404,467)(405,466)(406,465)(407,464)
(408,463)(409,462)(410,461)(411,460)(412,459)(413,458)(414,457)(415,456)
(416,455)(417,454)(418,453)(419,452)(420,451)(421,450)(422,449)(423,448)
(424,447)(425,446)(426,445)(427,444)(428,443)(429,442)(430,441)(431,440)
(432,439)(433,438)(434,437)(435,436);;
s2 := ( 1,239)( 2,238)( 3,316)( 4,315)( 5,314)( 6,313)( 7,312)( 8,311)
( 9,310)( 10,309)( 11,308)( 12,307)( 13,306)( 14,305)( 15,304)( 16,303)
( 17,302)( 18,301)( 19,300)( 20,299)( 21,298)( 22,297)( 23,296)( 24,295)
( 25,294)( 26,293)( 27,292)( 28,291)( 29,290)( 30,289)( 31,288)( 32,287)
( 33,286)( 34,285)( 35,284)( 36,283)( 37,282)( 38,281)( 39,280)( 40,279)
( 41,278)( 42,277)( 43,276)( 44,275)( 45,274)( 46,273)( 47,272)( 48,271)
( 49,270)( 50,269)( 51,268)( 52,267)( 53,266)( 54,265)( 55,264)( 56,263)
( 57,262)( 58,261)( 59,260)( 60,259)( 61,258)( 62,257)( 63,256)( 64,255)
( 65,254)( 66,253)( 67,252)( 68,251)( 69,250)( 70,249)( 71,248)( 72,247)
( 73,246)( 74,245)( 75,244)( 76,243)( 77,242)( 78,241)( 79,240)( 80,318)
( 81,317)( 82,395)( 83,394)( 84,393)( 85,392)( 86,391)( 87,390)( 88,389)
( 89,388)( 90,387)( 91,386)( 92,385)( 93,384)( 94,383)( 95,382)( 96,381)
( 97,380)( 98,379)( 99,378)(100,377)(101,376)(102,375)(103,374)(104,373)
(105,372)(106,371)(107,370)(108,369)(109,368)(110,367)(111,366)(112,365)
(113,364)(114,363)(115,362)(116,361)(117,360)(118,359)(119,358)(120,357)
(121,356)(122,355)(123,354)(124,353)(125,352)(126,351)(127,350)(128,349)
(129,348)(130,347)(131,346)(132,345)(133,344)(134,343)(135,342)(136,341)
(137,340)(138,339)(139,338)(140,337)(141,336)(142,335)(143,334)(144,333)
(145,332)(146,331)(147,330)(148,329)(149,328)(150,327)(151,326)(152,325)
(153,324)(154,323)(155,322)(156,321)(157,320)(158,319)(159,397)(160,396)
(161,474)(162,473)(163,472)(164,471)(165,470)(166,469)(167,468)(168,467)
(169,466)(170,465)(171,464)(172,463)(173,462)(174,461)(175,460)(176,459)
(177,458)(178,457)(179,456)(180,455)(181,454)(182,453)(183,452)(184,451)
(185,450)(186,449)(187,448)(188,447)(189,446)(190,445)(191,444)(192,443)
(193,442)(194,441)(195,440)(196,439)(197,438)(198,437)(199,436)(200,435)
(201,434)(202,433)(203,432)(204,431)(205,430)(206,429)(207,428)(208,427)
(209,426)(210,425)(211,424)(212,423)(213,422)(214,421)(215,420)(216,419)
(217,418)(218,417)(219,416)(220,415)(221,414)(222,413)(223,412)(224,411)
(225,410)(226,409)(227,408)(228,407)(229,406)(230,405)(231,404)(232,403)
(233,402)(234,401)(235,400)(236,399)(237,398);;
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(474)!( 80,159)( 81,160)( 82,161)( 83,162)( 84,163)( 85,164)( 86,165)
( 87,166)( 88,167)( 89,168)( 90,169)( 91,170)( 92,171)( 93,172)( 94,173)
( 95,174)( 96,175)( 97,176)( 98,177)( 99,178)(100,179)(101,180)(102,181)
(103,182)(104,183)(105,184)(106,185)(107,186)(108,187)(109,188)(110,189)
(111,190)(112,191)(113,192)(114,193)(115,194)(116,195)(117,196)(118,197)
(119,198)(120,199)(121,200)(122,201)(123,202)(124,203)(125,204)(126,205)
(127,206)(128,207)(129,208)(130,209)(131,210)(132,211)(133,212)(134,213)
(135,214)(136,215)(137,216)(138,217)(139,218)(140,219)(141,220)(142,221)
(143,222)(144,223)(145,224)(146,225)(147,226)(148,227)(149,228)(150,229)
(151,230)(152,231)(153,232)(154,233)(155,234)(156,235)(157,236)(158,237)
(317,396)(318,397)(319,398)(320,399)(321,400)(322,401)(323,402)(324,403)
(325,404)(326,405)(327,406)(328,407)(329,408)(330,409)(331,410)(332,411)
(333,412)(334,413)(335,414)(336,415)(337,416)(338,417)(339,418)(340,419)
(341,420)(342,421)(343,422)(344,423)(345,424)(346,425)(347,426)(348,427)
(349,428)(350,429)(351,430)(352,431)(353,432)(354,433)(355,434)(356,435)
(357,436)(358,437)(359,438)(360,439)(361,440)(362,441)(363,442)(364,443)
(365,444)(366,445)(367,446)(368,447)(369,448)(370,449)(371,450)(372,451)
(373,452)(374,453)(375,454)(376,455)(377,456)(378,457)(379,458)(380,459)
(381,460)(382,461)(383,462)(384,463)(385,464)(386,465)(387,466)(388,467)
(389,468)(390,469)(391,470)(392,471)(393,472)(394,473)(395,474);
s1 := Sym(474)!( 1, 80)( 2,158)( 3,157)( 4,156)( 5,155)( 6,154)( 7,153)
( 8,152)( 9,151)( 10,150)( 11,149)( 12,148)( 13,147)( 14,146)( 15,145)
( 16,144)( 17,143)( 18,142)( 19,141)( 20,140)( 21,139)( 22,138)( 23,137)
( 24,136)( 25,135)( 26,134)( 27,133)( 28,132)( 29,131)( 30,130)( 31,129)
( 32,128)( 33,127)( 34,126)( 35,125)( 36,124)( 37,123)( 38,122)( 39,121)
( 40,120)( 41,119)( 42,118)( 43,117)( 44,116)( 45,115)( 46,114)( 47,113)
( 48,112)( 49,111)( 50,110)( 51,109)( 52,108)( 53,107)( 54,106)( 55,105)
( 56,104)( 57,103)( 58,102)( 59,101)( 60,100)( 61, 99)( 62, 98)( 63, 97)
( 64, 96)( 65, 95)( 66, 94)( 67, 93)( 68, 92)( 69, 91)( 70, 90)( 71, 89)
( 72, 88)( 73, 87)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81)
(160,237)(161,236)(162,235)(163,234)(164,233)(165,232)(166,231)(167,230)
(168,229)(169,228)(170,227)(171,226)(172,225)(173,224)(174,223)(175,222)
(176,221)(177,220)(178,219)(179,218)(180,217)(181,216)(182,215)(183,214)
(184,213)(185,212)(186,211)(187,210)(188,209)(189,208)(190,207)(191,206)
(192,205)(193,204)(194,203)(195,202)(196,201)(197,200)(198,199)(238,317)
(239,395)(240,394)(241,393)(242,392)(243,391)(244,390)(245,389)(246,388)
(247,387)(248,386)(249,385)(250,384)(251,383)(252,382)(253,381)(254,380)
(255,379)(256,378)(257,377)(258,376)(259,375)(260,374)(261,373)(262,372)
(263,371)(264,370)(265,369)(266,368)(267,367)(268,366)(269,365)(270,364)
(271,363)(272,362)(273,361)(274,360)(275,359)(276,358)(277,357)(278,356)
(279,355)(280,354)(281,353)(282,352)(283,351)(284,350)(285,349)(286,348)
(287,347)(288,346)(289,345)(290,344)(291,343)(292,342)(293,341)(294,340)
(295,339)(296,338)(297,337)(298,336)(299,335)(300,334)(301,333)(302,332)
(303,331)(304,330)(305,329)(306,328)(307,327)(308,326)(309,325)(310,324)
(311,323)(312,322)(313,321)(314,320)(315,319)(316,318)(397,474)(398,473)
(399,472)(400,471)(401,470)(402,469)(403,468)(404,467)(405,466)(406,465)
(407,464)(408,463)(409,462)(410,461)(411,460)(412,459)(413,458)(414,457)
(415,456)(416,455)(417,454)(418,453)(419,452)(420,451)(421,450)(422,449)
(423,448)(424,447)(425,446)(426,445)(427,444)(428,443)(429,442)(430,441)
(431,440)(432,439)(433,438)(434,437)(435,436);
s2 := Sym(474)!( 1,239)( 2,238)( 3,316)( 4,315)( 5,314)( 6,313)( 7,312)
( 8,311)( 9,310)( 10,309)( 11,308)( 12,307)( 13,306)( 14,305)( 15,304)
( 16,303)( 17,302)( 18,301)( 19,300)( 20,299)( 21,298)( 22,297)( 23,296)
( 24,295)( 25,294)( 26,293)( 27,292)( 28,291)( 29,290)( 30,289)( 31,288)
( 32,287)( 33,286)( 34,285)( 35,284)( 36,283)( 37,282)( 38,281)( 39,280)
( 40,279)( 41,278)( 42,277)( 43,276)( 44,275)( 45,274)( 46,273)( 47,272)
( 48,271)( 49,270)( 50,269)( 51,268)( 52,267)( 53,266)( 54,265)( 55,264)
( 56,263)( 57,262)( 58,261)( 59,260)( 60,259)( 61,258)( 62,257)( 63,256)
( 64,255)( 65,254)( 66,253)( 67,252)( 68,251)( 69,250)( 70,249)( 71,248)
( 72,247)( 73,246)( 74,245)( 75,244)( 76,243)( 77,242)( 78,241)( 79,240)
( 80,318)( 81,317)( 82,395)( 83,394)( 84,393)( 85,392)( 86,391)( 87,390)
( 88,389)( 89,388)( 90,387)( 91,386)( 92,385)( 93,384)( 94,383)( 95,382)
( 96,381)( 97,380)( 98,379)( 99,378)(100,377)(101,376)(102,375)(103,374)
(104,373)(105,372)(106,371)(107,370)(108,369)(109,368)(110,367)(111,366)
(112,365)(113,364)(114,363)(115,362)(116,361)(117,360)(118,359)(119,358)
(120,357)(121,356)(122,355)(123,354)(124,353)(125,352)(126,351)(127,350)
(128,349)(129,348)(130,347)(131,346)(132,345)(133,344)(134,343)(135,342)
(136,341)(137,340)(138,339)(139,338)(140,337)(141,336)(142,335)(143,334)
(144,333)(145,332)(146,331)(147,330)(148,329)(149,328)(150,327)(151,326)
(152,325)(153,324)(154,323)(155,322)(156,321)(157,320)(158,319)(159,397)
(160,396)(161,474)(162,473)(163,472)(164,471)(165,470)(166,469)(167,468)
(168,467)(169,466)(170,465)(171,464)(172,463)(173,462)(174,461)(175,460)
(176,459)(177,458)(178,457)(179,456)(180,455)(181,454)(182,453)(183,452)
(184,451)(185,450)(186,449)(187,448)(188,447)(189,446)(190,445)(191,444)
(192,443)(193,442)(194,441)(195,440)(196,439)(197,438)(198,437)(199,436)
(200,435)(201,434)(202,433)(203,432)(204,431)(205,430)(206,429)(207,428)
(208,427)(209,426)(210,425)(211,424)(212,423)(213,422)(214,421)(215,420)
(216,419)(217,418)(218,417)(219,416)(220,415)(221,414)(222,413)(223,412)
(224,411)(225,410)(226,409)(227,408)(228,407)(229,406)(230,405)(231,404)
(232,403)(233,402)(234,401)(235,400)(236,399)(237,398);
poly := sub<Sym(474)|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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope