Polytope of Type {68,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {68,14}*1904
Also Known As : {68,14|2}. if this polytope has another name.
Group : SmallGroup(1904,123)
Rank : 3
Schlafli Type : {68,14}
Number of vertices, edges, etc : 68, 476, 14
Order of s0s1s2 : 476
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) :
2-fold quotients : {34,14}*952
7-fold quotients : {68,2}*272
14-fold quotients : {34,2}*136
17-fold quotients : {4,14}*112
28-fold quotients : {17,2}*68
34-fold quotients : {2,14}*56
68-fold quotients : {2,7}*28
119-fold quotients : {4,2}*16
238-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)( 9, 10)
( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)( 26, 27)
( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 43, 44)
( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)
( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 77, 78)
( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)
(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)
(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)
(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146)
(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)
(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)(179,180)
(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197)
(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)(213,214)
(223,238)(224,237)(225,236)(226,235)(227,234)(228,233)(229,232)(230,231)
(239,358)(240,374)(241,373)(242,372)(243,371)(244,370)(245,369)(246,368)
(247,367)(248,366)(249,365)(250,364)(251,363)(252,362)(253,361)(254,360)
(255,359)(256,375)(257,391)(258,390)(259,389)(260,388)(261,387)(262,386)
(263,385)(264,384)(265,383)(266,382)(267,381)(268,380)(269,379)(270,378)
(271,377)(272,376)(273,392)(274,408)(275,407)(276,406)(277,405)(278,404)
(279,403)(280,402)(281,401)(282,400)(283,399)(284,398)(285,397)(286,396)
(287,395)(288,394)(289,393)(290,409)(291,425)(292,424)(293,423)(294,422)
(295,421)(296,420)(297,419)(298,418)(299,417)(300,416)(301,415)(302,414)
(303,413)(304,412)(305,411)(306,410)(307,426)(308,442)(309,441)(310,440)
(311,439)(312,438)(313,437)(314,436)(315,435)(316,434)(317,433)(318,432)
(319,431)(320,430)(321,429)(322,428)(323,427)(324,443)(325,459)(326,458)
(327,457)(328,456)(329,455)(330,454)(331,453)(332,452)(333,451)(334,450)
(335,449)(336,448)(337,447)(338,446)(339,445)(340,444)(341,460)(342,476)
(343,475)(344,474)(345,473)(346,472)(347,471)(348,470)(349,469)(350,468)
(351,467)(352,466)(353,465)(354,464)(355,463)(356,462)(357,461);;
s1 := ( 1,240)( 2,239)( 3,255)( 4,254)( 5,253)( 6,252)( 7,251)( 8,250)
( 9,249)( 10,248)( 11,247)( 12,246)( 13,245)( 14,244)( 15,243)( 16,242)
( 17,241)( 18,342)( 19,341)( 20,357)( 21,356)( 22,355)( 23,354)( 24,353)
( 25,352)( 26,351)( 27,350)( 28,349)( 29,348)( 30,347)( 31,346)( 32,345)
( 33,344)( 34,343)( 35,325)( 36,324)( 37,340)( 38,339)( 39,338)( 40,337)
( 41,336)( 42,335)( 43,334)( 44,333)( 45,332)( 46,331)( 47,330)( 48,329)
( 49,328)( 50,327)( 51,326)( 52,308)( 53,307)( 54,323)( 55,322)( 56,321)
( 57,320)( 58,319)( 59,318)( 60,317)( 61,316)( 62,315)( 63,314)( 64,313)
( 65,312)( 66,311)( 67,310)( 68,309)( 69,291)( 70,290)( 71,306)( 72,305)
( 73,304)( 74,303)( 75,302)( 76,301)( 77,300)( 78,299)( 79,298)( 80,297)
( 81,296)( 82,295)( 83,294)( 84,293)( 85,292)( 86,274)( 87,273)( 88,289)
( 89,288)( 90,287)( 91,286)( 92,285)( 93,284)( 94,283)( 95,282)( 96,281)
( 97,280)( 98,279)( 99,278)(100,277)(101,276)(102,275)(103,257)(104,256)
(105,272)(106,271)(107,270)(108,269)(109,268)(110,267)(111,266)(112,265)
(113,264)(114,263)(115,262)(116,261)(117,260)(118,259)(119,258)(120,359)
(121,358)(122,374)(123,373)(124,372)(125,371)(126,370)(127,369)(128,368)
(129,367)(130,366)(131,365)(132,364)(133,363)(134,362)(135,361)(136,360)
(137,461)(138,460)(139,476)(140,475)(141,474)(142,473)(143,472)(144,471)
(145,470)(146,469)(147,468)(148,467)(149,466)(150,465)(151,464)(152,463)
(153,462)(154,444)(155,443)(156,459)(157,458)(158,457)(159,456)(160,455)
(161,454)(162,453)(163,452)(164,451)(165,450)(166,449)(167,448)(168,447)
(169,446)(170,445)(171,427)(172,426)(173,442)(174,441)(175,440)(176,439)
(177,438)(178,437)(179,436)(180,435)(181,434)(182,433)(183,432)(184,431)
(185,430)(186,429)(187,428)(188,410)(189,409)(190,425)(191,424)(192,423)
(193,422)(194,421)(195,420)(196,419)(197,418)(198,417)(199,416)(200,415)
(201,414)(202,413)(203,412)(204,411)(205,393)(206,392)(207,408)(208,407)
(209,406)(210,405)(211,404)(212,403)(213,402)(214,401)(215,400)(216,399)
(217,398)(218,397)(219,396)(220,395)(221,394)(222,376)(223,375)(224,391)
(225,390)(226,389)(227,388)(228,387)(229,386)(230,385)(231,384)(232,383)
(233,382)(234,381)(235,380)(236,379)(237,378)(238,377);;
s2 := ( 1, 18)( 2, 19)( 3, 20)( 4, 21)( 5, 22)( 6, 23)( 7, 24)( 8, 25)
( 9, 26)( 10, 27)( 11, 28)( 12, 29)( 13, 30)( 14, 31)( 15, 32)( 16, 33)
( 17, 34)( 35,103)( 36,104)( 37,105)( 38,106)( 39,107)( 40,108)( 41,109)
( 42,110)( 43,111)( 44,112)( 45,113)( 46,114)( 47,115)( 48,116)( 49,117)
( 50,118)( 51,119)( 52, 86)( 53, 87)( 54, 88)( 55, 89)( 56, 90)( 57, 91)
( 58, 92)( 59, 93)( 60, 94)( 61, 95)( 62, 96)( 63, 97)( 64, 98)( 65, 99)
( 66,100)( 67,101)( 68,102)(120,137)(121,138)(122,139)(123,140)(124,141)
(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)
(133,150)(134,151)(135,152)(136,153)(154,222)(155,223)(156,224)(157,225)
(158,226)(159,227)(160,228)(161,229)(162,230)(163,231)(164,232)(165,233)
(166,234)(167,235)(168,236)(169,237)(170,238)(171,205)(172,206)(173,207)
(174,208)(175,209)(176,210)(177,211)(178,212)(179,213)(180,214)(181,215)
(182,216)(183,217)(184,218)(185,219)(186,220)(187,221)(239,256)(240,257)
(241,258)(242,259)(243,260)(244,261)(245,262)(246,263)(247,264)(248,265)
(249,266)(250,267)(251,268)(252,269)(253,270)(254,271)(255,272)(273,341)
(274,342)(275,343)(276,344)(277,345)(278,346)(279,347)(280,348)(281,349)
(282,350)(283,351)(284,352)(285,353)(286,354)(287,355)(288,356)(289,357)
(290,324)(291,325)(292,326)(293,327)(294,328)(295,329)(296,330)(297,331)
(298,332)(299,333)(300,334)(301,335)(302,336)(303,337)(304,338)(305,339)
(306,340)(358,375)(359,376)(360,377)(361,378)(362,379)(363,380)(364,381)
(365,382)(366,383)(367,384)(368,385)(369,386)(370,387)(371,388)(372,389)
(373,390)(374,391)(392,460)(393,461)(394,462)(395,463)(396,464)(397,465)
(398,466)(399,467)(400,468)(401,469)(402,470)(403,471)(404,472)(405,473)
(406,474)(407,475)(408,476)(409,443)(410,444)(411,445)(412,446)(413,447)
(414,448)(415,449)(416,450)(417,451)(418,452)(419,453)(420,454)(421,455)
(422,456)(423,457)(424,458)(425,459);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(476)!( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)
( 9, 10)( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)
( 26, 27)( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)
( 43, 44)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)
( 77, 78)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)
( 94, 95)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)
(111,112)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)
(128,129)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)
(145,146)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)
(179,180)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)
(196,197)(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)
(213,214)(223,238)(224,237)(225,236)(226,235)(227,234)(228,233)(229,232)
(230,231)(239,358)(240,374)(241,373)(242,372)(243,371)(244,370)(245,369)
(246,368)(247,367)(248,366)(249,365)(250,364)(251,363)(252,362)(253,361)
(254,360)(255,359)(256,375)(257,391)(258,390)(259,389)(260,388)(261,387)
(262,386)(263,385)(264,384)(265,383)(266,382)(267,381)(268,380)(269,379)
(270,378)(271,377)(272,376)(273,392)(274,408)(275,407)(276,406)(277,405)
(278,404)(279,403)(280,402)(281,401)(282,400)(283,399)(284,398)(285,397)
(286,396)(287,395)(288,394)(289,393)(290,409)(291,425)(292,424)(293,423)
(294,422)(295,421)(296,420)(297,419)(298,418)(299,417)(300,416)(301,415)
(302,414)(303,413)(304,412)(305,411)(306,410)(307,426)(308,442)(309,441)
(310,440)(311,439)(312,438)(313,437)(314,436)(315,435)(316,434)(317,433)
(318,432)(319,431)(320,430)(321,429)(322,428)(323,427)(324,443)(325,459)
(326,458)(327,457)(328,456)(329,455)(330,454)(331,453)(332,452)(333,451)
(334,450)(335,449)(336,448)(337,447)(338,446)(339,445)(340,444)(341,460)
(342,476)(343,475)(344,474)(345,473)(346,472)(347,471)(348,470)(349,469)
(350,468)(351,467)(352,466)(353,465)(354,464)(355,463)(356,462)(357,461);
s1 := Sym(476)!( 1,240)( 2,239)( 3,255)( 4,254)( 5,253)( 6,252)( 7,251)
( 8,250)( 9,249)( 10,248)( 11,247)( 12,246)( 13,245)( 14,244)( 15,243)
( 16,242)( 17,241)( 18,342)( 19,341)( 20,357)( 21,356)( 22,355)( 23,354)
( 24,353)( 25,352)( 26,351)( 27,350)( 28,349)( 29,348)( 30,347)( 31,346)
( 32,345)( 33,344)( 34,343)( 35,325)( 36,324)( 37,340)( 38,339)( 39,338)
( 40,337)( 41,336)( 42,335)( 43,334)( 44,333)( 45,332)( 46,331)( 47,330)
( 48,329)( 49,328)( 50,327)( 51,326)( 52,308)( 53,307)( 54,323)( 55,322)
( 56,321)( 57,320)( 58,319)( 59,318)( 60,317)( 61,316)( 62,315)( 63,314)
( 64,313)( 65,312)( 66,311)( 67,310)( 68,309)( 69,291)( 70,290)( 71,306)
( 72,305)( 73,304)( 74,303)( 75,302)( 76,301)( 77,300)( 78,299)( 79,298)
( 80,297)( 81,296)( 82,295)( 83,294)( 84,293)( 85,292)( 86,274)( 87,273)
( 88,289)( 89,288)( 90,287)( 91,286)( 92,285)( 93,284)( 94,283)( 95,282)
( 96,281)( 97,280)( 98,279)( 99,278)(100,277)(101,276)(102,275)(103,257)
(104,256)(105,272)(106,271)(107,270)(108,269)(109,268)(110,267)(111,266)
(112,265)(113,264)(114,263)(115,262)(116,261)(117,260)(118,259)(119,258)
(120,359)(121,358)(122,374)(123,373)(124,372)(125,371)(126,370)(127,369)
(128,368)(129,367)(130,366)(131,365)(132,364)(133,363)(134,362)(135,361)
(136,360)(137,461)(138,460)(139,476)(140,475)(141,474)(142,473)(143,472)
(144,471)(145,470)(146,469)(147,468)(148,467)(149,466)(150,465)(151,464)
(152,463)(153,462)(154,444)(155,443)(156,459)(157,458)(158,457)(159,456)
(160,455)(161,454)(162,453)(163,452)(164,451)(165,450)(166,449)(167,448)
(168,447)(169,446)(170,445)(171,427)(172,426)(173,442)(174,441)(175,440)
(176,439)(177,438)(178,437)(179,436)(180,435)(181,434)(182,433)(183,432)
(184,431)(185,430)(186,429)(187,428)(188,410)(189,409)(190,425)(191,424)
(192,423)(193,422)(194,421)(195,420)(196,419)(197,418)(198,417)(199,416)
(200,415)(201,414)(202,413)(203,412)(204,411)(205,393)(206,392)(207,408)
(208,407)(209,406)(210,405)(211,404)(212,403)(213,402)(214,401)(215,400)
(216,399)(217,398)(218,397)(219,396)(220,395)(221,394)(222,376)(223,375)
(224,391)(225,390)(226,389)(227,388)(228,387)(229,386)(230,385)(231,384)
(232,383)(233,382)(234,381)(235,380)(236,379)(237,378)(238,377);
s2 := Sym(476)!( 1, 18)( 2, 19)( 3, 20)( 4, 21)( 5, 22)( 6, 23)( 7, 24)
( 8, 25)( 9, 26)( 10, 27)( 11, 28)( 12, 29)( 13, 30)( 14, 31)( 15, 32)
( 16, 33)( 17, 34)( 35,103)( 36,104)( 37,105)( 38,106)( 39,107)( 40,108)
( 41,109)( 42,110)( 43,111)( 44,112)( 45,113)( 46,114)( 47,115)( 48,116)
( 49,117)( 50,118)( 51,119)( 52, 86)( 53, 87)( 54, 88)( 55, 89)( 56, 90)
( 57, 91)( 58, 92)( 59, 93)( 60, 94)( 61, 95)( 62, 96)( 63, 97)( 64, 98)
( 65, 99)( 66,100)( 67,101)( 68,102)(120,137)(121,138)(122,139)(123,140)
(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)
(132,149)(133,150)(134,151)(135,152)(136,153)(154,222)(155,223)(156,224)
(157,225)(158,226)(159,227)(160,228)(161,229)(162,230)(163,231)(164,232)
(165,233)(166,234)(167,235)(168,236)(169,237)(170,238)(171,205)(172,206)
(173,207)(174,208)(175,209)(176,210)(177,211)(178,212)(179,213)(180,214)
(181,215)(182,216)(183,217)(184,218)(185,219)(186,220)(187,221)(239,256)
(240,257)(241,258)(242,259)(243,260)(244,261)(245,262)(246,263)(247,264)
(248,265)(249,266)(250,267)(251,268)(252,269)(253,270)(254,271)(255,272)
(273,341)(274,342)(275,343)(276,344)(277,345)(278,346)(279,347)(280,348)
(281,349)(282,350)(283,351)(284,352)(285,353)(286,354)(287,355)(288,356)
(289,357)(290,324)(291,325)(292,326)(293,327)(294,328)(295,329)(296,330)
(297,331)(298,332)(299,333)(300,334)(301,335)(302,336)(303,337)(304,338)
(305,339)(306,340)(358,375)(359,376)(360,377)(361,378)(362,379)(363,380)
(364,381)(365,382)(366,383)(367,384)(368,385)(369,386)(370,387)(371,388)
(372,389)(373,390)(374,391)(392,460)(393,461)(394,462)(395,463)(396,464)
(397,465)(398,466)(399,467)(400,468)(401,469)(402,470)(403,471)(404,472)
(405,473)(406,474)(407,475)(408,476)(409,443)(410,444)(411,445)(412,446)
(413,447)(414,448)(415,449)(416,450)(417,451)(418,452)(419,453)(420,454)
(421,455)(422,456)(423,457)(424,458)(425,459);
poly := sub<Sym(476)|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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope