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