Questions?
See the FAQ
or other info.

Polytope of Type {70,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {70,14}*1960b
Also Known As : {70,14|2}. if this polytope has another name.
Group : SmallGroup(1960,137)
Rank : 3
Schlafli Type : {70,14}
Number of vertices, edges, etc : 70, 490, 14
Order of s0s1s2 : 70
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {14,14}*392a
   7-fold quotients : {10,14}*280, {70,2}*280
   14-fold quotients : {35,2}*140
   35-fold quotients : {2,14}*56, {14,2}*56
   49-fold quotients : {10,2}*40
   70-fold quotients : {2,7}*28, {7,2}*28
   98-fold quotients : {5,2}*20
   245-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)
( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)
( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 50,197)( 51,198)( 52,199)
( 53,200)( 54,201)( 55,202)( 56,203)( 57,239)( 58,240)( 59,241)( 60,242)
( 61,243)( 62,244)( 63,245)( 64,232)( 65,233)( 66,234)( 67,235)( 68,236)
( 69,237)( 70,238)( 71,225)( 72,226)( 73,227)( 74,228)( 75,229)( 76,230)
( 77,231)( 78,218)( 79,219)( 80,220)( 81,221)( 82,222)( 83,223)( 84,224)
( 85,211)( 86,212)( 87,213)( 88,214)( 89,215)( 90,216)( 91,217)( 92,204)
( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)( 98,210)( 99,148)(100,149)
(101,150)(102,151)(103,152)(104,153)(105,154)(106,190)(107,191)(108,192)
(109,193)(110,194)(111,195)(112,196)(113,183)(114,184)(115,185)(116,186)
(117,187)(118,188)(119,189)(120,176)(121,177)(122,178)(123,179)(124,180)
(125,181)(126,182)(127,169)(128,170)(129,171)(130,172)(131,173)(132,174)
(133,175)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)(140,168)
(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(253,288)
(254,289)(255,290)(256,291)(257,292)(258,293)(259,294)(260,281)(261,282)
(262,283)(263,284)(264,285)(265,286)(266,287)(267,274)(268,275)(269,276)
(270,277)(271,278)(272,279)(273,280)(295,442)(296,443)(297,444)(298,445)
(299,446)(300,447)(301,448)(302,484)(303,485)(304,486)(305,487)(306,488)
(307,489)(308,490)(309,477)(310,478)(311,479)(312,480)(313,481)(314,482)
(315,483)(316,470)(317,471)(318,472)(319,473)(320,474)(321,475)(322,476)
(323,463)(324,464)(325,465)(326,466)(327,467)(328,468)(329,469)(330,456)
(331,457)(332,458)(333,459)(334,460)(335,461)(336,462)(337,449)(338,450)
(339,451)(340,452)(341,453)(342,454)(343,455)(344,393)(345,394)(346,395)
(347,396)(348,397)(349,398)(350,399)(351,435)(352,436)(353,437)(354,438)
(355,439)(356,440)(357,441)(358,428)(359,429)(360,430)(361,431)(362,432)
(363,433)(364,434)(365,421)(366,422)(367,423)(368,424)(369,425)(370,426)
(371,427)(372,414)(373,415)(374,416)(375,417)(376,418)(377,419)(378,420)
(379,407)(380,408)(381,409)(382,410)(383,411)(384,412)(385,413)(386,400)
(387,401)(388,402)(389,403)(390,404)(391,405)(392,406);;
s1 := (  1, 57)(  2, 63)(  3, 62)(  4, 61)(  5, 60)(  6, 59)(  7, 58)(  8, 50)
(  9, 56)( 10, 55)( 11, 54)( 12, 53)( 13, 52)( 14, 51)( 15, 92)( 16, 98)
( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 85)( 23, 91)( 24, 90)
( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 78)( 30, 84)( 31, 83)( 32, 82)
( 33, 81)( 34, 80)( 35, 79)( 36, 71)( 37, 77)( 38, 76)( 39, 75)( 40, 74)
( 41, 73)( 42, 72)( 43, 64)( 44, 70)( 45, 69)( 46, 68)( 47, 67)( 48, 66)
( 49, 65)( 99,204)(100,210)(101,209)(102,208)(103,207)(104,206)(105,205)
(106,197)(107,203)(108,202)(109,201)(110,200)(111,199)(112,198)(113,239)
(114,245)(115,244)(116,243)(117,242)(118,241)(119,240)(120,232)(121,238)
(122,237)(123,236)(124,235)(125,234)(126,233)(127,225)(128,231)(129,230)
(130,229)(131,228)(132,227)(133,226)(134,218)(135,224)(136,223)(137,222)
(138,221)(139,220)(140,219)(141,211)(142,217)(143,216)(144,215)(145,214)
(146,213)(147,212)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)
(154,156)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)
(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)
(178,181)(179,180)(246,302)(247,308)(248,307)(249,306)(250,305)(251,304)
(252,303)(253,295)(254,301)(255,300)(256,299)(257,298)(258,297)(259,296)
(260,337)(261,343)(262,342)(263,341)(264,340)(265,339)(266,338)(267,330)
(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)
(276,328)(277,327)(278,326)(279,325)(280,324)(281,316)(282,322)(283,321)
(284,320)(285,319)(286,318)(287,317)(288,309)(289,315)(290,314)(291,313)
(292,312)(293,311)(294,310)(344,449)(345,455)(346,454)(347,453)(348,452)
(349,451)(350,450)(351,442)(352,448)(353,447)(354,446)(355,445)(356,444)
(357,443)(358,484)(359,490)(360,489)(361,488)(362,487)(363,486)(364,485)
(365,477)(366,483)(367,482)(368,481)(369,480)(370,479)(371,478)(372,470)
(373,476)(374,475)(375,474)(376,473)(377,472)(378,471)(379,463)(380,469)
(381,468)(382,467)(383,466)(384,465)(385,464)(386,456)(387,462)(388,461)
(389,460)(390,459)(391,458)(392,457)(393,400)(394,406)(395,405)(396,404)
(397,403)(398,402)(399,401)(407,435)(408,441)(409,440)(410,439)(411,438)
(412,437)(413,436)(414,428)(415,434)(416,433)(417,432)(418,431)(419,430)
(420,429)(422,427)(423,426)(424,425);;
s2 := (  1,247)(  2,246)(  3,252)(  4,251)(  5,250)(  6,249)(  7,248)(  8,254)
(  9,253)( 10,259)( 11,258)( 12,257)( 13,256)( 14,255)( 15,261)( 16,260)
( 17,266)( 18,265)( 19,264)( 20,263)( 21,262)( 22,268)( 23,267)( 24,273)
( 25,272)( 26,271)( 27,270)( 28,269)( 29,275)( 30,274)( 31,280)( 32,279)
( 33,278)( 34,277)( 35,276)( 36,282)( 37,281)( 38,287)( 39,286)( 40,285)
( 41,284)( 42,283)( 43,289)( 44,288)( 45,294)( 46,293)( 47,292)( 48,291)
( 49,290)( 50,296)( 51,295)( 52,301)( 53,300)( 54,299)( 55,298)( 56,297)
( 57,303)( 58,302)( 59,308)( 60,307)( 61,306)( 62,305)( 63,304)( 64,310)
( 65,309)( 66,315)( 67,314)( 68,313)( 69,312)( 70,311)( 71,317)( 72,316)
( 73,322)( 74,321)( 75,320)( 76,319)( 77,318)( 78,324)( 79,323)( 80,329)
( 81,328)( 82,327)( 83,326)( 84,325)( 85,331)( 86,330)( 87,336)( 88,335)
( 89,334)( 90,333)( 91,332)( 92,338)( 93,337)( 94,343)( 95,342)( 96,341)
( 97,340)( 98,339)( 99,345)(100,344)(101,350)(102,349)(103,348)(104,347)
(105,346)(106,352)(107,351)(108,357)(109,356)(110,355)(111,354)(112,353)
(113,359)(114,358)(115,364)(116,363)(117,362)(118,361)(119,360)(120,366)
(121,365)(122,371)(123,370)(124,369)(125,368)(126,367)(127,373)(128,372)
(129,378)(130,377)(131,376)(132,375)(133,374)(134,380)(135,379)(136,385)
(137,384)(138,383)(139,382)(140,381)(141,387)(142,386)(143,392)(144,391)
(145,390)(146,389)(147,388)(148,394)(149,393)(150,399)(151,398)(152,397)
(153,396)(154,395)(155,401)(156,400)(157,406)(158,405)(159,404)(160,403)
(161,402)(162,408)(163,407)(164,413)(165,412)(166,411)(167,410)(168,409)
(169,415)(170,414)(171,420)(172,419)(173,418)(174,417)(175,416)(176,422)
(177,421)(178,427)(179,426)(180,425)(181,424)(182,423)(183,429)(184,428)
(185,434)(186,433)(187,432)(188,431)(189,430)(190,436)(191,435)(192,441)
(193,440)(194,439)(195,438)(196,437)(197,443)(198,442)(199,448)(200,447)
(201,446)(202,445)(203,444)(204,450)(205,449)(206,455)(207,454)(208,453)
(209,452)(210,451)(211,457)(212,456)(213,462)(214,461)(215,460)(216,459)
(217,458)(218,464)(219,463)(220,469)(221,468)(222,467)(223,466)(224,465)
(225,471)(226,470)(227,476)(228,475)(229,474)(230,473)(231,472)(232,478)
(233,477)(234,483)(235,482)(236,481)(237,480)(238,479)(239,485)(240,484)
(241,490)(242,489)(243,488)(244,487)(245,486);;
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*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(490)!(  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)
( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)
( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 50,197)( 51,198)
( 52,199)( 53,200)( 54,201)( 55,202)( 56,203)( 57,239)( 58,240)( 59,241)
( 60,242)( 61,243)( 62,244)( 63,245)( 64,232)( 65,233)( 66,234)( 67,235)
( 68,236)( 69,237)( 70,238)( 71,225)( 72,226)( 73,227)( 74,228)( 75,229)
( 76,230)( 77,231)( 78,218)( 79,219)( 80,220)( 81,221)( 82,222)( 83,223)
( 84,224)( 85,211)( 86,212)( 87,213)( 88,214)( 89,215)( 90,216)( 91,217)
( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)( 98,210)( 99,148)
(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,190)(107,191)
(108,192)(109,193)(110,194)(111,195)(112,196)(113,183)(114,184)(115,185)
(116,186)(117,187)(118,188)(119,189)(120,176)(121,177)(122,178)(123,179)
(124,180)(125,181)(126,182)(127,169)(128,170)(129,171)(130,172)(131,173)
(132,174)(133,175)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)
(140,168)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)
(253,288)(254,289)(255,290)(256,291)(257,292)(258,293)(259,294)(260,281)
(261,282)(262,283)(263,284)(264,285)(265,286)(266,287)(267,274)(268,275)
(269,276)(270,277)(271,278)(272,279)(273,280)(295,442)(296,443)(297,444)
(298,445)(299,446)(300,447)(301,448)(302,484)(303,485)(304,486)(305,487)
(306,488)(307,489)(308,490)(309,477)(310,478)(311,479)(312,480)(313,481)
(314,482)(315,483)(316,470)(317,471)(318,472)(319,473)(320,474)(321,475)
(322,476)(323,463)(324,464)(325,465)(326,466)(327,467)(328,468)(329,469)
(330,456)(331,457)(332,458)(333,459)(334,460)(335,461)(336,462)(337,449)
(338,450)(339,451)(340,452)(341,453)(342,454)(343,455)(344,393)(345,394)
(346,395)(347,396)(348,397)(349,398)(350,399)(351,435)(352,436)(353,437)
(354,438)(355,439)(356,440)(357,441)(358,428)(359,429)(360,430)(361,431)
(362,432)(363,433)(364,434)(365,421)(366,422)(367,423)(368,424)(369,425)
(370,426)(371,427)(372,414)(373,415)(374,416)(375,417)(376,418)(377,419)
(378,420)(379,407)(380,408)(381,409)(382,410)(383,411)(384,412)(385,413)
(386,400)(387,401)(388,402)(389,403)(390,404)(391,405)(392,406);
s1 := Sym(490)!(  1, 57)(  2, 63)(  3, 62)(  4, 61)(  5, 60)(  6, 59)(  7, 58)
(  8, 50)(  9, 56)( 10, 55)( 11, 54)( 12, 53)( 13, 52)( 14, 51)( 15, 92)
( 16, 98)( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 85)( 23, 91)
( 24, 90)( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 78)( 30, 84)( 31, 83)
( 32, 82)( 33, 81)( 34, 80)( 35, 79)( 36, 71)( 37, 77)( 38, 76)( 39, 75)
( 40, 74)( 41, 73)( 42, 72)( 43, 64)( 44, 70)( 45, 69)( 46, 68)( 47, 67)
( 48, 66)( 49, 65)( 99,204)(100,210)(101,209)(102,208)(103,207)(104,206)
(105,205)(106,197)(107,203)(108,202)(109,201)(110,200)(111,199)(112,198)
(113,239)(114,245)(115,244)(116,243)(117,242)(118,241)(119,240)(120,232)
(121,238)(122,237)(123,236)(124,235)(125,234)(126,233)(127,225)(128,231)
(129,230)(130,229)(131,228)(132,227)(133,226)(134,218)(135,224)(136,223)
(137,222)(138,221)(139,220)(140,219)(141,211)(142,217)(143,216)(144,215)
(145,214)(146,213)(147,212)(148,155)(149,161)(150,160)(151,159)(152,158)
(153,157)(154,156)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)
(168,191)(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)
(177,182)(178,181)(179,180)(246,302)(247,308)(248,307)(249,306)(250,305)
(251,304)(252,303)(253,295)(254,301)(255,300)(256,299)(257,298)(258,297)
(259,296)(260,337)(261,343)(262,342)(263,341)(264,340)(265,339)(266,338)
(267,330)(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)
(275,329)(276,328)(277,327)(278,326)(279,325)(280,324)(281,316)(282,322)
(283,321)(284,320)(285,319)(286,318)(287,317)(288,309)(289,315)(290,314)
(291,313)(292,312)(293,311)(294,310)(344,449)(345,455)(346,454)(347,453)
(348,452)(349,451)(350,450)(351,442)(352,448)(353,447)(354,446)(355,445)
(356,444)(357,443)(358,484)(359,490)(360,489)(361,488)(362,487)(363,486)
(364,485)(365,477)(366,483)(367,482)(368,481)(369,480)(370,479)(371,478)
(372,470)(373,476)(374,475)(375,474)(376,473)(377,472)(378,471)(379,463)
(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,456)(387,462)
(388,461)(389,460)(390,459)(391,458)(392,457)(393,400)(394,406)(395,405)
(396,404)(397,403)(398,402)(399,401)(407,435)(408,441)(409,440)(410,439)
(411,438)(412,437)(413,436)(414,428)(415,434)(416,433)(417,432)(418,431)
(419,430)(420,429)(422,427)(423,426)(424,425);
s2 := Sym(490)!(  1,247)(  2,246)(  3,252)(  4,251)(  5,250)(  6,249)(  7,248)
(  8,254)(  9,253)( 10,259)( 11,258)( 12,257)( 13,256)( 14,255)( 15,261)
( 16,260)( 17,266)( 18,265)( 19,264)( 20,263)( 21,262)( 22,268)( 23,267)
( 24,273)( 25,272)( 26,271)( 27,270)( 28,269)( 29,275)( 30,274)( 31,280)
( 32,279)( 33,278)( 34,277)( 35,276)( 36,282)( 37,281)( 38,287)( 39,286)
( 40,285)( 41,284)( 42,283)( 43,289)( 44,288)( 45,294)( 46,293)( 47,292)
( 48,291)( 49,290)( 50,296)( 51,295)( 52,301)( 53,300)( 54,299)( 55,298)
( 56,297)( 57,303)( 58,302)( 59,308)( 60,307)( 61,306)( 62,305)( 63,304)
( 64,310)( 65,309)( 66,315)( 67,314)( 68,313)( 69,312)( 70,311)( 71,317)
( 72,316)( 73,322)( 74,321)( 75,320)( 76,319)( 77,318)( 78,324)( 79,323)
( 80,329)( 81,328)( 82,327)( 83,326)( 84,325)( 85,331)( 86,330)( 87,336)
( 88,335)( 89,334)( 90,333)( 91,332)( 92,338)( 93,337)( 94,343)( 95,342)
( 96,341)( 97,340)( 98,339)( 99,345)(100,344)(101,350)(102,349)(103,348)
(104,347)(105,346)(106,352)(107,351)(108,357)(109,356)(110,355)(111,354)
(112,353)(113,359)(114,358)(115,364)(116,363)(117,362)(118,361)(119,360)
(120,366)(121,365)(122,371)(123,370)(124,369)(125,368)(126,367)(127,373)
(128,372)(129,378)(130,377)(131,376)(132,375)(133,374)(134,380)(135,379)
(136,385)(137,384)(138,383)(139,382)(140,381)(141,387)(142,386)(143,392)
(144,391)(145,390)(146,389)(147,388)(148,394)(149,393)(150,399)(151,398)
(152,397)(153,396)(154,395)(155,401)(156,400)(157,406)(158,405)(159,404)
(160,403)(161,402)(162,408)(163,407)(164,413)(165,412)(166,411)(167,410)
(168,409)(169,415)(170,414)(171,420)(172,419)(173,418)(174,417)(175,416)
(176,422)(177,421)(178,427)(179,426)(180,425)(181,424)(182,423)(183,429)
(184,428)(185,434)(186,433)(187,432)(188,431)(189,430)(190,436)(191,435)
(192,441)(193,440)(194,439)(195,438)(196,437)(197,443)(198,442)(199,448)
(200,447)(201,446)(202,445)(203,444)(204,450)(205,449)(206,455)(207,454)
(208,453)(209,452)(210,451)(211,457)(212,456)(213,462)(214,461)(215,460)
(216,459)(217,458)(218,464)(219,463)(220,469)(221,468)(222,467)(223,466)
(224,465)(225,471)(226,470)(227,476)(228,475)(229,474)(230,473)(231,472)
(232,478)(233,477)(234,483)(235,482)(236,481)(237,480)(238,479)(239,485)
(240,484)(241,490)(242,489)(243,488)(244,487)(245,486);
poly := sub<Sym(490)|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*s0*s1*s0*s1 >; 
 
References : None.
to this polytope