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Polytope of Type {14,70}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,70}*1960c
if this polytope has a name.
Group : SmallGroup(1960,137)
Rank : 3
Schlafli Type : {14,70}
Number of vertices, edges, etc : 14, 490, 70
Order of s0s1s2 : 70
Order of s0s1s2s1 : 14
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 : {14,35}*980
   5-fold quotients : {14,14}*392b
   7-fold quotients : {2,70}*280
   10-fold quotients : {14,7}*196
   14-fold quotients : {2,35}*140
   35-fold quotients : {2,14}*56
   49-fold quotients : {2,10}*40
   70-fold quotients : {2,7}*28
   98-fold quotients : {2,5}*20
   245-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)
( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)
( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)
( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)
( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)
(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)(129,132)
(130,131)(135,140)(136,139)(137,138)(142,147)(143,146)(144,145)(149,154)
(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)(165,166)
(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(184,189)(185,188)
(186,187)(191,196)(192,195)(193,194)(198,203)(199,202)(200,201)(205,210)
(206,209)(207,208)(212,217)(213,216)(214,215)(219,224)(220,223)(221,222)
(226,231)(227,230)(228,229)(233,238)(234,237)(235,236)(240,245)(241,244)
(242,243)(247,252)(248,251)(249,250)(254,259)(255,258)(256,257)(261,266)
(262,265)(263,264)(268,273)(269,272)(270,271)(275,280)(276,279)(277,278)
(282,287)(283,286)(284,285)(289,294)(290,293)(291,292)(296,301)(297,300)
(298,299)(303,308)(304,307)(305,306)(310,315)(311,314)(312,313)(317,322)
(318,321)(319,320)(324,329)(325,328)(326,327)(331,336)(332,335)(333,334)
(338,343)(339,342)(340,341)(345,350)(346,349)(347,348)(352,357)(353,356)
(354,355)(359,364)(360,363)(361,362)(366,371)(367,370)(368,369)(373,378)
(374,377)(375,376)(380,385)(381,384)(382,383)(387,392)(388,391)(389,390)
(394,399)(395,398)(396,397)(401,406)(402,405)(403,404)(408,413)(409,412)
(410,411)(415,420)(416,419)(417,418)(422,427)(423,426)(424,425)(429,434)
(430,433)(431,432)(436,441)(437,440)(438,439)(443,448)(444,447)(445,446)
(450,455)(451,454)(452,453)(457,462)(458,461)(459,460)(464,469)(465,468)
(466,467)(471,476)(472,475)(473,474)(478,483)(479,482)(480,481)(485,490)
(486,489)(487,488);;
s1 := (  1,  2)(  3,  7)(  4,  6)(  8, 44)(  9, 43)( 10, 49)( 11, 48)( 12, 47)
( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)( 20, 39)
( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)
( 50,198)( 51,197)( 52,203)( 53,202)( 54,201)( 55,200)( 56,199)( 57,240)
( 58,239)( 59,245)( 60,244)( 61,243)( 62,242)( 63,241)( 64,233)( 65,232)
( 66,238)( 67,237)( 68,236)( 69,235)( 70,234)( 71,226)( 72,225)( 73,231)
( 74,230)( 75,229)( 76,228)( 77,227)( 78,219)( 79,218)( 80,224)( 81,223)
( 82,222)( 83,221)( 84,220)( 85,212)( 86,211)( 87,217)( 88,216)( 89,215)
( 90,214)( 91,213)( 92,205)( 93,204)( 94,210)( 95,209)( 96,208)( 97,207)
( 98,206)( 99,149)(100,148)(101,154)(102,153)(103,152)(104,151)(105,150)
(106,191)(107,190)(108,196)(109,195)(110,194)(111,193)(112,192)(113,184)
(114,183)(115,189)(116,188)(117,187)(118,186)(119,185)(120,177)(121,176)
(122,182)(123,181)(124,180)(125,179)(126,178)(127,170)(128,169)(129,175)
(130,174)(131,173)(132,172)(133,171)(134,163)(135,162)(136,168)(137,167)
(138,166)(139,165)(140,164)(141,156)(142,155)(143,161)(144,160)(145,159)
(146,158)(147,157)(246,247)(248,252)(249,251)(253,289)(254,288)(255,294)
(256,293)(257,292)(258,291)(259,290)(260,282)(261,281)(262,287)(263,286)
(264,285)(265,284)(266,283)(267,275)(268,274)(269,280)(270,279)(271,278)
(272,277)(273,276)(295,443)(296,442)(297,448)(298,447)(299,446)(300,445)
(301,444)(302,485)(303,484)(304,490)(305,489)(306,488)(307,487)(308,486)
(309,478)(310,477)(311,483)(312,482)(313,481)(314,480)(315,479)(316,471)
(317,470)(318,476)(319,475)(320,474)(321,473)(322,472)(323,464)(324,463)
(325,469)(326,468)(327,467)(328,466)(329,465)(330,457)(331,456)(332,462)
(333,461)(334,460)(335,459)(336,458)(337,450)(338,449)(339,455)(340,454)
(341,453)(342,452)(343,451)(344,394)(345,393)(346,399)(347,398)(348,397)
(349,396)(350,395)(351,436)(352,435)(353,441)(354,440)(355,439)(356,438)
(357,437)(358,429)(359,428)(360,434)(361,433)(362,432)(363,431)(364,430)
(365,422)(366,421)(367,427)(368,426)(369,425)(370,424)(371,423)(372,415)
(373,414)(374,420)(375,419)(376,418)(377,417)(378,416)(379,408)(380,407)
(381,413)(382,412)(383,411)(384,410)(385,409)(386,401)(387,400)(388,406)
(389,405)(390,404)(391,403)(392,402);;
s2 := (  1,302)(  2,308)(  3,307)(  4,306)(  5,305)(  6,304)(  7,303)(  8,295)
(  9,301)( 10,300)( 11,299)( 12,298)( 13,297)( 14,296)( 15,337)( 16,343)
( 17,342)( 18,341)( 19,340)( 20,339)( 21,338)( 22,330)( 23,336)( 24,335)
( 25,334)( 26,333)( 27,332)( 28,331)( 29,323)( 30,329)( 31,328)( 32,327)
( 33,326)( 34,325)( 35,324)( 36,316)( 37,322)( 38,321)( 39,320)( 40,319)
( 41,318)( 42,317)( 43,309)( 44,315)( 45,314)( 46,313)( 47,312)( 48,311)
( 49,310)( 50,253)( 51,259)( 52,258)( 53,257)( 54,256)( 55,255)( 56,254)
( 57,246)( 58,252)( 59,251)( 60,250)( 61,249)( 62,248)( 63,247)( 64,288)
( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,281)( 72,287)
( 73,286)( 74,285)( 75,284)( 76,283)( 77,282)( 78,274)( 79,280)( 80,279)
( 81,278)( 82,277)( 83,276)( 84,275)( 85,267)( 86,273)( 87,272)( 88,271)
( 89,270)( 90,269)( 91,268)( 92,260)( 93,266)( 94,265)( 95,264)( 96,263)
( 97,262)( 98,261)( 99,449)(100,455)(101,454)(102,453)(103,452)(104,451)
(105,450)(106,442)(107,448)(108,447)(109,446)(110,445)(111,444)(112,443)
(113,484)(114,490)(115,489)(116,488)(117,487)(118,486)(119,485)(120,477)
(121,483)(122,482)(123,481)(124,480)(125,479)(126,478)(127,470)(128,476)
(129,475)(130,474)(131,473)(132,472)(133,471)(134,463)(135,469)(136,468)
(137,467)(138,466)(139,465)(140,464)(141,456)(142,462)(143,461)(144,460)
(145,459)(146,458)(147,457)(148,400)(149,406)(150,405)(151,404)(152,403)
(153,402)(154,401)(155,393)(156,399)(157,398)(158,397)(159,396)(160,395)
(161,394)(162,435)(163,441)(164,440)(165,439)(166,438)(167,437)(168,436)
(169,428)(170,434)(171,433)(172,432)(173,431)(174,430)(175,429)(176,421)
(177,427)(178,426)(179,425)(180,424)(181,423)(182,422)(183,414)(184,420)
(185,419)(186,418)(187,417)(188,416)(189,415)(190,407)(191,413)(192,412)
(193,411)(194,410)(195,409)(196,408)(197,351)(198,357)(199,356)(200,355)
(201,354)(202,353)(203,352)(204,344)(205,350)(206,349)(207,348)(208,347)
(209,346)(210,345)(211,386)(212,392)(213,391)(214,390)(215,389)(216,388)
(217,387)(218,379)(219,385)(220,384)(221,383)(222,382)(223,381)(224,380)
(225,372)(226,378)(227,377)(228,376)(229,375)(230,374)(231,373)(232,365)
(233,371)(234,370)(235,369)(236,368)(237,367)(238,366)(239,358)(240,364)
(241,363)(242,362)(243,361)(244,360)(245,359);;
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, s2*s0*s1*s0*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(490)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)
( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)
( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)
( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)
(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)
(129,132)(130,131)(135,140)(136,139)(137,138)(142,147)(143,146)(144,145)
(149,154)(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)
(165,166)(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(184,189)
(185,188)(186,187)(191,196)(192,195)(193,194)(198,203)(199,202)(200,201)
(205,210)(206,209)(207,208)(212,217)(213,216)(214,215)(219,224)(220,223)
(221,222)(226,231)(227,230)(228,229)(233,238)(234,237)(235,236)(240,245)
(241,244)(242,243)(247,252)(248,251)(249,250)(254,259)(255,258)(256,257)
(261,266)(262,265)(263,264)(268,273)(269,272)(270,271)(275,280)(276,279)
(277,278)(282,287)(283,286)(284,285)(289,294)(290,293)(291,292)(296,301)
(297,300)(298,299)(303,308)(304,307)(305,306)(310,315)(311,314)(312,313)
(317,322)(318,321)(319,320)(324,329)(325,328)(326,327)(331,336)(332,335)
(333,334)(338,343)(339,342)(340,341)(345,350)(346,349)(347,348)(352,357)
(353,356)(354,355)(359,364)(360,363)(361,362)(366,371)(367,370)(368,369)
(373,378)(374,377)(375,376)(380,385)(381,384)(382,383)(387,392)(388,391)
(389,390)(394,399)(395,398)(396,397)(401,406)(402,405)(403,404)(408,413)
(409,412)(410,411)(415,420)(416,419)(417,418)(422,427)(423,426)(424,425)
(429,434)(430,433)(431,432)(436,441)(437,440)(438,439)(443,448)(444,447)
(445,446)(450,455)(451,454)(452,453)(457,462)(458,461)(459,460)(464,469)
(465,468)(466,467)(471,476)(472,475)(473,474)(478,483)(479,482)(480,481)
(485,490)(486,489)(487,488);
s1 := Sym(490)!(  1,  2)(  3,  7)(  4,  6)(  8, 44)(  9, 43)( 10, 49)( 11, 48)
( 12, 47)( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)
( 20, 39)( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 50,198)( 51,197)( 52,203)( 53,202)( 54,201)( 55,200)( 56,199)
( 57,240)( 58,239)( 59,245)( 60,244)( 61,243)( 62,242)( 63,241)( 64,233)
( 65,232)( 66,238)( 67,237)( 68,236)( 69,235)( 70,234)( 71,226)( 72,225)
( 73,231)( 74,230)( 75,229)( 76,228)( 77,227)( 78,219)( 79,218)( 80,224)
( 81,223)( 82,222)( 83,221)( 84,220)( 85,212)( 86,211)( 87,217)( 88,216)
( 89,215)( 90,214)( 91,213)( 92,205)( 93,204)( 94,210)( 95,209)( 96,208)
( 97,207)( 98,206)( 99,149)(100,148)(101,154)(102,153)(103,152)(104,151)
(105,150)(106,191)(107,190)(108,196)(109,195)(110,194)(111,193)(112,192)
(113,184)(114,183)(115,189)(116,188)(117,187)(118,186)(119,185)(120,177)
(121,176)(122,182)(123,181)(124,180)(125,179)(126,178)(127,170)(128,169)
(129,175)(130,174)(131,173)(132,172)(133,171)(134,163)(135,162)(136,168)
(137,167)(138,166)(139,165)(140,164)(141,156)(142,155)(143,161)(144,160)
(145,159)(146,158)(147,157)(246,247)(248,252)(249,251)(253,289)(254,288)
(255,294)(256,293)(257,292)(258,291)(259,290)(260,282)(261,281)(262,287)
(263,286)(264,285)(265,284)(266,283)(267,275)(268,274)(269,280)(270,279)
(271,278)(272,277)(273,276)(295,443)(296,442)(297,448)(298,447)(299,446)
(300,445)(301,444)(302,485)(303,484)(304,490)(305,489)(306,488)(307,487)
(308,486)(309,478)(310,477)(311,483)(312,482)(313,481)(314,480)(315,479)
(316,471)(317,470)(318,476)(319,475)(320,474)(321,473)(322,472)(323,464)
(324,463)(325,469)(326,468)(327,467)(328,466)(329,465)(330,457)(331,456)
(332,462)(333,461)(334,460)(335,459)(336,458)(337,450)(338,449)(339,455)
(340,454)(341,453)(342,452)(343,451)(344,394)(345,393)(346,399)(347,398)
(348,397)(349,396)(350,395)(351,436)(352,435)(353,441)(354,440)(355,439)
(356,438)(357,437)(358,429)(359,428)(360,434)(361,433)(362,432)(363,431)
(364,430)(365,422)(366,421)(367,427)(368,426)(369,425)(370,424)(371,423)
(372,415)(373,414)(374,420)(375,419)(376,418)(377,417)(378,416)(379,408)
(380,407)(381,413)(382,412)(383,411)(384,410)(385,409)(386,401)(387,400)
(388,406)(389,405)(390,404)(391,403)(392,402);
s2 := Sym(490)!(  1,302)(  2,308)(  3,307)(  4,306)(  5,305)(  6,304)(  7,303)
(  8,295)(  9,301)( 10,300)( 11,299)( 12,298)( 13,297)( 14,296)( 15,337)
( 16,343)( 17,342)( 18,341)( 19,340)( 20,339)( 21,338)( 22,330)( 23,336)
( 24,335)( 25,334)( 26,333)( 27,332)( 28,331)( 29,323)( 30,329)( 31,328)
( 32,327)( 33,326)( 34,325)( 35,324)( 36,316)( 37,322)( 38,321)( 39,320)
( 40,319)( 41,318)( 42,317)( 43,309)( 44,315)( 45,314)( 46,313)( 47,312)
( 48,311)( 49,310)( 50,253)( 51,259)( 52,258)( 53,257)( 54,256)( 55,255)
( 56,254)( 57,246)( 58,252)( 59,251)( 60,250)( 61,249)( 62,248)( 63,247)
( 64,288)( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,281)
( 72,287)( 73,286)( 74,285)( 75,284)( 76,283)( 77,282)( 78,274)( 79,280)
( 80,279)( 81,278)( 82,277)( 83,276)( 84,275)( 85,267)( 86,273)( 87,272)
( 88,271)( 89,270)( 90,269)( 91,268)( 92,260)( 93,266)( 94,265)( 95,264)
( 96,263)( 97,262)( 98,261)( 99,449)(100,455)(101,454)(102,453)(103,452)
(104,451)(105,450)(106,442)(107,448)(108,447)(109,446)(110,445)(111,444)
(112,443)(113,484)(114,490)(115,489)(116,488)(117,487)(118,486)(119,485)
(120,477)(121,483)(122,482)(123,481)(124,480)(125,479)(126,478)(127,470)
(128,476)(129,475)(130,474)(131,473)(132,472)(133,471)(134,463)(135,469)
(136,468)(137,467)(138,466)(139,465)(140,464)(141,456)(142,462)(143,461)
(144,460)(145,459)(146,458)(147,457)(148,400)(149,406)(150,405)(151,404)
(152,403)(153,402)(154,401)(155,393)(156,399)(157,398)(158,397)(159,396)
(160,395)(161,394)(162,435)(163,441)(164,440)(165,439)(166,438)(167,437)
(168,436)(169,428)(170,434)(171,433)(172,432)(173,431)(174,430)(175,429)
(176,421)(177,427)(178,426)(179,425)(180,424)(181,423)(182,422)(183,414)
(184,420)(185,419)(186,418)(187,417)(188,416)(189,415)(190,407)(191,413)
(192,412)(193,411)(194,410)(195,409)(196,408)(197,351)(198,357)(199,356)
(200,355)(201,354)(202,353)(203,352)(204,344)(205,350)(206,349)(207,348)
(208,347)(209,346)(210,345)(211,386)(212,392)(213,391)(214,390)(215,389)
(216,388)(217,387)(218,379)(219,385)(220,384)(221,383)(222,382)(223,381)
(224,380)(225,372)(226,378)(227,377)(228,376)(229,375)(230,374)(231,373)
(232,365)(233,371)(234,370)(235,369)(236,368)(237,367)(238,366)(239,358)
(240,364)(241,363)(242,362)(243,361)(244,360)(245,359);
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, s2*s0*s1*s0*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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