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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}*1960b
Also Known As : {14,70|2}. if this polytope has another 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 : 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) :
   5-fold quotients : {14,14}*392a
   7-fold quotients : {14,10}*280, {2,70}*280
   14-fold quotients : {2,35}*140
   35-fold quotients : {2,14}*56, {14,2}*56
   49-fold quotients : {2,10}*40
   70-fold quotients : {2,7}*28, {7,2}*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)(  2,303)(  3,304)(  4,305)(  5,306)(  6,307)(  7,308)(  8,295)
(  9,296)( 10,297)( 11,298)( 12,299)( 13,300)( 14,301)( 15,337)( 16,338)
( 17,339)( 18,340)( 19,341)( 20,342)( 21,343)( 22,330)( 23,331)( 24,332)
( 25,333)( 26,334)( 27,335)( 28,336)( 29,323)( 30,324)( 31,325)( 32,326)
( 33,327)( 34,328)( 35,329)( 36,316)( 37,317)( 38,318)( 39,319)( 40,320)
( 41,321)( 42,322)( 43,309)( 44,310)( 45,311)( 46,312)( 47,313)( 48,314)
( 49,315)( 50,253)( 51,254)( 52,255)( 53,256)( 54,257)( 55,258)( 56,259)
( 57,246)( 58,247)( 59,248)( 60,249)( 61,250)( 62,251)( 63,252)( 64,288)
( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,281)( 72,282)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,274)( 79,275)( 80,276)
( 81,277)( 82,278)( 83,279)( 84,280)( 85,267)( 86,268)( 87,269)( 88,270)
( 89,271)( 90,272)( 91,273)( 92,260)( 93,261)( 94,262)( 95,263)( 96,264)
( 97,265)( 98,266)( 99,449)(100,450)(101,451)(102,452)(103,453)(104,454)
(105,455)(106,442)(107,443)(108,444)(109,445)(110,446)(111,447)(112,448)
(113,484)(114,485)(115,486)(116,487)(117,488)(118,489)(119,490)(120,477)
(121,478)(122,479)(123,480)(124,481)(125,482)(126,483)(127,470)(128,471)
(129,472)(130,473)(131,474)(132,475)(133,476)(134,463)(135,464)(136,465)
(137,466)(138,467)(139,468)(140,469)(141,456)(142,457)(143,458)(144,459)
(145,460)(146,461)(147,462)(148,400)(149,401)(150,402)(151,403)(152,404)
(153,405)(154,406)(155,393)(156,394)(157,395)(158,396)(159,397)(160,398)
(161,399)(162,435)(163,436)(164,437)(165,438)(166,439)(167,440)(168,441)
(169,428)(170,429)(171,430)(172,431)(173,432)(174,433)(175,434)(176,421)
(177,422)(178,423)(179,424)(180,425)(181,426)(182,427)(183,414)(184,415)
(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)(192,409)
(193,410)(194,411)(195,412)(196,413)(197,351)(198,352)(199,353)(200,354)
(201,355)(202,356)(203,357)(204,344)(205,345)(206,346)(207,347)(208,348)
(209,349)(210,350)(211,386)(212,387)(213,388)(214,389)(215,390)(216,391)
(217,392)(218,379)(219,380)(220,381)(221,382)(222,383)(223,384)(224,385)
(225,372)(226,373)(227,374)(228,375)(229,376)(230,377)(231,378)(232,365)
(233,366)(234,367)(235,368)(236,369)(237,370)(238,371)(239,358)(240,359)
(241,360)(242,361)(243,362)(244,363)(245,364);;
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*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)(  2,303)(  3,304)(  4,305)(  5,306)(  6,307)(  7,308)
(  8,295)(  9,296)( 10,297)( 11,298)( 12,299)( 13,300)( 14,301)( 15,337)
( 16,338)( 17,339)( 18,340)( 19,341)( 20,342)( 21,343)( 22,330)( 23,331)
( 24,332)( 25,333)( 26,334)( 27,335)( 28,336)( 29,323)( 30,324)( 31,325)
( 32,326)( 33,327)( 34,328)( 35,329)( 36,316)( 37,317)( 38,318)( 39,319)
( 40,320)( 41,321)( 42,322)( 43,309)( 44,310)( 45,311)( 46,312)( 47,313)
( 48,314)( 49,315)( 50,253)( 51,254)( 52,255)( 53,256)( 54,257)( 55,258)
( 56,259)( 57,246)( 58,247)( 59,248)( 60,249)( 61,250)( 62,251)( 63,252)
( 64,288)( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,281)
( 72,282)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,274)( 79,275)
( 80,276)( 81,277)( 82,278)( 83,279)( 84,280)( 85,267)( 86,268)( 87,269)
( 88,270)( 89,271)( 90,272)( 91,273)( 92,260)( 93,261)( 94,262)( 95,263)
( 96,264)( 97,265)( 98,266)( 99,449)(100,450)(101,451)(102,452)(103,453)
(104,454)(105,455)(106,442)(107,443)(108,444)(109,445)(110,446)(111,447)
(112,448)(113,484)(114,485)(115,486)(116,487)(117,488)(118,489)(119,490)
(120,477)(121,478)(122,479)(123,480)(124,481)(125,482)(126,483)(127,470)
(128,471)(129,472)(130,473)(131,474)(132,475)(133,476)(134,463)(135,464)
(136,465)(137,466)(138,467)(139,468)(140,469)(141,456)(142,457)(143,458)
(144,459)(145,460)(146,461)(147,462)(148,400)(149,401)(150,402)(151,403)
(152,404)(153,405)(154,406)(155,393)(156,394)(157,395)(158,396)(159,397)
(160,398)(161,399)(162,435)(163,436)(164,437)(165,438)(166,439)(167,440)
(168,441)(169,428)(170,429)(171,430)(172,431)(173,432)(174,433)(175,434)
(176,421)(177,422)(178,423)(179,424)(180,425)(181,426)(182,427)(183,414)
(184,415)(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)
(192,409)(193,410)(194,411)(195,412)(196,413)(197,351)(198,352)(199,353)
(200,354)(201,355)(202,356)(203,357)(204,344)(205,345)(206,346)(207,347)
(208,348)(209,349)(210,350)(211,386)(212,387)(213,388)(214,389)(215,390)
(216,391)(217,392)(218,379)(219,380)(220,381)(221,382)(222,383)(223,384)
(224,385)(225,372)(226,373)(227,374)(228,375)(229,376)(230,377)(231,378)
(232,365)(233,366)(234,367)(235,368)(236,369)(237,370)(238,371)(239,358)
(240,359)(241,360)(242,361)(243,362)(244,363)(245,364);
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, 
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