Polytope of Type {70,14}

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