Polytope of Type {14,58}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,58}*1624
Also Known As : {14,58|2}. if this polytope has another name.
Group : SmallGroup(1624,52)
Rank : 3
Schlafli Type : {14,58}
Number of vertices, edges, etc : 14, 406, 58
Order of s0s1s2 : 406
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) :
7-fold quotients : {2,58}*232
14-fold quotients : {2,29}*116
29-fold quotients : {14,2}*56
58-fold quotients : {7,2}*28
203-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 30,175)( 31,176)( 32,177)( 33,178)( 34,179)( 35,180)( 36,181)( 37,182)
( 38,183)( 39,184)( 40,185)( 41,186)( 42,187)( 43,188)( 44,189)( 45,190)
( 46,191)( 47,192)( 48,193)( 49,194)( 50,195)( 51,196)( 52,197)( 53,198)
( 54,199)( 55,200)( 56,201)( 57,202)( 58,203)( 59,146)( 60,147)( 61,148)
( 62,149)( 63,150)( 64,151)( 65,152)( 66,153)( 67,154)( 68,155)( 69,156)
( 70,157)( 71,158)( 72,159)( 73,160)( 74,161)( 75,162)( 76,163)( 77,164)
( 78,165)( 79,166)( 80,167)( 81,168)( 82,169)( 83,170)( 84,171)( 85,172)
( 86,173)( 87,174)( 88,117)( 89,118)( 90,119)( 91,120)( 92,121)( 93,122)
( 94,123)( 95,124)( 96,125)( 97,126)( 98,127)( 99,128)(100,129)(101,130)
(102,131)(103,132)(104,133)(105,134)(106,135)(107,136)(108,137)(109,138)
(110,139)(111,140)(112,141)(113,142)(114,143)(115,144)(116,145)(233,378)
(234,379)(235,380)(236,381)(237,382)(238,383)(239,384)(240,385)(241,386)
(242,387)(243,388)(244,389)(245,390)(246,391)(247,392)(248,393)(249,394)
(250,395)(251,396)(252,397)(253,398)(254,399)(255,400)(256,401)(257,402)
(258,403)(259,404)(260,405)(261,406)(262,349)(263,350)(264,351)(265,352)
(266,353)(267,354)(268,355)(269,356)(270,357)(271,358)(272,359)(273,360)
(274,361)(275,362)(276,363)(277,364)(278,365)(279,366)(280,367)(281,368)
(282,369)(283,370)(284,371)(285,372)(286,373)(287,374)(288,375)(289,376)
(290,377)(291,320)(292,321)(293,322)(294,323)(295,324)(296,325)(297,326)
(298,327)(299,328)(300,329)(301,330)(302,331)(303,332)(304,333)(305,334)
(306,335)(307,336)(308,337)(309,338)(310,339)(311,340)(312,341)(313,342)
(314,343)(315,344)(316,345)(317,346)(318,347)(319,348);;
s1 := ( 1, 30)( 2, 58)( 3, 57)( 4, 56)( 5, 55)( 6, 54)( 7, 53)( 8, 52)
( 9, 51)( 10, 50)( 11, 49)( 12, 48)( 13, 47)( 14, 46)( 15, 45)( 16, 44)
( 17, 43)( 18, 42)( 19, 41)( 20, 40)( 21, 39)( 22, 38)( 23, 37)( 24, 36)
( 25, 35)( 26, 34)( 27, 33)( 28, 32)( 29, 31)( 59,175)( 60,203)( 61,202)
( 62,201)( 63,200)( 64,199)( 65,198)( 66,197)( 67,196)( 68,195)( 69,194)
( 70,193)( 71,192)( 72,191)( 73,190)( 74,189)( 75,188)( 76,187)( 77,186)
( 78,185)( 79,184)( 80,183)( 81,182)( 82,181)( 83,180)( 84,179)( 85,178)
( 86,177)( 87,176)( 88,146)( 89,174)( 90,173)( 91,172)( 92,171)( 93,170)
( 94,169)( 95,168)( 96,167)( 97,166)( 98,165)( 99,164)(100,163)(101,162)
(102,161)(103,160)(104,159)(105,158)(106,157)(107,156)(108,155)(109,154)
(110,153)(111,152)(112,151)(113,150)(114,149)(115,148)(116,147)(118,145)
(119,144)(120,143)(121,142)(122,141)(123,140)(124,139)(125,138)(126,137)
(127,136)(128,135)(129,134)(130,133)(131,132)(204,233)(205,261)(206,260)
(207,259)(208,258)(209,257)(210,256)(211,255)(212,254)(213,253)(214,252)
(215,251)(216,250)(217,249)(218,248)(219,247)(220,246)(221,245)(222,244)
(223,243)(224,242)(225,241)(226,240)(227,239)(228,238)(229,237)(230,236)
(231,235)(232,234)(262,378)(263,406)(264,405)(265,404)(266,403)(267,402)
(268,401)(269,400)(270,399)(271,398)(272,397)(273,396)(274,395)(275,394)
(276,393)(277,392)(278,391)(279,390)(280,389)(281,388)(282,387)(283,386)
(284,385)(285,384)(286,383)(287,382)(288,381)(289,380)(290,379)(291,349)
(292,377)(293,376)(294,375)(295,374)(296,373)(297,372)(298,371)(299,370)
(300,369)(301,368)(302,367)(303,366)(304,365)(305,364)(306,363)(307,362)
(308,361)(309,360)(310,359)(311,358)(312,357)(313,356)(314,355)(315,354)
(316,353)(317,352)(318,351)(319,350)(321,348)(322,347)(323,346)(324,345)
(325,344)(326,343)(327,342)(328,341)(329,340)(330,339)(331,338)(332,337)
(333,336)(334,335);;
s2 := ( 1,205)( 2,204)( 3,232)( 4,231)( 5,230)( 6,229)( 7,228)( 8,227)
( 9,226)( 10,225)( 11,224)( 12,223)( 13,222)( 14,221)( 15,220)( 16,219)
( 17,218)( 18,217)( 19,216)( 20,215)( 21,214)( 22,213)( 23,212)( 24,211)
( 25,210)( 26,209)( 27,208)( 28,207)( 29,206)( 30,234)( 31,233)( 32,261)
( 33,260)( 34,259)( 35,258)( 36,257)( 37,256)( 38,255)( 39,254)( 40,253)
( 41,252)( 42,251)( 43,250)( 44,249)( 45,248)( 46,247)( 47,246)( 48,245)
( 49,244)( 50,243)( 51,242)( 52,241)( 53,240)( 54,239)( 55,238)( 56,237)
( 57,236)( 58,235)( 59,263)( 60,262)( 61,290)( 62,289)( 63,288)( 64,287)
( 65,286)( 66,285)( 67,284)( 68,283)( 69,282)( 70,281)( 71,280)( 72,279)
( 73,278)( 74,277)( 75,276)( 76,275)( 77,274)( 78,273)( 79,272)( 80,271)
( 81,270)( 82,269)( 83,268)( 84,267)( 85,266)( 86,265)( 87,264)( 88,292)
( 89,291)( 90,319)( 91,318)( 92,317)( 93,316)( 94,315)( 95,314)( 96,313)
( 97,312)( 98,311)( 99,310)(100,309)(101,308)(102,307)(103,306)(104,305)
(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,298)(112,297)
(113,296)(114,295)(115,294)(116,293)(117,321)(118,320)(119,348)(120,347)
(121,346)(122,345)(123,344)(124,343)(125,342)(126,341)(127,340)(128,339)
(129,338)(130,337)(131,336)(132,335)(133,334)(134,333)(135,332)(136,331)
(137,330)(138,329)(139,328)(140,327)(141,326)(142,325)(143,324)(144,323)
(145,322)(146,350)(147,349)(148,377)(149,376)(150,375)(151,374)(152,373)
(153,372)(154,371)(155,370)(156,369)(157,368)(158,367)(159,366)(160,365)
(161,364)(162,363)(163,362)(164,361)(165,360)(166,359)(167,358)(168,357)
(169,356)(170,355)(171,354)(172,353)(173,352)(174,351)(175,379)(176,378)
(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,400)(184,399)
(185,398)(186,397)(187,396)(188,395)(189,394)(190,393)(191,392)(192,391)
(193,390)(194,389)(195,388)(196,387)(197,386)(198,385)(199,384)(200,383)
(201,382)(202,381)(203,380);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(406)!( 30,175)( 31,176)( 32,177)( 33,178)( 34,179)( 35,180)( 36,181)
( 37,182)( 38,183)( 39,184)( 40,185)( 41,186)( 42,187)( 43,188)( 44,189)
( 45,190)( 46,191)( 47,192)( 48,193)( 49,194)( 50,195)( 51,196)( 52,197)
( 53,198)( 54,199)( 55,200)( 56,201)( 57,202)( 58,203)( 59,146)( 60,147)
( 61,148)( 62,149)( 63,150)( 64,151)( 65,152)( 66,153)( 67,154)( 68,155)
( 69,156)( 70,157)( 71,158)( 72,159)( 73,160)( 74,161)( 75,162)( 76,163)
( 77,164)( 78,165)( 79,166)( 80,167)( 81,168)( 82,169)( 83,170)( 84,171)
( 85,172)( 86,173)( 87,174)( 88,117)( 89,118)( 90,119)( 91,120)( 92,121)
( 93,122)( 94,123)( 95,124)( 96,125)( 97,126)( 98,127)( 99,128)(100,129)
(101,130)(102,131)(103,132)(104,133)(105,134)(106,135)(107,136)(108,137)
(109,138)(110,139)(111,140)(112,141)(113,142)(114,143)(115,144)(116,145)
(233,378)(234,379)(235,380)(236,381)(237,382)(238,383)(239,384)(240,385)
(241,386)(242,387)(243,388)(244,389)(245,390)(246,391)(247,392)(248,393)
(249,394)(250,395)(251,396)(252,397)(253,398)(254,399)(255,400)(256,401)
(257,402)(258,403)(259,404)(260,405)(261,406)(262,349)(263,350)(264,351)
(265,352)(266,353)(267,354)(268,355)(269,356)(270,357)(271,358)(272,359)
(273,360)(274,361)(275,362)(276,363)(277,364)(278,365)(279,366)(280,367)
(281,368)(282,369)(283,370)(284,371)(285,372)(286,373)(287,374)(288,375)
(289,376)(290,377)(291,320)(292,321)(293,322)(294,323)(295,324)(296,325)
(297,326)(298,327)(299,328)(300,329)(301,330)(302,331)(303,332)(304,333)
(305,334)(306,335)(307,336)(308,337)(309,338)(310,339)(311,340)(312,341)
(313,342)(314,343)(315,344)(316,345)(317,346)(318,347)(319,348);
s1 := Sym(406)!( 1, 30)( 2, 58)( 3, 57)( 4, 56)( 5, 55)( 6, 54)( 7, 53)
( 8, 52)( 9, 51)( 10, 50)( 11, 49)( 12, 48)( 13, 47)( 14, 46)( 15, 45)
( 16, 44)( 17, 43)( 18, 42)( 19, 41)( 20, 40)( 21, 39)( 22, 38)( 23, 37)
( 24, 36)( 25, 35)( 26, 34)( 27, 33)( 28, 32)( 29, 31)( 59,175)( 60,203)
( 61,202)( 62,201)( 63,200)( 64,199)( 65,198)( 66,197)( 67,196)( 68,195)
( 69,194)( 70,193)( 71,192)( 72,191)( 73,190)( 74,189)( 75,188)( 76,187)
( 77,186)( 78,185)( 79,184)( 80,183)( 81,182)( 82,181)( 83,180)( 84,179)
( 85,178)( 86,177)( 87,176)( 88,146)( 89,174)( 90,173)( 91,172)( 92,171)
( 93,170)( 94,169)( 95,168)( 96,167)( 97,166)( 98,165)( 99,164)(100,163)
(101,162)(102,161)(103,160)(104,159)(105,158)(106,157)(107,156)(108,155)
(109,154)(110,153)(111,152)(112,151)(113,150)(114,149)(115,148)(116,147)
(118,145)(119,144)(120,143)(121,142)(122,141)(123,140)(124,139)(125,138)
(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(204,233)(205,261)
(206,260)(207,259)(208,258)(209,257)(210,256)(211,255)(212,254)(213,253)
(214,252)(215,251)(216,250)(217,249)(218,248)(219,247)(220,246)(221,245)
(222,244)(223,243)(224,242)(225,241)(226,240)(227,239)(228,238)(229,237)
(230,236)(231,235)(232,234)(262,378)(263,406)(264,405)(265,404)(266,403)
(267,402)(268,401)(269,400)(270,399)(271,398)(272,397)(273,396)(274,395)
(275,394)(276,393)(277,392)(278,391)(279,390)(280,389)(281,388)(282,387)
(283,386)(284,385)(285,384)(286,383)(287,382)(288,381)(289,380)(290,379)
(291,349)(292,377)(293,376)(294,375)(295,374)(296,373)(297,372)(298,371)
(299,370)(300,369)(301,368)(302,367)(303,366)(304,365)(305,364)(306,363)
(307,362)(308,361)(309,360)(310,359)(311,358)(312,357)(313,356)(314,355)
(315,354)(316,353)(317,352)(318,351)(319,350)(321,348)(322,347)(323,346)
(324,345)(325,344)(326,343)(327,342)(328,341)(329,340)(330,339)(331,338)
(332,337)(333,336)(334,335);
s2 := Sym(406)!( 1,205)( 2,204)( 3,232)( 4,231)( 5,230)( 6,229)( 7,228)
( 8,227)( 9,226)( 10,225)( 11,224)( 12,223)( 13,222)( 14,221)( 15,220)
( 16,219)( 17,218)( 18,217)( 19,216)( 20,215)( 21,214)( 22,213)( 23,212)
( 24,211)( 25,210)( 26,209)( 27,208)( 28,207)( 29,206)( 30,234)( 31,233)
( 32,261)( 33,260)( 34,259)( 35,258)( 36,257)( 37,256)( 38,255)( 39,254)
( 40,253)( 41,252)( 42,251)( 43,250)( 44,249)( 45,248)( 46,247)( 47,246)
( 48,245)( 49,244)( 50,243)( 51,242)( 52,241)( 53,240)( 54,239)( 55,238)
( 56,237)( 57,236)( 58,235)( 59,263)( 60,262)( 61,290)( 62,289)( 63,288)
( 64,287)( 65,286)( 66,285)( 67,284)( 68,283)( 69,282)( 70,281)( 71,280)
( 72,279)( 73,278)( 74,277)( 75,276)( 76,275)( 77,274)( 78,273)( 79,272)
( 80,271)( 81,270)( 82,269)( 83,268)( 84,267)( 85,266)( 86,265)( 87,264)
( 88,292)( 89,291)( 90,319)( 91,318)( 92,317)( 93,316)( 94,315)( 95,314)
( 96,313)( 97,312)( 98,311)( 99,310)(100,309)(101,308)(102,307)(103,306)
(104,305)(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,298)
(112,297)(113,296)(114,295)(115,294)(116,293)(117,321)(118,320)(119,348)
(120,347)(121,346)(122,345)(123,344)(124,343)(125,342)(126,341)(127,340)
(128,339)(129,338)(130,337)(131,336)(132,335)(133,334)(134,333)(135,332)
(136,331)(137,330)(138,329)(139,328)(140,327)(141,326)(142,325)(143,324)
(144,323)(145,322)(146,350)(147,349)(148,377)(149,376)(150,375)(151,374)
(152,373)(153,372)(154,371)(155,370)(156,369)(157,368)(158,367)(159,366)
(160,365)(161,364)(162,363)(163,362)(164,361)(165,360)(166,359)(167,358)
(168,357)(169,356)(170,355)(171,354)(172,353)(173,352)(174,351)(175,379)
(176,378)(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,400)
(184,399)(185,398)(186,397)(187,396)(188,395)(189,394)(190,393)(191,392)
(192,391)(193,390)(194,389)(195,388)(196,387)(197,386)(198,385)(199,384)
(200,383)(201,382)(202,381)(203,380);
poly := sub<Sym(406)|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 >;
References : None.
to this polytope