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