Polytope of Type {12,58}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,58}*1392
Also Known As : {12,58|2}. if this polytope has another name.
Group : SmallGroup(1392,130)
Rank : 3
Schlafli Type : {12,58}
Number of vertices, edges, etc : 12, 348, 58
Order of s0s1s2 : 348
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) :
2-fold quotients : {6,58}*696
3-fold quotients : {4,58}*464
6-fold quotients : {2,58}*232
12-fold quotients : {2,29}*116
29-fold quotients : {12,2}*48
58-fold quotients : {6,2}*24
87-fold quotients : {4,2}*16
116-fold quotients : {3,2}*12
174-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 30, 59)( 31, 60)( 32, 61)( 33, 62)( 34, 63)( 35, 64)( 36, 65)( 37, 66)
( 38, 67)( 39, 68)( 40, 69)( 41, 70)( 42, 71)( 43, 72)( 44, 73)( 45, 74)
( 46, 75)( 47, 76)( 48, 77)( 49, 78)( 50, 79)( 51, 80)( 52, 81)( 53, 82)
( 54, 83)( 55, 84)( 56, 85)( 57, 86)( 58, 87)(117,146)(118,147)(119,148)
(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)
(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)
(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)(142,171)(143,172)
(144,173)(145,174)(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)(204,320)
(205,321)(206,322)(207,323)(208,324)(209,325)(210,326)(211,327)(212,328)
(213,329)(214,330)(215,331)(216,332)(217,333)(218,334)(219,335)(220,336)
(221,337)(222,338)(223,339)(224,340)(225,341)(226,342)(227,343)(228,344)
(229,345)(230,346)(231,347)(232,348)(233,291)(234,292)(235,293)(236,294)
(237,295)(238,296)(239,297)(240,298)(241,299)(242,300)(243,301)(244,302)
(245,303)(246,304)(247,305)(248,306)(249,307)(250,308)(251,309)(252,310)
(253,311)(254,312)(255,313)(256,314)(257,315)(258,316)(259,317)(260,318)
(261,319);;
s1 := ( 1,204)( 2,232)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)( 8,226)
( 9,225)( 10,224)( 11,223)( 12,222)( 13,221)( 14,220)( 15,219)( 16,218)
( 17,217)( 18,216)( 19,215)( 20,214)( 21,213)( 22,212)( 23,211)( 24,210)
( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,175)( 31,203)( 32,202)
( 33,201)( 34,200)( 35,199)( 36,198)( 37,197)( 38,196)( 39,195)( 40,194)
( 41,193)( 42,192)( 43,191)( 44,190)( 45,189)( 46,188)( 47,187)( 48,186)
( 49,185)( 50,184)( 51,183)( 52,182)( 53,181)( 54,180)( 55,179)( 56,178)
( 57,177)( 58,176)( 59,233)( 60,261)( 61,260)( 62,259)( 63,258)( 64,257)
( 65,256)( 66,255)( 67,254)( 68,253)( 69,252)( 70,251)( 71,250)( 72,249)
( 73,248)( 74,247)( 75,246)( 76,245)( 77,244)( 78,243)( 79,242)( 80,241)
( 81,240)( 82,239)( 83,238)( 84,237)( 85,236)( 86,235)( 87,234)( 88,291)
( 89,319)( 90,318)( 91,317)( 92,316)( 93,315)( 94,314)( 95,313)( 96,312)
( 97,311)( 98,310)( 99,309)(100,308)(101,307)(102,306)(103,305)(104,304)
(105,303)(106,302)(107,301)(108,300)(109,299)(110,298)(111,297)(112,296)
(113,295)(114,294)(115,293)(116,292)(117,262)(118,290)(119,289)(120,288)
(121,287)(122,286)(123,285)(124,284)(125,283)(126,282)(127,281)(128,280)
(129,279)(130,278)(131,277)(132,276)(133,275)(134,274)(135,273)(136,272)
(137,271)(138,270)(139,269)(140,268)(141,267)(142,266)(143,265)(144,264)
(145,263)(146,320)(147,348)(148,347)(149,346)(150,345)(151,344)(152,343)
(153,342)(154,341)(155,340)(156,339)(157,338)(158,337)(159,336)(160,335)
(161,334)(162,333)(163,332)(164,331)(165,330)(166,329)(167,328)(168,327)
(169,326)(170,325)(171,324)(172,323)(173,322)(174,321);;
s2 := ( 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, 31)( 32, 58)
( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)( 40, 50)
( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)( 63, 85)
( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)
( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)
( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)(102,104)
(117,118)(119,145)(120,144)(121,143)(122,142)(123,141)(124,140)(125,139)
(126,138)(127,137)(128,136)(129,135)(130,134)(131,133)(146,147)(148,174)
(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,167)(156,166)
(157,165)(158,164)(159,163)(160,162)(175,176)(177,203)(178,202)(179,201)
(180,200)(181,199)(182,198)(183,197)(184,196)(185,195)(186,194)(187,193)
(188,192)(189,191)(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)
(233,234)(235,261)(236,260)(237,259)(238,258)(239,257)(240,256)(241,255)
(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)(262,263)(264,290)
(265,289)(266,288)(267,287)(268,286)(269,285)(270,284)(271,283)(272,282)
(273,281)(274,280)(275,279)(276,278)(291,292)(293,319)(294,318)(295,317)
(296,316)(297,315)(298,314)(299,313)(300,312)(301,311)(302,310)(303,309)
(304,308)(305,307)(320,321)(322,348)(323,347)(324,346)(325,345)(326,344)
(327,343)(328,342)(329,341)(330,340)(331,339)(332,338)(333,337)(334,336);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(348)!( 30, 59)( 31, 60)( 32, 61)( 33, 62)( 34, 63)( 35, 64)( 36, 65)
( 37, 66)( 38, 67)( 39, 68)( 40, 69)( 41, 70)( 42, 71)( 43, 72)( 44, 73)
( 45, 74)( 46, 75)( 47, 76)( 48, 77)( 49, 78)( 50, 79)( 51, 80)( 52, 81)
( 53, 82)( 54, 83)( 55, 84)( 56, 85)( 57, 86)( 58, 87)(117,146)(118,147)
(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)
(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)
(135,164)(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)(142,171)
(143,172)(144,173)(145,174)(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)
(204,320)(205,321)(206,322)(207,323)(208,324)(209,325)(210,326)(211,327)
(212,328)(213,329)(214,330)(215,331)(216,332)(217,333)(218,334)(219,335)
(220,336)(221,337)(222,338)(223,339)(224,340)(225,341)(226,342)(227,343)
(228,344)(229,345)(230,346)(231,347)(232,348)(233,291)(234,292)(235,293)
(236,294)(237,295)(238,296)(239,297)(240,298)(241,299)(242,300)(243,301)
(244,302)(245,303)(246,304)(247,305)(248,306)(249,307)(250,308)(251,309)
(252,310)(253,311)(254,312)(255,313)(256,314)(257,315)(258,316)(259,317)
(260,318)(261,319);
s1 := Sym(348)!( 1,204)( 2,232)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)
( 8,226)( 9,225)( 10,224)( 11,223)( 12,222)( 13,221)( 14,220)( 15,219)
( 16,218)( 17,217)( 18,216)( 19,215)( 20,214)( 21,213)( 22,212)( 23,211)
( 24,210)( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,175)( 31,203)
( 32,202)( 33,201)( 34,200)( 35,199)( 36,198)( 37,197)( 38,196)( 39,195)
( 40,194)( 41,193)( 42,192)( 43,191)( 44,190)( 45,189)( 46,188)( 47,187)
( 48,186)( 49,185)( 50,184)( 51,183)( 52,182)( 53,181)( 54,180)( 55,179)
( 56,178)( 57,177)( 58,176)( 59,233)( 60,261)( 61,260)( 62,259)( 63,258)
( 64,257)( 65,256)( 66,255)( 67,254)( 68,253)( 69,252)( 70,251)( 71,250)
( 72,249)( 73,248)( 74,247)( 75,246)( 76,245)( 77,244)( 78,243)( 79,242)
( 80,241)( 81,240)( 82,239)( 83,238)( 84,237)( 85,236)( 86,235)( 87,234)
( 88,291)( 89,319)( 90,318)( 91,317)( 92,316)( 93,315)( 94,314)( 95,313)
( 96,312)( 97,311)( 98,310)( 99,309)(100,308)(101,307)(102,306)(103,305)
(104,304)(105,303)(106,302)(107,301)(108,300)(109,299)(110,298)(111,297)
(112,296)(113,295)(114,294)(115,293)(116,292)(117,262)(118,290)(119,289)
(120,288)(121,287)(122,286)(123,285)(124,284)(125,283)(126,282)(127,281)
(128,280)(129,279)(130,278)(131,277)(132,276)(133,275)(134,274)(135,273)
(136,272)(137,271)(138,270)(139,269)(140,268)(141,267)(142,266)(143,265)
(144,264)(145,263)(146,320)(147,348)(148,347)(149,346)(150,345)(151,344)
(152,343)(153,342)(154,341)(155,340)(156,339)(157,338)(158,337)(159,336)
(160,335)(161,334)(162,333)(163,332)(164,331)(165,330)(166,329)(167,328)
(168,327)(169,326)(170,325)(171,324)(172,323)(173,322)(174,321);
s2 := Sym(348)!( 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, 31)
( 32, 58)( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)
( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)
( 63, 85)( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)
( 71, 77)( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)
(102,104)(117,118)(119,145)(120,144)(121,143)(122,142)(123,141)(124,140)
(125,139)(126,138)(127,137)(128,136)(129,135)(130,134)(131,133)(146,147)
(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,167)
(156,166)(157,165)(158,164)(159,163)(160,162)(175,176)(177,203)(178,202)
(179,201)(180,200)(181,199)(182,198)(183,197)(184,196)(185,195)(186,194)
(187,193)(188,192)(189,191)(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)(233,234)(235,261)(236,260)(237,259)(238,258)(239,257)(240,256)
(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)(262,263)
(264,290)(265,289)(266,288)(267,287)(268,286)(269,285)(270,284)(271,283)
(272,282)(273,281)(274,280)(275,279)(276,278)(291,292)(293,319)(294,318)
(295,317)(296,316)(297,315)(298,314)(299,313)(300,312)(301,311)(302,310)
(303,309)(304,308)(305,307)(320,321)(322,348)(323,347)(324,346)(325,345)
(326,344)(327,343)(328,342)(329,341)(330,340)(331,339)(332,338)(333,337)
(334,336);
poly := sub<Sym(348)|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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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