Polytope of Type {58,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {58,12}*1392
Also Known As : {58,12|2}. if this polytope has another name.
Group : SmallGroup(1392,130)
Rank : 3
Schlafli Type : {58,12}
Number of vertices, edges, etc : 58, 348, 12
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 : {58,6}*696
   3-fold quotients : {58,4}*464
   6-fold quotients : {58,2}*232
   12-fold quotients : {29,2}*116
   29-fold quotients : {2,12}*48
   58-fold quotients : {2,6}*24
   87-fold quotients : {2,4}*16
   116-fold quotients : {2,3}*12
   174-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);;
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, 60)( 31, 59)
( 32, 87)( 33, 86)( 34, 85)( 35, 84)( 36, 83)( 37, 82)( 38, 81)( 39, 80)
( 40, 79)( 41, 78)( 42, 77)( 43, 76)( 44, 75)( 45, 74)( 46, 73)( 47, 72)
( 48, 71)( 49, 70)( 50, 69)( 51, 68)( 52, 67)( 53, 66)( 54, 65)( 55, 64)
( 56, 63)( 57, 62)( 58, 61)( 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)(117,147)(118,146)(119,174)(120,173)(121,172)(122,171)(123,170)
(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)(131,162)
(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,154)
(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(175,263)(176,262)
(177,290)(178,289)(179,288)(180,287)(181,286)(182,285)(183,284)(184,283)
(185,282)(186,281)(187,280)(188,279)(189,278)(190,277)(191,276)(192,275)
(193,274)(194,273)(195,272)(196,271)(197,270)(198,269)(199,268)(200,267)
(201,266)(202,265)(203,264)(204,321)(205,320)(206,348)(207,347)(208,346)
(209,345)(210,344)(211,343)(212,342)(213,341)(214,340)(215,339)(216,338)
(217,337)(218,336)(219,335)(220,334)(221,333)(222,332)(223,331)(224,330)
(225,329)(226,328)(227,327)(228,326)(229,325)(230,324)(231,323)(232,322)
(233,292)(234,291)(235,319)(236,318)(237,317)(238,316)(239,315)(240,314)
(241,313)(242,312)(243,311)(244,310)(245,309)(246,308)(247,307)(248,306)
(249,305)(250,304)(251,303)(252,302)(253,301)(254,300)(255,299)(256,298)
(257,297)(258,296)(259,295)(260,294)(261,293);;
s2 := (  1,204)(  2,205)(  3,206)(  4,207)(  5,208)(  6,209)(  7,210)(  8,211)
(  9,212)( 10,213)( 11,214)( 12,215)( 13,216)( 14,217)( 15,218)( 16,219)
( 17,220)( 18,221)( 19,222)( 20,223)( 21,224)( 22,225)( 23,226)( 24,227)
( 25,228)( 26,229)( 27,230)( 28,231)( 29,232)( 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)( 59,233)( 60,234)( 61,235)( 62,236)( 63,237)( 64,238)
( 65,239)( 66,240)( 67,241)( 68,242)( 69,243)( 70,244)( 71,245)( 72,246)
( 73,247)( 74,248)( 75,249)( 76,250)( 77,251)( 78,252)( 79,253)( 80,254)
( 81,255)( 82,256)( 83,257)( 84,258)( 85,259)( 86,260)( 87,261)( 88,291)
( 89,292)( 90,293)( 91,294)( 92,295)( 93,296)( 94,297)( 95,298)( 96,299)
( 97,300)( 98,301)( 99,302)(100,303)(101,304)(102,305)(103,306)(104,307)
(105,308)(106,309)(107,310)(108,311)(109,312)(110,313)(111,314)(112,315)
(113,316)(114,317)(115,318)(116,319)(117,262)(118,263)(119,264)(120,265)
(121,266)(122,267)(123,268)(124,269)(125,270)(126,271)(127,272)(128,273)
(129,274)(130,275)(131,276)(132,277)(133,278)(134,279)(135,280)(136,281)
(137,282)(138,283)(139,284)(140,285)(141,286)(142,287)(143,288)(144,289)
(145,290)(146,320)(147,321)(148,322)(149,323)(150,324)(151,325)(152,326)
(153,327)(154,328)(155,329)(156,330)(157,331)(158,332)(159,333)(160,334)
(161,335)(162,336)(163,337)(164,338)(165,339)(166,340)(167,341)(168,342)
(169,343)(170,344)(171,345)(172,346)(173,347)(174,348);;
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, 
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(348)!(  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);
s1 := 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, 60)
( 31, 59)( 32, 87)( 33, 86)( 34, 85)( 35, 84)( 36, 83)( 37, 82)( 38, 81)
( 39, 80)( 40, 79)( 41, 78)( 42, 77)( 43, 76)( 44, 75)( 45, 74)( 46, 73)
( 47, 72)( 48, 71)( 49, 70)( 50, 69)( 51, 68)( 52, 67)( 53, 66)( 54, 65)
( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 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)(117,147)(118,146)(119,174)(120,173)(121,172)(122,171)
(123,170)(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)
(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)
(139,154)(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(175,263)
(176,262)(177,290)(178,289)(179,288)(180,287)(181,286)(182,285)(183,284)
(184,283)(185,282)(186,281)(187,280)(188,279)(189,278)(190,277)(191,276)
(192,275)(193,274)(194,273)(195,272)(196,271)(197,270)(198,269)(199,268)
(200,267)(201,266)(202,265)(203,264)(204,321)(205,320)(206,348)(207,347)
(208,346)(209,345)(210,344)(211,343)(212,342)(213,341)(214,340)(215,339)
(216,338)(217,337)(218,336)(219,335)(220,334)(221,333)(222,332)(223,331)
(224,330)(225,329)(226,328)(227,327)(228,326)(229,325)(230,324)(231,323)
(232,322)(233,292)(234,291)(235,319)(236,318)(237,317)(238,316)(239,315)
(240,314)(241,313)(242,312)(243,311)(244,310)(245,309)(246,308)(247,307)
(248,306)(249,305)(250,304)(251,303)(252,302)(253,301)(254,300)(255,299)
(256,298)(257,297)(258,296)(259,295)(260,294)(261,293);
s2 := Sym(348)!(  1,204)(  2,205)(  3,206)(  4,207)(  5,208)(  6,209)(  7,210)
(  8,211)(  9,212)( 10,213)( 11,214)( 12,215)( 13,216)( 14,217)( 15,218)
( 16,219)( 17,220)( 18,221)( 19,222)( 20,223)( 21,224)( 22,225)( 23,226)
( 24,227)( 25,228)( 26,229)( 27,230)( 28,231)( 29,232)( 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)( 59,233)( 60,234)( 61,235)( 62,236)( 63,237)
( 64,238)( 65,239)( 66,240)( 67,241)( 68,242)( 69,243)( 70,244)( 71,245)
( 72,246)( 73,247)( 74,248)( 75,249)( 76,250)( 77,251)( 78,252)( 79,253)
( 80,254)( 81,255)( 82,256)( 83,257)( 84,258)( 85,259)( 86,260)( 87,261)
( 88,291)( 89,292)( 90,293)( 91,294)( 92,295)( 93,296)( 94,297)( 95,298)
( 96,299)( 97,300)( 98,301)( 99,302)(100,303)(101,304)(102,305)(103,306)
(104,307)(105,308)(106,309)(107,310)(108,311)(109,312)(110,313)(111,314)
(112,315)(113,316)(114,317)(115,318)(116,319)(117,262)(118,263)(119,264)
(120,265)(121,266)(122,267)(123,268)(124,269)(125,270)(126,271)(127,272)
(128,273)(129,274)(130,275)(131,276)(132,277)(133,278)(134,279)(135,280)
(136,281)(137,282)(138,283)(139,284)(140,285)(141,286)(142,287)(143,288)
(144,289)(145,290)(146,320)(147,321)(148,322)(149,323)(150,324)(151,325)
(152,326)(153,327)(154,328)(155,329)(156,330)(157,331)(158,332)(159,333)
(160,334)(161,335)(162,336)(163,337)(164,338)(165,339)(166,340)(167,341)
(168,342)(169,343)(170,344)(171,345)(172,346)(173,347)(174,348);
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, 
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