Polytope of Type {58,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {58,10}*1160
Also Known As : {58,10|2}. if this polytope has another name.
Group : SmallGroup(1160,45)
Rank : 3
Schlafli Type : {58,10}
Number of vertices, edges, etc : 58, 290, 10
Order of s₀s₁s₂ : 290
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) :
   5-fold quotients : {58,2}*232
   10-fold quotients : {29,2}*116
   29-fold quotients : {2,10}*40
   58-fold quotients : {2,5}*20
   145-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);;
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)( 30,118)( 31,117)
( 32,145)( 33,144)( 34,143)( 35,142)( 36,141)( 37,140)( 38,139)( 39,138)
( 40,137)( 41,136)( 42,135)( 43,134)( 44,133)( 45,132)( 46,131)( 47,130)
( 48,129)( 49,128)( 50,127)( 51,126)( 52,125)( 53,124)( 54,123)( 55,122)
( 56,121)( 57,120)( 58,119)( 59, 89)( 60, 88)( 61,116)( 62,115)( 63,114)
( 64,113)( 65,112)( 66,111)( 67,110)( 68,109)( 69,108)( 70,107)( 71,106)
( 72,105)( 73,104)( 74,103)( 75,102)( 76,101)( 77,100)( 78, 99)( 79, 98)
( 80, 97)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 90)
(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)(175,263)(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)(204,234)(205,233)(206,261)(207,260)(208,259)
(209,258)(210,257)(211,256)(212,255)(213,254)(214,253)(215,252)(216,251)
(217,250)(218,249)(219,248)(220,247)(221,246)(222,245)(223,244)(224,243)
(225,242)(226,241)(227,240)(228,239)(229,238)(230,237)(231,236)(232,235);;
s2 := (  1,175)(  2,176)(  3,177)(  4,178)(  5,179)(  6,180)(  7,181)(  8,182)
(  9,183)( 10,184)( 11,185)( 12,186)( 13,187)( 14,188)( 15,189)( 16,190)
( 17,191)( 18,192)( 19,193)( 20,194)( 21,195)( 22,196)( 23,197)( 24,198)
( 25,199)( 26,200)( 27,201)( 28,202)( 29,203)( 30,146)( 31,147)( 32,148)
( 33,149)( 34,150)( 35,151)( 36,152)( 37,153)( 38,154)( 39,155)( 40,156)
( 41,157)( 42,158)( 43,159)( 44,160)( 45,161)( 46,162)( 47,163)( 48,164)
( 49,165)( 50,166)( 51,167)( 52,168)( 53,169)( 54,170)( 55,171)( 56,172)
( 57,173)( 58,174)( 59,262)( 60,263)( 61,264)( 62,265)( 63,266)( 64,267)
( 65,268)( 66,269)( 67,270)( 68,271)( 69,272)( 70,273)( 71,274)( 72,275)
( 73,276)( 74,277)( 75,278)( 76,279)( 77,280)( 78,281)( 79,282)( 80,283)
( 81,284)( 82,285)( 83,286)( 84,287)( 85,288)( 86,289)( 87,290)( 88,233)
( 89,234)( 90,235)( 91,236)( 92,237)( 93,238)( 94,239)( 95,240)( 96,241)
( 97,242)( 98,243)( 99,244)(100,245)(101,246)(102,247)(103,248)(104,249)
(105,250)(106,251)(107,252)(108,253)(109,254)(110,255)(111,256)(112,257)
(113,258)(114,259)(115,260)(116,261)(117,204)(118,205)(119,206)(120,207)
(121,208)(122,209)(123,210)(124,211)(125,212)(126,213)(127,214)(128,215)
(129,216)(130,217)(131,218)(132,219)(133,220)(134,221)(135,222)(136,223)
(137,224)(138,225)(139,226)(140,227)(141,228)(142,229)(143,230)(144,231)
(145,232);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(290)!(  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);
s1 := Sym(290)!(  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)( 30,118)
( 31,117)( 32,145)( 33,144)( 34,143)( 35,142)( 36,141)( 37,140)( 38,139)
( 39,138)( 40,137)( 41,136)( 42,135)( 43,134)( 44,133)( 45,132)( 46,131)
( 47,130)( 48,129)( 49,128)( 50,127)( 51,126)( 52,125)( 53,124)( 54,123)
( 55,122)( 56,121)( 57,120)( 58,119)( 59, 89)( 60, 88)( 61,116)( 62,115)
( 63,114)( 64,113)( 65,112)( 66,111)( 67,110)( 68,109)( 69,108)( 70,107)
( 71,106)( 72,105)( 73,104)( 74,103)( 75,102)( 76,101)( 77,100)( 78, 99)
( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 92)( 86, 91)
( 87, 90)(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)(175,263)
(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)(204,234)(205,233)(206,261)(207,260)
(208,259)(209,258)(210,257)(211,256)(212,255)(213,254)(214,253)(215,252)
(216,251)(217,250)(218,249)(219,248)(220,247)(221,246)(222,245)(223,244)
(224,243)(225,242)(226,241)(227,240)(228,239)(229,238)(230,237)(231,236)
(232,235);
s2 := Sym(290)!(  1,175)(  2,176)(  3,177)(  4,178)(  5,179)(  6,180)(  7,181)
(  8,182)(  9,183)( 10,184)( 11,185)( 12,186)( 13,187)( 14,188)( 15,189)
( 16,190)( 17,191)( 18,192)( 19,193)( 20,194)( 21,195)( 22,196)( 23,197)
( 24,198)( 25,199)( 26,200)( 27,201)( 28,202)( 29,203)( 30,146)( 31,147)
( 32,148)( 33,149)( 34,150)( 35,151)( 36,152)( 37,153)( 38,154)( 39,155)
( 40,156)( 41,157)( 42,158)( 43,159)( 44,160)( 45,161)( 46,162)( 47,163)
( 48,164)( 49,165)( 50,166)( 51,167)( 52,168)( 53,169)( 54,170)( 55,171)
( 56,172)( 57,173)( 58,174)( 59,262)( 60,263)( 61,264)( 62,265)( 63,266)
( 64,267)( 65,268)( 66,269)( 67,270)( 68,271)( 69,272)( 70,273)( 71,274)
( 72,275)( 73,276)( 74,277)( 75,278)( 76,279)( 77,280)( 78,281)( 79,282)
( 80,283)( 81,284)( 82,285)( 83,286)( 84,287)( 85,288)( 86,289)( 87,290)
( 88,233)( 89,234)( 90,235)( 91,236)( 92,237)( 93,238)( 94,239)( 95,240)
( 96,241)( 97,242)( 98,243)( 99,244)(100,245)(101,246)(102,247)(103,248)
(104,249)(105,250)(106,251)(107,252)(108,253)(109,254)(110,255)(111,256)
(112,257)(113,258)(114,259)(115,260)(116,261)(117,204)(118,205)(119,206)
(120,207)(121,208)(122,209)(123,210)(124,211)(125,212)(126,213)(127,214)
(128,215)(129,216)(130,217)(131,218)(132,219)(133,220)(134,221)(135,222)
(136,223)(137,224)(138,225)(139,226)(140,227)(141,228)(142,229)(143,230)
(144,231)(145,232);
poly := sub<Sym(290)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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