Polytope of Type {10,58}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,58}*1160
Also Known As : {10,58|2}. if this polytope has another name.
Group : SmallGroup(1160,45)
Rank : 3
Schlafli Type : {10,58}
Number of vertices, edges, etc : 10, 290, 58
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 : {2,58}*232
   10-fold quotients : {2,29}*116
   29-fold quotients : {10,2}*40
   58-fold quotients : {5,2}*20
   145-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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