Polytope of Type {10,62}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,62}*1240
Also Known As : {10,62|2}. if this polytope has another name.
Group : SmallGroup(1240,47)
Rank : 3
Schlafli Type : {10,62}
Number of vertices, edges, etc : 10, 310, 62
Order of s₀s₁s₂ : 310
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 : {2,62}*248
   10-fold quotients : {2,31}*124
   31-fold quotients : {10,2}*40
   62-fold quotients : {5,2}*20
   155-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 32,125)( 33,126)( 34,127)( 35,128)( 36,129)( 37,130)( 38,131)( 39,132)
( 40,133)( 41,134)( 42,135)( 43,136)( 44,137)( 45,138)( 46,139)( 47,140)
( 48,141)( 49,142)( 50,143)( 51,144)( 52,145)( 53,146)( 54,147)( 55,148)
( 56,149)( 57,150)( 58,151)( 59,152)( 60,153)( 61,154)( 62,155)( 63, 94)
( 64, 95)( 65, 96)( 66, 97)( 67, 98)( 68, 99)( 69,100)( 70,101)( 71,102)
( 72,103)( 73,104)( 74,105)( 75,106)( 76,107)( 77,108)( 78,109)( 79,110)
( 80,111)( 81,112)( 82,113)( 83,114)( 84,115)( 85,116)( 86,117)( 87,118)
( 88,119)( 89,120)( 90,121)( 91,122)( 92,123)( 93,124)(187,280)(188,281)
(189,282)(190,283)(191,284)(192,285)(193,286)(194,287)(195,288)(196,289)
(197,290)(198,291)(199,292)(200,293)(201,294)(202,295)(203,296)(204,297)
(205,298)(206,299)(207,300)(208,301)(209,302)(210,303)(211,304)(212,305)
(213,306)(214,307)(215,308)(216,309)(217,310)(218,249)(219,250)(220,251)
(221,252)(222,253)(223,254)(224,255)(225,256)(226,257)(227,258)(228,259)
(229,260)(230,261)(231,262)(232,263)(233,264)(234,265)(235,266)(236,267)
(237,268)(238,269)(239,270)(240,271)(241,272)(242,273)(243,274)(244,275)
(245,276)(246,277)(247,278)(248,279);;
s1 := (  1, 32)(  2, 62)(  3, 61)(  4, 60)(  5, 59)(  6, 58)(  7, 57)(  8, 56)
(  9, 55)( 10, 54)( 11, 53)( 12, 52)( 13, 51)( 14, 50)( 15, 49)( 16, 48)
( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)( 24, 40)
( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)( 63,125)
( 64,155)( 65,154)( 66,153)( 67,152)( 68,151)( 69,150)( 70,149)( 71,148)
( 72,147)( 73,146)( 74,145)( 75,144)( 76,143)( 77,142)( 78,141)( 79,140)
( 80,139)( 81,138)( 82,137)( 83,136)( 84,135)( 85,134)( 86,133)( 87,132)
( 88,131)( 89,130)( 90,129)( 91,128)( 92,127)( 93,126)( 95,124)( 96,123)
( 97,122)( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)(104,115)
(105,114)(106,113)(107,112)(108,111)(109,110)(156,187)(157,217)(158,216)
(159,215)(160,214)(161,213)(162,212)(163,211)(164,210)(165,209)(166,208)
(167,207)(168,206)(169,205)(170,204)(171,203)(172,202)(173,201)(174,200)
(175,199)(176,198)(177,197)(178,196)(179,195)(180,194)(181,193)(182,192)
(183,191)(184,190)(185,189)(186,188)(218,280)(219,310)(220,309)(221,308)
(222,307)(223,306)(224,305)(225,304)(226,303)(227,302)(228,301)(229,300)
(230,299)(231,298)(232,297)(233,296)(234,295)(235,294)(236,293)(237,292)
(238,291)(239,290)(240,289)(241,288)(242,287)(243,286)(244,285)(245,284)
(246,283)(247,282)(248,281)(250,279)(251,278)(252,277)(253,276)(254,275)
(255,274)(256,273)(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)
(263,266)(264,265);;
s2 := (  1,157)(  2,156)(  3,186)(  4,185)(  5,184)(  6,183)(  7,182)(  8,181)
(  9,180)( 10,179)( 11,178)( 12,177)( 13,176)( 14,175)( 15,174)( 16,173)
( 17,172)( 18,171)( 19,170)( 20,169)( 21,168)( 22,167)( 23,166)( 24,165)
( 25,164)( 26,163)( 27,162)( 28,161)( 29,160)( 30,159)( 31,158)( 32,188)
( 33,187)( 34,217)( 35,216)( 36,215)( 37,214)( 38,213)( 39,212)( 40,211)
( 41,210)( 42,209)( 43,208)( 44,207)( 45,206)( 46,205)( 47,204)( 48,203)
( 49,202)( 50,201)( 51,200)( 52,199)( 53,198)( 54,197)( 55,196)( 56,195)
( 57,194)( 58,193)( 59,192)( 60,191)( 61,190)( 62,189)( 63,219)( 64,218)
( 65,248)( 66,247)( 67,246)( 68,245)( 69,244)( 70,243)( 71,242)( 72,241)
( 73,240)( 74,239)( 75,238)( 76,237)( 77,236)( 78,235)( 79,234)( 80,233)
( 81,232)( 82,231)( 83,230)( 84,229)( 85,228)( 86,227)( 87,226)( 88,225)
( 89,224)( 90,223)( 91,222)( 92,221)( 93,220)( 94,250)( 95,249)( 96,279)
( 97,278)( 98,277)( 99,276)(100,275)(101,274)(102,273)(103,272)(104,271)
(105,270)(106,269)(107,268)(108,267)(109,266)(110,265)(111,264)(112,263)
(113,262)(114,261)(115,260)(116,259)(117,258)(118,257)(119,256)(120,255)
(121,254)(122,253)(123,252)(124,251)(125,281)(126,280)(127,310)(128,309)
(129,308)(130,307)(131,306)(132,305)(133,304)(134,303)(135,302)(136,301)
(137,300)(138,299)(139,298)(140,297)(141,296)(142,295)(143,294)(144,293)
(145,292)(146,291)(147,290)(148,289)(149,288)(150,287)(151,286)(152,285)
(153,284)(154,283)(155,282);;
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(310)!( 32,125)( 33,126)( 34,127)( 35,128)( 36,129)( 37,130)( 38,131)
( 39,132)( 40,133)( 41,134)( 42,135)( 43,136)( 44,137)( 45,138)( 46,139)
( 47,140)( 48,141)( 49,142)( 50,143)( 51,144)( 52,145)( 53,146)( 54,147)
( 55,148)( 56,149)( 57,150)( 58,151)( 59,152)( 60,153)( 61,154)( 62,155)
( 63, 94)( 64, 95)( 65, 96)( 66, 97)( 67, 98)( 68, 99)( 69,100)( 70,101)
( 71,102)( 72,103)( 73,104)( 74,105)( 75,106)( 76,107)( 77,108)( 78,109)
( 79,110)( 80,111)( 81,112)( 82,113)( 83,114)( 84,115)( 85,116)( 86,117)
( 87,118)( 88,119)( 89,120)( 90,121)( 91,122)( 92,123)( 93,124)(187,280)
(188,281)(189,282)(190,283)(191,284)(192,285)(193,286)(194,287)(195,288)
(196,289)(197,290)(198,291)(199,292)(200,293)(201,294)(202,295)(203,296)
(204,297)(205,298)(206,299)(207,300)(208,301)(209,302)(210,303)(211,304)
(212,305)(213,306)(214,307)(215,308)(216,309)(217,310)(218,249)(219,250)
(220,251)(221,252)(222,253)(223,254)(224,255)(225,256)(226,257)(227,258)
(228,259)(229,260)(230,261)(231,262)(232,263)(233,264)(234,265)(235,266)
(236,267)(237,268)(238,269)(239,270)(240,271)(241,272)(242,273)(243,274)
(244,275)(245,276)(246,277)(247,278)(248,279);
s1 := Sym(310)!(  1, 32)(  2, 62)(  3, 61)(  4, 60)(  5, 59)(  6, 58)(  7, 57)
(  8, 56)(  9, 55)( 10, 54)( 11, 53)( 12, 52)( 13, 51)( 14, 50)( 15, 49)
( 16, 48)( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)
( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)
( 63,125)( 64,155)( 65,154)( 66,153)( 67,152)( 68,151)( 69,150)( 70,149)
( 71,148)( 72,147)( 73,146)( 74,145)( 75,144)( 76,143)( 77,142)( 78,141)
( 79,140)( 80,139)( 81,138)( 82,137)( 83,136)( 84,135)( 85,134)( 86,133)
( 87,132)( 88,131)( 89,130)( 90,129)( 91,128)( 92,127)( 93,126)( 95,124)
( 96,123)( 97,122)( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)
(104,115)(105,114)(106,113)(107,112)(108,111)(109,110)(156,187)(157,217)
(158,216)(159,215)(160,214)(161,213)(162,212)(163,211)(164,210)(165,209)
(166,208)(167,207)(168,206)(169,205)(170,204)(171,203)(172,202)(173,201)
(174,200)(175,199)(176,198)(177,197)(178,196)(179,195)(180,194)(181,193)
(182,192)(183,191)(184,190)(185,189)(186,188)(218,280)(219,310)(220,309)
(221,308)(222,307)(223,306)(224,305)(225,304)(226,303)(227,302)(228,301)
(229,300)(230,299)(231,298)(232,297)(233,296)(234,295)(235,294)(236,293)
(237,292)(238,291)(239,290)(240,289)(241,288)(242,287)(243,286)(244,285)
(245,284)(246,283)(247,282)(248,281)(250,279)(251,278)(252,277)(253,276)
(254,275)(255,274)(256,273)(257,272)(258,271)(259,270)(260,269)(261,268)
(262,267)(263,266)(264,265);
s2 := Sym(310)!(  1,157)(  2,156)(  3,186)(  4,185)(  5,184)(  6,183)(  7,182)
(  8,181)(  9,180)( 10,179)( 11,178)( 12,177)( 13,176)( 14,175)( 15,174)
( 16,173)( 17,172)( 18,171)( 19,170)( 20,169)( 21,168)( 22,167)( 23,166)
( 24,165)( 25,164)( 26,163)( 27,162)( 28,161)( 29,160)( 30,159)( 31,158)
( 32,188)( 33,187)( 34,217)( 35,216)( 36,215)( 37,214)( 38,213)( 39,212)
( 40,211)( 41,210)( 42,209)( 43,208)( 44,207)( 45,206)( 46,205)( 47,204)
( 48,203)( 49,202)( 50,201)( 51,200)( 52,199)( 53,198)( 54,197)( 55,196)
( 56,195)( 57,194)( 58,193)( 59,192)( 60,191)( 61,190)( 62,189)( 63,219)
( 64,218)( 65,248)( 66,247)( 67,246)( 68,245)( 69,244)( 70,243)( 71,242)
( 72,241)( 73,240)( 74,239)( 75,238)( 76,237)( 77,236)( 78,235)( 79,234)
( 80,233)( 81,232)( 82,231)( 83,230)( 84,229)( 85,228)( 86,227)( 87,226)
( 88,225)( 89,224)( 90,223)( 91,222)( 92,221)( 93,220)( 94,250)( 95,249)
( 96,279)( 97,278)( 98,277)( 99,276)(100,275)(101,274)(102,273)(103,272)
(104,271)(105,270)(106,269)(107,268)(108,267)(109,266)(110,265)(111,264)
(112,263)(113,262)(114,261)(115,260)(116,259)(117,258)(118,257)(119,256)
(120,255)(121,254)(122,253)(123,252)(124,251)(125,281)(126,280)(127,310)
(128,309)(129,308)(130,307)(131,306)(132,305)(133,304)(134,303)(135,302)
(136,301)(137,300)(138,299)(139,298)(140,297)(141,296)(142,295)(143,294)
(144,293)(145,292)(146,291)(147,290)(148,289)(149,288)(150,287)(151,286)
(152,285)(153,284)(154,283)(155,282);
poly := sub<Sym(310)|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*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope