Polytope of Type {62,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {62,10}*1240
Also Known As : {62,10|2}. if this polytope has another name.
Group : SmallGroup(1240,47)
Rank : 3
Schlafli Type : {62,10}
Number of vertices, edges, etc : 62, 310, 10
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 : {62,2}*248
10-fold quotients : {31,2}*124
31-fold quotients : {2,10}*40
62-fold quotients : {2,5}*20
155-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 31)( 3, 30)( 4, 29)( 5, 28)( 6, 27)( 7, 26)( 8, 25)( 9, 24)
( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)( 33, 62)
( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)( 41, 54)
( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 64, 93)( 65, 92)
( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)
( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 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)(126,155)(127,154)(128,153)(129,152)
(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)
(138,143)(139,142)(140,141)(157,186)(158,185)(159,184)(160,183)(161,182)
(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(169,174)
(170,173)(171,172)(188,217)(189,216)(190,215)(191,214)(192,213)(193,212)
(194,211)(195,210)(196,209)(197,208)(198,207)(199,206)(200,205)(201,204)
(202,203)(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)(233,234)
(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)(281,310)
(282,309)(283,308)(284,307)(285,306)(286,305)(287,304)(288,303)(289,302)
(290,301)(291,300)(292,299)(293,298)(294,297)(295,296);;
s1 := ( 1, 2)( 3, 31)( 4, 30)( 5, 29)( 6, 28)( 7, 27)( 8, 26)( 9, 25)
( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 32,126)
( 33,125)( 34,155)( 35,154)( 36,153)( 37,152)( 38,151)( 39,150)( 40,149)
( 41,148)( 42,147)( 43,146)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)
( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)( 56,133)
( 57,132)( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63, 95)( 64, 94)
( 65,124)( 66,123)( 67,122)( 68,121)( 69,120)( 70,119)( 71,118)( 72,117)
( 73,116)( 74,115)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)( 80,109)
( 81,108)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)
( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)(156,157)(158,186)(159,185)
(160,184)(161,183)(162,182)(163,181)(164,180)(165,179)(166,178)(167,177)
(168,176)(169,175)(170,174)(171,173)(187,281)(188,280)(189,310)(190,309)
(191,308)(192,307)(193,306)(194,305)(195,304)(196,303)(197,302)(198,301)
(199,300)(200,299)(201,298)(202,297)(203,296)(204,295)(205,294)(206,293)
(207,292)(208,291)(209,290)(210,289)(211,288)(212,287)(213,286)(214,285)
(215,284)(216,283)(217,282)(218,250)(219,249)(220,279)(221,278)(222,277)
(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)(229,270)(230,269)
(231,268)(232,267)(233,266)(234,265)(235,264)(236,263)(237,262)(238,261)
(239,260)(240,259)(241,258)(242,257)(243,256)(244,255)(245,254)(246,253)
(247,252)(248,251);;
s2 := ( 1,187)( 2,188)( 3,189)( 4,190)( 5,191)( 6,192)( 7,193)( 8,194)
( 9,195)( 10,196)( 11,197)( 12,198)( 13,199)( 14,200)( 15,201)( 16,202)
( 17,203)( 18,204)( 19,205)( 20,206)( 21,207)( 22,208)( 23,209)( 24,210)
( 25,211)( 26,212)( 27,213)( 28,214)( 29,215)( 30,216)( 31,217)( 32,156)
( 33,157)( 34,158)( 35,159)( 36,160)( 37,161)( 38,162)( 39,163)( 40,164)
( 41,165)( 42,166)( 43,167)( 44,168)( 45,169)( 46,170)( 47,171)( 48,172)
( 49,173)( 50,174)( 51,175)( 52,176)( 53,177)( 54,178)( 55,179)( 56,180)
( 57,181)( 58,182)( 59,183)( 60,184)( 61,185)( 62,186)( 63,280)( 64,281)
( 65,282)( 66,283)( 67,284)( 68,285)( 69,286)( 70,287)( 71,288)( 72,289)
( 73,290)( 74,291)( 75,292)( 76,293)( 77,294)( 78,295)( 79,296)( 80,297)
( 81,298)( 82,299)( 83,300)( 84,301)( 85,302)( 86,303)( 87,304)( 88,305)
( 89,306)( 90,307)( 91,308)( 92,309)( 93,310)( 94,249)( 95,250)( 96,251)
( 97,252)( 98,253)( 99,254)(100,255)(101,256)(102,257)(103,258)(104,259)
(105,260)(106,261)(107,262)(108,263)(109,264)(110,265)(111,266)(112,267)
(113,268)(114,269)(115,270)(116,271)(117,272)(118,273)(119,274)(120,275)
(121,276)(122,277)(123,278)(124,279)(125,218)(126,219)(127,220)(128,221)
(129,222)(130,223)(131,224)(132,225)(133,226)(134,227)(135,228)(136,229)
(137,230)(138,231)(139,232)(140,233)(141,234)(142,235)(143,236)(144,237)
(145,238)(146,239)(147,240)(148,241)(149,242)(150,243)(151,244)(152,245)
(153,246)(154,247)(155,248);;
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(310)!( 2, 31)( 3, 30)( 4, 29)( 5, 28)( 6, 27)( 7, 26)( 8, 25)
( 9, 24)( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)
( 33, 62)( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)
( 41, 54)( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 64, 93)
( 65, 92)( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)
( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 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)(126,155)(127,154)(128,153)
(129,152)(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)
(137,144)(138,143)(139,142)(140,141)(157,186)(158,185)(159,184)(160,183)
(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)
(169,174)(170,173)(171,172)(188,217)(189,216)(190,215)(191,214)(192,213)
(193,212)(194,211)(195,210)(196,209)(197,208)(198,207)(199,206)(200,205)
(201,204)(202,203)(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)
(233,234)(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)
(281,310)(282,309)(283,308)(284,307)(285,306)(286,305)(287,304)(288,303)
(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296);
s1 := Sym(310)!( 1, 2)( 3, 31)( 4, 30)( 5, 29)( 6, 28)( 7, 27)( 8, 26)
( 9, 25)( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)
( 32,126)( 33,125)( 34,155)( 35,154)( 36,153)( 37,152)( 38,151)( 39,150)
( 40,149)( 41,148)( 42,147)( 43,146)( 44,145)( 45,144)( 46,143)( 47,142)
( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)
( 56,133)( 57,132)( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63, 95)
( 64, 94)( 65,124)( 66,123)( 67,122)( 68,121)( 69,120)( 70,119)( 71,118)
( 72,117)( 73,116)( 74,115)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)
( 80,109)( 81,108)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)
( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)(156,157)(158,186)
(159,185)(160,184)(161,183)(162,182)(163,181)(164,180)(165,179)(166,178)
(167,177)(168,176)(169,175)(170,174)(171,173)(187,281)(188,280)(189,310)
(190,309)(191,308)(192,307)(193,306)(194,305)(195,304)(196,303)(197,302)
(198,301)(199,300)(200,299)(201,298)(202,297)(203,296)(204,295)(205,294)
(206,293)(207,292)(208,291)(209,290)(210,289)(211,288)(212,287)(213,286)
(214,285)(215,284)(216,283)(217,282)(218,250)(219,249)(220,279)(221,278)
(222,277)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)(229,270)
(230,269)(231,268)(232,267)(233,266)(234,265)(235,264)(236,263)(237,262)
(238,261)(239,260)(240,259)(241,258)(242,257)(243,256)(244,255)(245,254)
(246,253)(247,252)(248,251);
s2 := Sym(310)!( 1,187)( 2,188)( 3,189)( 4,190)( 5,191)( 6,192)( 7,193)
( 8,194)( 9,195)( 10,196)( 11,197)( 12,198)( 13,199)( 14,200)( 15,201)
( 16,202)( 17,203)( 18,204)( 19,205)( 20,206)( 21,207)( 22,208)( 23,209)
( 24,210)( 25,211)( 26,212)( 27,213)( 28,214)( 29,215)( 30,216)( 31,217)
( 32,156)( 33,157)( 34,158)( 35,159)( 36,160)( 37,161)( 38,162)( 39,163)
( 40,164)( 41,165)( 42,166)( 43,167)( 44,168)( 45,169)( 46,170)( 47,171)
( 48,172)( 49,173)( 50,174)( 51,175)( 52,176)( 53,177)( 54,178)( 55,179)
( 56,180)( 57,181)( 58,182)( 59,183)( 60,184)( 61,185)( 62,186)( 63,280)
( 64,281)( 65,282)( 66,283)( 67,284)( 68,285)( 69,286)( 70,287)( 71,288)
( 72,289)( 73,290)( 74,291)( 75,292)( 76,293)( 77,294)( 78,295)( 79,296)
( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,302)( 86,303)( 87,304)
( 88,305)( 89,306)( 90,307)( 91,308)( 92,309)( 93,310)( 94,249)( 95,250)
( 96,251)( 97,252)( 98,253)( 99,254)(100,255)(101,256)(102,257)(103,258)
(104,259)(105,260)(106,261)(107,262)(108,263)(109,264)(110,265)(111,266)
(112,267)(113,268)(114,269)(115,270)(116,271)(117,272)(118,273)(119,274)
(120,275)(121,276)(122,277)(123,278)(124,279)(125,218)(126,219)(127,220)
(128,221)(129,222)(130,223)(131,224)(132,225)(133,226)(134,227)(135,228)
(136,229)(137,230)(138,231)(139,232)(140,233)(141,234)(142,235)(143,236)
(144,237)(145,238)(146,239)(147,240)(148,241)(149,242)(150,243)(151,244)
(152,245)(153,246)(154,247)(155,248);
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,
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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope