Polytope of Type {62,10} with group SmallGroup(1240,47)

Overview

Group: SmallGroup(1240,47)
Rank: 3
Schläfli Type: {62,10}
Vertices, edges, …: 62, 310, 10
Order of s₀s₁s₂: 310
Order of s₀s₁s₂s₁: 2
Also known as: {62,10|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

5-fold

{62,2}*248

10-fold

{31,2}*124

31-fold

{2,10}*40

62-fold

{2,5}*20

155-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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