Polytope of Type {14,46} with group SmallGroup(1288,31)

Overview

Group: SmallGroup(1288,31)
Rank: 3
Schläfli Type: {14,46}
Vertices, edges, …: 14, 322, 46
Order of s₀s₁s₂: 322
Order of s₀s₁s₂s₁: 2
Also known as: {14,46|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

7-fold

{2,46}*184

14-fold

{2,23}*92

23-fold

{14,2}*56

46-fold

{7,2}*28

161-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 := ( 24,139)( 25,140)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,146)( 32,147)( 33,148)( 34,149)( 35,150)( 36,151)( 37,152)( 38,153)( 39,154)( 40,155)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,161)( 47,116)( 48,117)( 49,118)( 50,119)( 51,120)( 52,121)( 53,122)( 54,123)( 55,124)( 56,125)( 57,126)( 58,127)( 59,128)( 60,129)( 61,130)( 62,131)( 63,132)( 64,133)( 65,134)( 66,135)( 67,136)( 68,137)( 69,138)( 70, 93)( 71, 94)( 72, 95)( 73, 96)( 74, 97)( 75, 98)( 76, 99)( 77,100)( 78,101)( 79,102)( 80,103)( 81,104)( 82,105)( 83,106)( 84,107)( 85,108)( 86,109)( 87,110)( 88,111)( 89,112)( 90,113)( 91,114)( 92,115)(185,300)(186,301)(187,302)(188,303)(189,304)(190,305)(191,306)(192,307)(193,308)(194,309)(195,310)(196,311)(197,312)(198,313)(199,314)(200,315)(201,316)(202,317)(203,318)(204,319)(205,320)(206,321)(207,322)(208,277)(209,278)(210,279)(211,280)(212,281)(213,282)(214,283)(215,284)(216,285)(217,286)(218,287)(219,288)(220,289)(221,290)(222,291)(223,292)(224,293)(225,294)(226,295)(227,296)(228,297)(229,298)(230,299)(231,254)(232,255)(233,256)(234,257)(235,258)(236,259)(237,260)(238,261)(239,262)(240,263)(241,264)(242,265)(243,266)(244,267)(245,268)(246,269)(247,270)(248,271)(249,272)(250,273)(251,274)(252,275)(253,276);;
s1 := (  1, 24)(  2, 46)(  3, 45)(  4, 44)(  5, 43)(  6, 42)(  7, 41)(  8, 40)(  9, 39)( 10, 38)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)( 16, 32)( 17, 31)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 47,139)( 48,161)( 49,160)( 50,159)( 51,158)( 52,157)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)( 58,151)( 59,150)( 60,149)( 61,148)( 62,147)( 63,146)( 64,145)( 65,144)( 66,143)( 67,142)( 68,141)( 69,140)( 70,116)( 71,138)( 72,137)( 73,136)( 74,135)( 75,134)( 76,133)( 77,132)( 78,131)( 79,130)( 80,129)( 81,128)( 82,127)( 83,126)( 84,125)( 85,124)( 86,123)( 87,122)( 88,121)( 89,120)( 90,119)( 91,118)( 92,117)( 94,115)( 95,114)( 96,113)( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(162,185)(163,207)(164,206)(165,205)(166,204)(167,203)(168,202)(169,201)(170,200)(171,199)(172,198)(173,197)(174,196)(175,195)(176,194)(177,193)(178,192)(179,191)(180,190)(181,189)(182,188)(183,187)(184,186)(208,300)(209,322)(210,321)(211,320)(212,319)(213,318)(214,317)(215,316)(216,315)(217,314)(218,313)(219,312)(220,311)(221,310)(222,309)(223,308)(224,307)(225,306)(226,305)(227,304)(228,303)(229,302)(230,301)(231,277)(232,299)(233,298)(234,297)(235,296)(236,295)(237,294)(238,293)(239,292)(240,291)(241,290)(242,289)(243,288)(244,287)(245,286)(246,285)(247,284)(248,283)(249,282)(250,281)(251,280)(252,279)(253,278)(255,276)(256,275)(257,274)(258,273)(259,272)(260,271)(261,270)(262,269)(263,268)(264,267)(265,266);;
s2 := (  1,163)(  2,162)(  3,184)(  4,183)(  5,182)(  6,181)(  7,180)(  8,179)(  9,178)( 10,177)( 11,176)( 12,175)( 13,174)( 14,173)( 15,172)( 16,171)( 17,170)( 18,169)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)( 24,186)( 25,185)( 26,207)( 27,206)( 28,205)( 29,204)( 30,203)( 31,202)( 32,201)( 33,200)( 34,199)( 35,198)( 36,197)( 37,196)( 38,195)( 39,194)( 40,193)( 41,192)( 42,191)( 43,190)( 44,189)( 45,188)( 46,187)( 47,209)( 48,208)( 49,230)( 50,229)( 51,228)( 52,227)( 53,226)( 54,225)( 55,224)( 56,223)( 57,222)( 58,221)( 59,220)( 60,219)( 61,218)( 62,217)( 63,216)( 64,215)( 65,214)( 66,213)( 67,212)( 68,211)( 69,210)( 70,232)( 71,231)( 72,253)( 73,252)( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)( 80,245)( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)( 88,237)( 89,236)( 90,235)( 91,234)( 92,233)( 93,255)( 94,254)( 95,276)( 96,275)( 97,274)( 98,273)( 99,272)(100,271)(101,270)(102,269)(103,268)(104,267)(105,266)(106,265)(107,264)(108,263)(109,262)(110,261)(111,260)(112,259)(113,258)(114,257)(115,256)(116,278)(117,277)(118,299)(119,298)(120,297)(121,296)(122,295)(123,294)(124,293)(125,292)(126,291)(127,290)(128,289)(129,288)(130,287)(131,286)(132,285)(133,284)(134,283)(135,282)(136,281)(137,280)(138,279)(139,301)(140,300)(141,322)(142,321)(143,320)(144,319)(145,318)(146,317)(147,316)(148,315)(149,314)(150,313)(151,312)(152,311)(153,310)(154,309)(155,308)(156,307)(157,306)(158,305)(159,304)(160,303)(161,302);;
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*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 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(322)!( 24,139)( 25,140)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,146)( 32,147)( 33,148)( 34,149)( 35,150)( 36,151)( 37,152)( 38,153)( 39,154)( 40,155)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,161)( 47,116)( 48,117)( 49,118)( 50,119)( 51,120)( 52,121)( 53,122)( 54,123)( 55,124)( 56,125)( 57,126)( 58,127)( 59,128)( 60,129)( 61,130)( 62,131)( 63,132)( 64,133)( 65,134)( 66,135)( 67,136)( 68,137)( 69,138)( 70, 93)( 71, 94)( 72, 95)( 73, 96)( 74, 97)( 75, 98)( 76, 99)( 77,100)( 78,101)( 79,102)( 80,103)( 81,104)( 82,105)( 83,106)( 84,107)( 85,108)( 86,109)( 87,110)( 88,111)( 89,112)( 90,113)( 91,114)( 92,115)(185,300)(186,301)(187,302)(188,303)(189,304)(190,305)(191,306)(192,307)(193,308)(194,309)(195,310)(196,311)(197,312)(198,313)(199,314)(200,315)(201,316)(202,317)(203,318)(204,319)(205,320)(206,321)(207,322)(208,277)(209,278)(210,279)(211,280)(212,281)(213,282)(214,283)(215,284)(216,285)(217,286)(218,287)(219,288)(220,289)(221,290)(222,291)(223,292)(224,293)(225,294)(226,295)(227,296)(228,297)(229,298)(230,299)(231,254)(232,255)(233,256)(234,257)(235,258)(236,259)(237,260)(238,261)(239,262)(240,263)(241,264)(242,265)(243,266)(244,267)(245,268)(246,269)(247,270)(248,271)(249,272)(250,273)(251,274)(252,275)(253,276);
s1 := Sym(322)!(  1, 24)(  2, 46)(  3, 45)(  4, 44)(  5, 43)(  6, 42)(  7, 41)(  8, 40)(  9, 39)( 10, 38)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)( 16, 32)( 17, 31)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 47,139)( 48,161)( 49,160)( 50,159)( 51,158)( 52,157)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)( 58,151)( 59,150)( 60,149)( 61,148)( 62,147)( 63,146)( 64,145)( 65,144)( 66,143)( 67,142)( 68,141)( 69,140)( 70,116)( 71,138)( 72,137)( 73,136)( 74,135)( 75,134)( 76,133)( 77,132)( 78,131)( 79,130)( 80,129)( 81,128)( 82,127)( 83,126)( 84,125)( 85,124)( 86,123)( 87,122)( 88,121)( 89,120)( 90,119)( 91,118)( 92,117)( 94,115)( 95,114)( 96,113)( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(162,185)(163,207)(164,206)(165,205)(166,204)(167,203)(168,202)(169,201)(170,200)(171,199)(172,198)(173,197)(174,196)(175,195)(176,194)(177,193)(178,192)(179,191)(180,190)(181,189)(182,188)(183,187)(184,186)(208,300)(209,322)(210,321)(211,320)(212,319)(213,318)(214,317)(215,316)(216,315)(217,314)(218,313)(219,312)(220,311)(221,310)(222,309)(223,308)(224,307)(225,306)(226,305)(227,304)(228,303)(229,302)(230,301)(231,277)(232,299)(233,298)(234,297)(235,296)(236,295)(237,294)(238,293)(239,292)(240,291)(241,290)(242,289)(243,288)(244,287)(245,286)(246,285)(247,284)(248,283)(249,282)(250,281)(251,280)(252,279)(253,278)(255,276)(256,275)(257,274)(258,273)(259,272)(260,271)(261,270)(262,269)(263,268)(264,267)(265,266);
s2 := Sym(322)!(  1,163)(  2,162)(  3,184)(  4,183)(  5,182)(  6,181)(  7,180)(  8,179)(  9,178)( 10,177)( 11,176)( 12,175)( 13,174)( 14,173)( 15,172)( 16,171)( 17,170)( 18,169)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)( 24,186)( 25,185)( 26,207)( 27,206)( 28,205)( 29,204)( 30,203)( 31,202)( 32,201)( 33,200)( 34,199)( 35,198)( 36,197)( 37,196)( 38,195)( 39,194)( 40,193)( 41,192)( 42,191)( 43,190)( 44,189)( 45,188)( 46,187)( 47,209)( 48,208)( 49,230)( 50,229)( 51,228)( 52,227)( 53,226)( 54,225)( 55,224)( 56,223)( 57,222)( 58,221)( 59,220)( 60,219)( 61,218)( 62,217)( 63,216)( 64,215)( 65,214)( 66,213)( 67,212)( 68,211)( 69,210)( 70,232)( 71,231)( 72,253)( 73,252)( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)( 80,245)( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)( 88,237)( 89,236)( 90,235)( 91,234)( 92,233)( 93,255)( 94,254)( 95,276)( 96,275)( 97,274)( 98,273)( 99,272)(100,271)(101,270)(102,269)(103,268)(104,267)(105,266)(106,265)(107,264)(108,263)(109,262)(110,261)(111,260)(112,259)(113,258)(114,257)(115,256)(116,278)(117,277)(118,299)(119,298)(120,297)(121,296)(122,295)(123,294)(124,293)(125,292)(126,291)(127,290)(128,289)(129,288)(130,287)(131,286)(132,285)(133,284)(134,283)(135,282)(136,281)(137,280)(138,279)(139,301)(140,300)(141,322)(142,321)(143,320)(144,319)(145,318)(146,317)(147,316)(148,315)(149,314)(150,313)(151,312)(152,311)(153,310)(154,309)(155,308)(156,307)(157,306)(158,305)(159,304)(160,303)(161,302);
poly := sub<Sym(322)|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*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 >;

References