Polytope of Type {26,26} with group SmallGroup(1352,49)

Overview

Group: SmallGroup(1352,49)
Rank: 3
Schläfli Type: {26,26}
Vertices, edges, …: 26, 338, 26
Order of s₀s₁s₂: 26
Order of s₀s₁s₂s₁: 26
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{13,26}*676

13-fold

{26,2}*104

26-fold

{13,2}*52

169-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, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14,157)( 15,169)( 16,168)( 17,167)( 18,166)( 19,165)( 20,164)( 21,163)( 22,162)( 23,161)( 24,160)( 25,159)( 26,158)( 27,144)( 28,156)( 29,155)( 30,154)( 31,153)( 32,152)( 33,151)( 34,150)( 35,149)( 36,148)( 37,147)( 38,146)( 39,145)( 40,131)( 41,143)( 42,142)( 43,141)( 44,140)( 45,139)( 46,138)( 47,137)( 48,136)( 49,135)( 50,134)( 51,133)( 52,132)( 53,118)( 54,130)( 55,129)( 56,128)( 57,127)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)( 63,121)( 64,120)( 65,119)( 66,105)( 67,117)( 68,116)( 69,115)( 70,114)( 71,113)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78,106)( 79, 92)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)(171,182)(172,181)(173,180)(174,179)(175,178)(176,177)(183,326)(184,338)(185,337)(186,336)(187,335)(188,334)(189,333)(190,332)(191,331)(192,330)(193,329)(194,328)(195,327)(196,313)(197,325)(198,324)(199,323)(200,322)(201,321)(202,320)(203,319)(204,318)(205,317)(206,316)(207,315)(208,314)(209,300)(210,312)(211,311)(212,310)(213,309)(214,308)(215,307)(216,306)(217,305)(218,304)(219,303)(220,302)(221,301)(222,287)(223,299)(224,298)(225,297)(226,296)(227,295)(228,294)(229,293)(230,292)(231,291)(232,290)(233,289)(234,288)(235,274)(236,286)(237,285)(238,284)(239,283)(240,282)(241,281)(242,280)(243,279)(244,278)(245,277)(246,276)(247,275)(248,261)(249,273)(250,272)(251,271)(252,270)(253,269)(254,268)(255,267)(256,266)(257,265)(258,264)(259,263)(260,262);;
s1 := (  1,184)(  2,183)(  3,195)(  4,194)(  5,193)(  6,192)(  7,191)(  8,190)(  9,189)( 10,188)( 11,187)( 12,186)( 13,185)( 14,171)( 15,170)( 16,182)( 17,181)( 18,180)( 19,179)( 20,178)( 21,177)( 22,176)( 23,175)( 24,174)( 25,173)( 26,172)( 27,327)( 28,326)( 29,338)( 30,337)( 31,336)( 32,335)( 33,334)( 34,333)( 35,332)( 36,331)( 37,330)( 38,329)( 39,328)( 40,314)( 41,313)( 42,325)( 43,324)( 44,323)( 45,322)( 46,321)( 47,320)( 48,319)( 49,318)( 50,317)( 51,316)( 52,315)( 53,301)( 54,300)( 55,312)( 56,311)( 57,310)( 58,309)( 59,308)( 60,307)( 61,306)( 62,305)( 63,304)( 64,303)( 65,302)( 66,288)( 67,287)( 68,299)( 69,298)( 70,297)( 71,296)( 72,295)( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,289)( 79,275)( 80,274)( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)( 88,279)( 89,278)( 90,277)( 91,276)( 92,262)( 93,261)( 94,273)( 95,272)( 96,271)( 97,270)( 98,269)( 99,268)(100,267)(101,266)(102,265)(103,264)(104,263)(105,249)(106,248)(107,260)(108,259)(109,258)(110,257)(111,256)(112,255)(113,254)(114,253)(115,252)(116,251)(117,250)(118,236)(119,235)(120,247)(121,246)(122,245)(123,244)(124,243)(125,242)(126,241)(127,240)(128,239)(129,238)(130,237)(131,223)(132,222)(133,234)(134,233)(135,232)(136,231)(137,230)(138,229)(139,228)(140,227)(141,226)(142,225)(143,224)(144,210)(145,209)(146,221)(147,220)(148,219)(149,218)(150,217)(151,216)(152,215)(153,214)(154,213)(155,212)(156,211)(157,197)(158,196)(159,208)(160,207)(161,206)(162,205)(163,204)(164,203)(165,202)(166,201)(167,200)(168,199)(169,198);;
s2 := ( 14,157)( 15,158)( 16,159)( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,166)( 24,167)( 25,168)( 26,169)( 27,144)( 28,145)( 29,146)( 30,147)( 31,148)( 32,149)( 33,150)( 34,151)( 35,152)( 36,153)( 37,154)( 38,155)( 39,156)( 40,131)( 41,132)( 42,133)( 43,134)( 44,135)( 45,136)( 46,137)( 47,138)( 48,139)( 49,140)( 50,141)( 51,142)( 52,143)( 53,118)( 54,119)( 55,120)( 56,121)( 57,122)( 58,123)( 59,124)( 60,125)( 61,126)( 62,127)( 63,128)( 64,129)( 65,130)( 66,105)( 67,106)( 68,107)( 69,108)( 70,109)( 71,110)( 72,111)( 73,112)( 74,113)( 75,114)( 76,115)( 77,116)( 78,117)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(183,326)(184,327)(185,328)(186,329)(187,330)(188,331)(189,332)(190,333)(191,334)(192,335)(193,336)(194,337)(195,338)(196,313)(197,314)(198,315)(199,316)(200,317)(201,318)(202,319)(203,320)(204,321)(205,322)(206,323)(207,324)(208,325)(209,300)(210,301)(211,302)(212,303)(213,304)(214,305)(215,306)(216,307)(217,308)(218,309)(219,310)(220,311)(221,312)(222,287)(223,288)(224,289)(225,290)(226,291)(227,292)(228,293)(229,294)(230,295)(231,296)(232,297)(233,298)(234,299)(235,274)(236,275)(237,276)(238,277)(239,278)(240,279)(241,280)(242,281)(243,282)(244,283)(245,284)(246,285)(247,286)(248,261)(249,262)(250,263)(251,264)(252,265)(253,266)(254,267)(255,268)(256,269)(257,270)(258,271)(259,272)(260,273);;
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, s2*s0*s1*s2*s1*s2*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*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*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*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(338)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14,157)( 15,169)( 16,168)( 17,167)( 18,166)( 19,165)( 20,164)( 21,163)( 22,162)( 23,161)( 24,160)( 25,159)( 26,158)( 27,144)( 28,156)( 29,155)( 30,154)( 31,153)( 32,152)( 33,151)( 34,150)( 35,149)( 36,148)( 37,147)( 38,146)( 39,145)( 40,131)( 41,143)( 42,142)( 43,141)( 44,140)( 45,139)( 46,138)( 47,137)( 48,136)( 49,135)( 50,134)( 51,133)( 52,132)( 53,118)( 54,130)( 55,129)( 56,128)( 57,127)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)( 63,121)( 64,120)( 65,119)( 66,105)( 67,117)( 68,116)( 69,115)( 70,114)( 71,113)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78,106)( 79, 92)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)(171,182)(172,181)(173,180)(174,179)(175,178)(176,177)(183,326)(184,338)(185,337)(186,336)(187,335)(188,334)(189,333)(190,332)(191,331)(192,330)(193,329)(194,328)(195,327)(196,313)(197,325)(198,324)(199,323)(200,322)(201,321)(202,320)(203,319)(204,318)(205,317)(206,316)(207,315)(208,314)(209,300)(210,312)(211,311)(212,310)(213,309)(214,308)(215,307)(216,306)(217,305)(218,304)(219,303)(220,302)(221,301)(222,287)(223,299)(224,298)(225,297)(226,296)(227,295)(228,294)(229,293)(230,292)(231,291)(232,290)(233,289)(234,288)(235,274)(236,286)(237,285)(238,284)(239,283)(240,282)(241,281)(242,280)(243,279)(244,278)(245,277)(246,276)(247,275)(248,261)(249,273)(250,272)(251,271)(252,270)(253,269)(254,268)(255,267)(256,266)(257,265)(258,264)(259,263)(260,262);
s1 := Sym(338)!(  1,184)(  2,183)(  3,195)(  4,194)(  5,193)(  6,192)(  7,191)(  8,190)(  9,189)( 10,188)( 11,187)( 12,186)( 13,185)( 14,171)( 15,170)( 16,182)( 17,181)( 18,180)( 19,179)( 20,178)( 21,177)( 22,176)( 23,175)( 24,174)( 25,173)( 26,172)( 27,327)( 28,326)( 29,338)( 30,337)( 31,336)( 32,335)( 33,334)( 34,333)( 35,332)( 36,331)( 37,330)( 38,329)( 39,328)( 40,314)( 41,313)( 42,325)( 43,324)( 44,323)( 45,322)( 46,321)( 47,320)( 48,319)( 49,318)( 50,317)( 51,316)( 52,315)( 53,301)( 54,300)( 55,312)( 56,311)( 57,310)( 58,309)( 59,308)( 60,307)( 61,306)( 62,305)( 63,304)( 64,303)( 65,302)( 66,288)( 67,287)( 68,299)( 69,298)( 70,297)( 71,296)( 72,295)( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,289)( 79,275)( 80,274)( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)( 88,279)( 89,278)( 90,277)( 91,276)( 92,262)( 93,261)( 94,273)( 95,272)( 96,271)( 97,270)( 98,269)( 99,268)(100,267)(101,266)(102,265)(103,264)(104,263)(105,249)(106,248)(107,260)(108,259)(109,258)(110,257)(111,256)(112,255)(113,254)(114,253)(115,252)(116,251)(117,250)(118,236)(119,235)(120,247)(121,246)(122,245)(123,244)(124,243)(125,242)(126,241)(127,240)(128,239)(129,238)(130,237)(131,223)(132,222)(133,234)(134,233)(135,232)(136,231)(137,230)(138,229)(139,228)(140,227)(141,226)(142,225)(143,224)(144,210)(145,209)(146,221)(147,220)(148,219)(149,218)(150,217)(151,216)(152,215)(153,214)(154,213)(155,212)(156,211)(157,197)(158,196)(159,208)(160,207)(161,206)(162,205)(163,204)(164,203)(165,202)(166,201)(167,200)(168,199)(169,198);
s2 := Sym(338)!( 14,157)( 15,158)( 16,159)( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,166)( 24,167)( 25,168)( 26,169)( 27,144)( 28,145)( 29,146)( 30,147)( 31,148)( 32,149)( 33,150)( 34,151)( 35,152)( 36,153)( 37,154)( 38,155)( 39,156)( 40,131)( 41,132)( 42,133)( 43,134)( 44,135)( 45,136)( 46,137)( 47,138)( 48,139)( 49,140)( 50,141)( 51,142)( 52,143)( 53,118)( 54,119)( 55,120)( 56,121)( 57,122)( 58,123)( 59,124)( 60,125)( 61,126)( 62,127)( 63,128)( 64,129)( 65,130)( 66,105)( 67,106)( 68,107)( 69,108)( 70,109)( 71,110)( 72,111)( 73,112)( 74,113)( 75,114)( 76,115)( 77,116)( 78,117)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(183,326)(184,327)(185,328)(186,329)(187,330)(188,331)(189,332)(190,333)(191,334)(192,335)(193,336)(194,337)(195,338)(196,313)(197,314)(198,315)(199,316)(200,317)(201,318)(202,319)(203,320)(204,321)(205,322)(206,323)(207,324)(208,325)(209,300)(210,301)(211,302)(212,303)(213,304)(214,305)(215,306)(216,307)(217,308)(218,309)(219,310)(220,311)(221,312)(222,287)(223,288)(224,289)(225,290)(226,291)(227,292)(228,293)(229,294)(230,295)(231,296)(232,297)(233,298)(234,299)(235,274)(236,275)(237,276)(238,277)(239,278)(240,279)(241,280)(242,281)(243,282)(244,283)(245,284)(246,285)(247,286)(248,261)(249,262)(250,263)(251,264)(252,265)(253,266)(254,267)(255,268)(256,269)(257,270)(258,271)(259,272)(260,273);
poly := sub<Sym(338)|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, s2*s0*s1*s2*s1*s2*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*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*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*s2*s1 >;

References