Polytope of Type {26,26}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,26}*1352c
if this polytope has a name.
Group : SmallGroup(1352,49)
Rank : 3
Schlafli Type : {26,26}
Number of vertices, edges, etc : 26, 338, 26
Order of s0s1s2 : 26
Order of s0s1s2s1 : 26
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {13,26}*676
13-fold quotients : {26,2}*104
26-fold quotients : {13,2}*52
169-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
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*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*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(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*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*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