Polytope of Type {26,26}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,26}*1352a
Also Known As : {26,26|2}. if this polytope has another 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 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Dual
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) :
13-fold quotients : {2,26}*104, {26,2}*104
26-fold quotients : {2,13}*52, {13,2}*52
169-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1, 14)( 2, 26)( 3, 25)( 4, 24)( 5, 23)( 6, 22)( 7, 21)( 8, 20)
( 9, 19)( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 27,157)( 28,169)( 29,168)
( 30,167)( 31,166)( 32,165)( 33,164)( 34,163)( 35,162)( 36,161)( 37,160)
( 38,159)( 39,158)( 40,144)( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)
( 46,151)( 47,150)( 48,149)( 49,148)( 50,147)( 51,146)( 52,145)( 53,131)
( 54,143)( 55,142)( 56,141)( 57,140)( 58,139)( 59,138)( 60,137)( 61,136)
( 62,135)( 63,134)( 64,133)( 65,132)( 66,118)( 67,130)( 68,129)( 69,128)
( 70,127)( 71,126)( 72,125)( 73,124)( 74,123)( 75,122)( 76,121)( 77,120)
( 78,119)( 79,105)( 80,117)( 81,116)( 82,115)( 83,114)( 84,113)( 85,112)
( 86,111)( 87,110)( 88,109)( 89,108)( 90,107)( 91,106)( 93,104)( 94,103)
( 95,102)( 96,101)( 97,100)( 98, 99)(170,183)(171,195)(172,194)(173,193)
(174,192)(175,191)(176,190)(177,189)(178,188)(179,187)(180,186)(181,185)
(182,184)(196,326)(197,338)(198,337)(199,336)(200,335)(201,334)(202,333)
(203,332)(204,331)(205,330)(206,329)(207,328)(208,327)(209,313)(210,325)
(211,324)(212,323)(213,322)(214,321)(215,320)(216,319)(217,318)(218,317)
(219,316)(220,315)(221,314)(222,300)(223,312)(224,311)(225,310)(226,309)
(227,308)(228,307)(229,306)(230,305)(231,304)(232,303)(233,302)(234,301)
(235,287)(236,299)(237,298)(238,297)(239,296)(240,295)(241,294)(242,293)
(243,292)(244,291)(245,290)(246,289)(247,288)(248,274)(249,286)(250,285)
(251,284)(252,283)(253,282)(254,281)(255,280)(256,279)(257,278)(258,277)
(259,276)(260,275)(262,273)(263,272)(264,271)(265,270)(266,269)(267,268);;
s2 := ( 1,171)( 2,170)( 3,182)( 4,181)( 5,180)( 6,179)( 7,178)( 8,177)
( 9,176)( 10,175)( 11,174)( 12,173)( 13,172)( 14,184)( 15,183)( 16,195)
( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)( 24,187)
( 25,186)( 26,185)( 27,197)( 28,196)( 29,208)( 30,207)( 31,206)( 32,205)
( 33,204)( 34,203)( 35,202)( 36,201)( 37,200)( 38,199)( 39,198)( 40,210)
( 41,209)( 42,221)( 43,220)( 44,219)( 45,218)( 46,217)( 47,216)( 48,215)
( 49,214)( 50,213)( 51,212)( 52,211)( 53,223)( 54,222)( 55,234)( 56,233)
( 57,232)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)( 64,225)
( 65,224)( 66,236)( 67,235)( 68,247)( 69,246)( 70,245)( 71,244)( 72,243)
( 73,242)( 74,241)( 75,240)( 76,239)( 77,238)( 78,237)( 79,249)( 80,248)
( 81,260)( 82,259)( 83,258)( 84,257)( 85,256)( 86,255)( 87,254)( 88,253)
( 89,252)( 90,251)( 91,250)( 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)
(105,275)(106,274)(107,286)(108,285)(109,284)(110,283)(111,282)(112,281)
(113,280)(114,279)(115,278)(116,277)(117,276)(118,288)(119,287)(120,299)
(121,298)(122,297)(123,296)(124,295)(125,294)(126,293)(127,292)(128,291)
(129,290)(130,289)(131,301)(132,300)(133,312)(134,311)(135,310)(136,309)
(137,308)(138,307)(139,306)(140,305)(141,304)(142,303)(143,302)(144,314)
(145,313)(146,325)(147,324)(148,323)(149,322)(150,321)(151,320)(152,319)
(153,318)(154,317)(155,316)(156,315)(157,327)(158,326)(159,338)(160,337)
(161,336)(162,335)(163,334)(164,333)(165,332)(166,331)(167,330)(168,329)
(169,328);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(338)!( 1, 14)( 2, 26)( 3, 25)( 4, 24)( 5, 23)( 6, 22)( 7, 21)
( 8, 20)( 9, 19)( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 27,157)( 28,169)
( 29,168)( 30,167)( 31,166)( 32,165)( 33,164)( 34,163)( 35,162)( 36,161)
( 37,160)( 38,159)( 39,158)( 40,144)( 41,156)( 42,155)( 43,154)( 44,153)
( 45,152)( 46,151)( 47,150)( 48,149)( 49,148)( 50,147)( 51,146)( 52,145)
( 53,131)( 54,143)( 55,142)( 56,141)( 57,140)( 58,139)( 59,138)( 60,137)
( 61,136)( 62,135)( 63,134)( 64,133)( 65,132)( 66,118)( 67,130)( 68,129)
( 69,128)( 70,127)( 71,126)( 72,125)( 73,124)( 74,123)( 75,122)( 76,121)
( 77,120)( 78,119)( 79,105)( 80,117)( 81,116)( 82,115)( 83,114)( 84,113)
( 85,112)( 86,111)( 87,110)( 88,109)( 89,108)( 90,107)( 91,106)( 93,104)
( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)(170,183)(171,195)(172,194)
(173,193)(174,192)(175,191)(176,190)(177,189)(178,188)(179,187)(180,186)
(181,185)(182,184)(196,326)(197,338)(198,337)(199,336)(200,335)(201,334)
(202,333)(203,332)(204,331)(205,330)(206,329)(207,328)(208,327)(209,313)
(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)(216,319)(217,318)
(218,317)(219,316)(220,315)(221,314)(222,300)(223,312)(224,311)(225,310)
(226,309)(227,308)(228,307)(229,306)(230,305)(231,304)(232,303)(233,302)
(234,301)(235,287)(236,299)(237,298)(238,297)(239,296)(240,295)(241,294)
(242,293)(243,292)(244,291)(245,290)(246,289)(247,288)(248,274)(249,286)
(250,285)(251,284)(252,283)(253,282)(254,281)(255,280)(256,279)(257,278)
(258,277)(259,276)(260,275)(262,273)(263,272)(264,271)(265,270)(266,269)
(267,268);
s2 := Sym(338)!( 1,171)( 2,170)( 3,182)( 4,181)( 5,180)( 6,179)( 7,178)
( 8,177)( 9,176)( 10,175)( 11,174)( 12,173)( 13,172)( 14,184)( 15,183)
( 16,195)( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)
( 24,187)( 25,186)( 26,185)( 27,197)( 28,196)( 29,208)( 30,207)( 31,206)
( 32,205)( 33,204)( 34,203)( 35,202)( 36,201)( 37,200)( 38,199)( 39,198)
( 40,210)( 41,209)( 42,221)( 43,220)( 44,219)( 45,218)( 46,217)( 47,216)
( 48,215)( 49,214)( 50,213)( 51,212)( 52,211)( 53,223)( 54,222)( 55,234)
( 56,233)( 57,232)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)
( 64,225)( 65,224)( 66,236)( 67,235)( 68,247)( 69,246)( 70,245)( 71,244)
( 72,243)( 73,242)( 74,241)( 75,240)( 76,239)( 77,238)( 78,237)( 79,249)
( 80,248)( 81,260)( 82,259)( 83,258)( 84,257)( 85,256)( 86,255)( 87,254)
( 88,253)( 89,252)( 90,251)( 91,250)( 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)(105,275)(106,274)(107,286)(108,285)(109,284)(110,283)(111,282)
(112,281)(113,280)(114,279)(115,278)(116,277)(117,276)(118,288)(119,287)
(120,299)(121,298)(122,297)(123,296)(124,295)(125,294)(126,293)(127,292)
(128,291)(129,290)(130,289)(131,301)(132,300)(133,312)(134,311)(135,310)
(136,309)(137,308)(138,307)(139,306)(140,305)(141,304)(142,303)(143,302)
(144,314)(145,313)(146,325)(147,324)(148,323)(149,322)(150,321)(151,320)
(152,319)(153,318)(154,317)(155,316)(156,315)(157,327)(158,326)(159,338)
(160,337)(161,336)(162,335)(163,334)(164,333)(165,332)(166,331)(167,330)
(168,329)(169,328);
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, 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*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 >;
References : None.
to this polytope