Polytope of Type {26,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,4,3}*1248
Also Known As : {{26,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(1248,1438)
Rank : 4
Schlafli Type : {26,4,3}
Number of vertices, edges, etc : 26, 104, 12, 6
Order of s0s1s2s3 : 78
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {26,2,3}*312
8-fold quotients : {13,2,3}*156
13-fold quotients : {2,4,3}*96
26-fold quotients : {2,4,3}*48
52-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 49)( 6, 50)( 7, 51)( 8, 52)( 9, 45)( 10, 46)( 11, 47)( 12, 48)
( 13, 41)( 14, 42)( 15, 43)( 16, 44)( 17, 37)( 18, 38)( 19, 39)( 20, 40)
( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 25, 29)( 26, 30)( 27, 31)( 28, 32)
( 57,101)( 58,102)( 59,103)( 60,104)( 61, 97)( 62, 98)( 63, 99)( 64,100)
( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 89)( 70, 90)( 71, 91)( 72, 92)
( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 81)( 78, 82)( 79, 83)( 80, 84)
(109,153)(110,154)(111,155)(112,156)(113,149)(114,150)(115,151)(116,152)
(117,145)(118,146)(119,147)(120,148)(121,141)(122,142)(123,143)(124,144)
(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)
(161,205)(162,206)(163,207)(164,208)(165,201)(166,202)(167,203)(168,204)
(169,197)(170,198)(171,199)(172,200)(173,193)(174,194)(175,195)(176,196)
(177,189)(178,190)(179,191)(180,192)(181,185)(182,186)(183,187)(184,188)
(213,257)(214,258)(215,259)(216,260)(217,253)(218,254)(219,255)(220,256)
(221,249)(222,250)(223,251)(224,252)(225,245)(226,246)(227,247)(228,248)
(229,241)(230,242)(231,243)(232,244)(233,237)(234,238)(235,239)(236,240)
(265,309)(266,310)(267,311)(268,312)(269,305)(270,306)(271,307)(272,308)
(273,301)(274,302)(275,303)(276,304)(277,297)(278,298)(279,299)(280,300)
(281,293)(282,294)(283,295)(284,296)(285,289)(286,290)(287,291)(288,292);;
s1 := ( 1,163)( 2,164)( 3,161)( 4,162)( 5,159)( 6,160)( 7,157)( 8,158)
( 9,207)( 10,208)( 11,205)( 12,206)( 13,203)( 14,204)( 15,201)( 16,202)
( 17,199)( 18,200)( 19,197)( 20,198)( 21,195)( 22,196)( 23,193)( 24,194)
( 25,191)( 26,192)( 27,189)( 28,190)( 29,187)( 30,188)( 31,185)( 32,186)
( 33,183)( 34,184)( 35,181)( 36,182)( 37,179)( 38,180)( 39,177)( 40,178)
( 41,175)( 42,176)( 43,173)( 44,174)( 45,171)( 46,172)( 47,169)( 48,170)
( 49,167)( 50,168)( 51,165)( 52,166)( 53,215)( 54,216)( 55,213)( 56,214)
( 57,211)( 58,212)( 59,209)( 60,210)( 61,259)( 62,260)( 63,257)( 64,258)
( 65,255)( 66,256)( 67,253)( 68,254)( 69,251)( 70,252)( 71,249)( 72,250)
( 73,247)( 74,248)( 75,245)( 76,246)( 77,243)( 78,244)( 79,241)( 80,242)
( 81,239)( 82,240)( 83,237)( 84,238)( 85,235)( 86,236)( 87,233)( 88,234)
( 89,231)( 90,232)( 91,229)( 92,230)( 93,227)( 94,228)( 95,225)( 96,226)
( 97,223)( 98,224)( 99,221)(100,222)(101,219)(102,220)(103,217)(104,218)
(105,267)(106,268)(107,265)(108,266)(109,263)(110,264)(111,261)(112,262)
(113,311)(114,312)(115,309)(116,310)(117,307)(118,308)(119,305)(120,306)
(121,303)(122,304)(123,301)(124,302)(125,299)(126,300)(127,297)(128,298)
(129,295)(130,296)(131,293)(132,294)(133,291)(134,292)(135,289)(136,290)
(137,287)(138,288)(139,285)(140,286)(141,283)(142,284)(143,281)(144,282)
(145,279)(146,280)(147,277)(148,278)(149,275)(150,276)(151,273)(152,274)
(153,271)(154,272)(155,269)(156,270);;
s2 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 53,105)( 54,106)( 55,108)
( 56,107)( 57,109)( 58,110)( 59,112)( 60,111)( 61,113)( 62,114)( 63,116)
( 64,115)( 65,117)( 66,118)( 67,120)( 68,119)( 69,121)( 70,122)( 71,124)
( 72,123)( 73,125)( 74,126)( 75,128)( 76,127)( 77,129)( 78,130)( 79,132)
( 80,131)( 81,133)( 82,134)( 83,136)( 84,135)( 85,137)( 86,138)( 87,140)
( 88,139)( 89,141)( 90,142)( 91,144)( 92,143)( 93,145)( 94,146)( 95,148)
( 96,147)( 97,149)( 98,150)( 99,152)(100,151)(101,153)(102,154)(103,156)
(104,155)(159,160)(163,164)(167,168)(171,172)(175,176)(179,180)(183,184)
(187,188)(191,192)(195,196)(199,200)(203,204)(207,208)(209,261)(210,262)
(211,264)(212,263)(213,265)(214,266)(215,268)(216,267)(217,269)(218,270)
(219,272)(220,271)(221,273)(222,274)(223,276)(224,275)(225,277)(226,278)
(227,280)(228,279)(229,281)(230,282)(231,284)(232,283)(233,285)(234,286)
(235,288)(236,287)(237,289)(238,290)(239,292)(240,291)(241,293)(242,294)
(243,296)(244,295)(245,297)(246,298)(247,300)(248,299)(249,301)(250,302)
(251,304)(252,303)(253,305)(254,306)(255,308)(256,307)(257,309)(258,310)
(259,312)(260,311);;
s3 := ( 1, 53)( 2, 56)( 3, 55)( 4, 54)( 5, 57)( 6, 60)( 7, 59)( 8, 58)
( 9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 65)( 14, 68)( 15, 67)( 16, 66)
( 17, 69)( 18, 72)( 19, 71)( 20, 70)( 21, 73)( 22, 76)( 23, 75)( 24, 74)
( 25, 77)( 26, 80)( 27, 79)( 28, 78)( 29, 81)( 30, 84)( 31, 83)( 32, 82)
( 33, 85)( 34, 88)( 35, 87)( 36, 86)( 37, 89)( 38, 92)( 39, 91)( 40, 90)
( 41, 93)( 42, 96)( 43, 95)( 44, 94)( 45, 97)( 46,100)( 47, 99)( 48, 98)
( 49,101)( 50,104)( 51,103)( 52,102)(106,108)(110,112)(114,116)(118,120)
(122,124)(126,128)(130,132)(134,136)(138,140)(142,144)(146,148)(150,152)
(154,156)(157,209)(158,212)(159,211)(160,210)(161,213)(162,216)(163,215)
(164,214)(165,217)(166,220)(167,219)(168,218)(169,221)(170,224)(171,223)
(172,222)(173,225)(174,228)(175,227)(176,226)(177,229)(178,232)(179,231)
(180,230)(181,233)(182,236)(183,235)(184,234)(185,237)(186,240)(187,239)
(188,238)(189,241)(190,244)(191,243)(192,242)(193,245)(194,248)(195,247)
(196,246)(197,249)(198,252)(199,251)(200,250)(201,253)(202,256)(203,255)
(204,254)(205,257)(206,260)(207,259)(208,258)(262,264)(266,268)(270,272)
(274,276)(278,280)(282,284)(286,288)(290,292)(294,296)(298,300)(302,304)
(306,308)(310,312);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, 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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(312)!( 5, 49)( 6, 50)( 7, 51)( 8, 52)( 9, 45)( 10, 46)( 11, 47)
( 12, 48)( 13, 41)( 14, 42)( 15, 43)( 16, 44)( 17, 37)( 18, 38)( 19, 39)
( 20, 40)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 25, 29)( 26, 30)( 27, 31)
( 28, 32)( 57,101)( 58,102)( 59,103)( 60,104)( 61, 97)( 62, 98)( 63, 99)
( 64,100)( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 89)( 70, 90)( 71, 91)
( 72, 92)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 81)( 78, 82)( 79, 83)
( 80, 84)(109,153)(110,154)(111,155)(112,156)(113,149)(114,150)(115,151)
(116,152)(117,145)(118,146)(119,147)(120,148)(121,141)(122,142)(123,143)
(124,144)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)
(132,136)(161,205)(162,206)(163,207)(164,208)(165,201)(166,202)(167,203)
(168,204)(169,197)(170,198)(171,199)(172,200)(173,193)(174,194)(175,195)
(176,196)(177,189)(178,190)(179,191)(180,192)(181,185)(182,186)(183,187)
(184,188)(213,257)(214,258)(215,259)(216,260)(217,253)(218,254)(219,255)
(220,256)(221,249)(222,250)(223,251)(224,252)(225,245)(226,246)(227,247)
(228,248)(229,241)(230,242)(231,243)(232,244)(233,237)(234,238)(235,239)
(236,240)(265,309)(266,310)(267,311)(268,312)(269,305)(270,306)(271,307)
(272,308)(273,301)(274,302)(275,303)(276,304)(277,297)(278,298)(279,299)
(280,300)(281,293)(282,294)(283,295)(284,296)(285,289)(286,290)(287,291)
(288,292);
s1 := Sym(312)!( 1,163)( 2,164)( 3,161)( 4,162)( 5,159)( 6,160)( 7,157)
( 8,158)( 9,207)( 10,208)( 11,205)( 12,206)( 13,203)( 14,204)( 15,201)
( 16,202)( 17,199)( 18,200)( 19,197)( 20,198)( 21,195)( 22,196)( 23,193)
( 24,194)( 25,191)( 26,192)( 27,189)( 28,190)( 29,187)( 30,188)( 31,185)
( 32,186)( 33,183)( 34,184)( 35,181)( 36,182)( 37,179)( 38,180)( 39,177)
( 40,178)( 41,175)( 42,176)( 43,173)( 44,174)( 45,171)( 46,172)( 47,169)
( 48,170)( 49,167)( 50,168)( 51,165)( 52,166)( 53,215)( 54,216)( 55,213)
( 56,214)( 57,211)( 58,212)( 59,209)( 60,210)( 61,259)( 62,260)( 63,257)
( 64,258)( 65,255)( 66,256)( 67,253)( 68,254)( 69,251)( 70,252)( 71,249)
( 72,250)( 73,247)( 74,248)( 75,245)( 76,246)( 77,243)( 78,244)( 79,241)
( 80,242)( 81,239)( 82,240)( 83,237)( 84,238)( 85,235)( 86,236)( 87,233)
( 88,234)( 89,231)( 90,232)( 91,229)( 92,230)( 93,227)( 94,228)( 95,225)
( 96,226)( 97,223)( 98,224)( 99,221)(100,222)(101,219)(102,220)(103,217)
(104,218)(105,267)(106,268)(107,265)(108,266)(109,263)(110,264)(111,261)
(112,262)(113,311)(114,312)(115,309)(116,310)(117,307)(118,308)(119,305)
(120,306)(121,303)(122,304)(123,301)(124,302)(125,299)(126,300)(127,297)
(128,298)(129,295)(130,296)(131,293)(132,294)(133,291)(134,292)(135,289)
(136,290)(137,287)(138,288)(139,285)(140,286)(141,283)(142,284)(143,281)
(144,282)(145,279)(146,280)(147,277)(148,278)(149,275)(150,276)(151,273)
(152,274)(153,271)(154,272)(155,269)(156,270);
s2 := Sym(312)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 53,105)( 54,106)
( 55,108)( 56,107)( 57,109)( 58,110)( 59,112)( 60,111)( 61,113)( 62,114)
( 63,116)( 64,115)( 65,117)( 66,118)( 67,120)( 68,119)( 69,121)( 70,122)
( 71,124)( 72,123)( 73,125)( 74,126)( 75,128)( 76,127)( 77,129)( 78,130)
( 79,132)( 80,131)( 81,133)( 82,134)( 83,136)( 84,135)( 85,137)( 86,138)
( 87,140)( 88,139)( 89,141)( 90,142)( 91,144)( 92,143)( 93,145)( 94,146)
( 95,148)( 96,147)( 97,149)( 98,150)( 99,152)(100,151)(101,153)(102,154)
(103,156)(104,155)(159,160)(163,164)(167,168)(171,172)(175,176)(179,180)
(183,184)(187,188)(191,192)(195,196)(199,200)(203,204)(207,208)(209,261)
(210,262)(211,264)(212,263)(213,265)(214,266)(215,268)(216,267)(217,269)
(218,270)(219,272)(220,271)(221,273)(222,274)(223,276)(224,275)(225,277)
(226,278)(227,280)(228,279)(229,281)(230,282)(231,284)(232,283)(233,285)
(234,286)(235,288)(236,287)(237,289)(238,290)(239,292)(240,291)(241,293)
(242,294)(243,296)(244,295)(245,297)(246,298)(247,300)(248,299)(249,301)
(250,302)(251,304)(252,303)(253,305)(254,306)(255,308)(256,307)(257,309)
(258,310)(259,312)(260,311);
s3 := Sym(312)!( 1, 53)( 2, 56)( 3, 55)( 4, 54)( 5, 57)( 6, 60)( 7, 59)
( 8, 58)( 9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 65)( 14, 68)( 15, 67)
( 16, 66)( 17, 69)( 18, 72)( 19, 71)( 20, 70)( 21, 73)( 22, 76)( 23, 75)
( 24, 74)( 25, 77)( 26, 80)( 27, 79)( 28, 78)( 29, 81)( 30, 84)( 31, 83)
( 32, 82)( 33, 85)( 34, 88)( 35, 87)( 36, 86)( 37, 89)( 38, 92)( 39, 91)
( 40, 90)( 41, 93)( 42, 96)( 43, 95)( 44, 94)( 45, 97)( 46,100)( 47, 99)
( 48, 98)( 49,101)( 50,104)( 51,103)( 52,102)(106,108)(110,112)(114,116)
(118,120)(122,124)(126,128)(130,132)(134,136)(138,140)(142,144)(146,148)
(150,152)(154,156)(157,209)(158,212)(159,211)(160,210)(161,213)(162,216)
(163,215)(164,214)(165,217)(166,220)(167,219)(168,218)(169,221)(170,224)
(171,223)(172,222)(173,225)(174,228)(175,227)(176,226)(177,229)(178,232)
(179,231)(180,230)(181,233)(182,236)(183,235)(184,234)(185,237)(186,240)
(187,239)(188,238)(189,241)(190,244)(191,243)(192,242)(193,245)(194,248)
(195,247)(196,246)(197,249)(198,252)(199,251)(200,250)(201,253)(202,256)
(203,255)(204,254)(205,257)(206,260)(207,259)(208,258)(262,264)(266,268)
(270,272)(274,276)(278,280)(282,284)(286,288)(290,292)(294,296)(298,300)
(302,304)(306,308)(310,312);
poly := sub<Sym(312)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
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 >;
References : None.
to this polytope