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