Polytope of Type {26,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,6,4}*1248b
if this polytope has a name.
Group : SmallGroup(1248,1438)
Rank : 4
Schlafli Type : {26,6,4}
Number of vertices, edges, etc : 26, 78, 12, 4
Order of s0s1s2s3 : 78
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {2,6,4}*96c
26-fold quotients : {2,3,4}*48
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, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 49)( 10, 50)( 11, 52)( 12, 51)
( 13, 45)( 14, 46)( 15, 48)( 16, 47)( 17, 41)( 18, 42)( 19, 44)( 20, 43)
( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 33)( 26, 34)( 27, 36)( 28, 35)
( 31, 32)( 53,109)( 54,110)( 55,112)( 56,111)( 57,105)( 58,106)( 59,108)
( 60,107)( 61,153)( 62,154)( 63,156)( 64,155)( 65,149)( 66,150)( 67,152)
( 68,151)( 69,145)( 70,146)( 71,148)( 72,147)( 73,141)( 74,142)( 75,144)
( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,133)( 82,134)( 83,136)
( 84,135)( 85,129)( 86,130)( 87,132)( 88,131)( 89,125)( 90,126)( 91,128)
( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)( 97,117)( 98,118)( 99,120)
(100,119)(101,113)(102,114)(103,116)(104,115)(157,161)(158,162)(159,164)
(160,163)(165,205)(166,206)(167,208)(168,207)(169,201)(170,202)(171,204)
(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)(178,194)(179,196)
(180,195)(181,189)(182,190)(183,192)(184,191)(187,188)(209,265)(210,266)
(211,268)(212,267)(213,261)(214,262)(215,264)(216,263)(217,309)(218,310)
(219,312)(220,311)(221,305)(222,306)(223,308)(224,307)(225,301)(226,302)
(227,304)(228,303)(229,297)(230,298)(231,300)(232,299)(233,293)(234,294)
(235,296)(236,295)(237,289)(238,290)(239,292)(240,291)(241,285)(242,286)
(243,288)(244,287)(245,281)(246,282)(247,284)(248,283)(249,277)(250,278)
(251,280)(252,279)(253,273)(254,274)(255,276)(256,275)(257,269)(258,270)
(259,272)(260,271);;
s2 := ( 1,209)( 2,212)( 3,211)( 4,210)( 5,213)( 6,216)( 7,215)( 8,214)
( 9,217)( 10,220)( 11,219)( 12,218)( 13,221)( 14,224)( 15,223)( 16,222)
( 17,225)( 18,228)( 19,227)( 20,226)( 21,229)( 22,232)( 23,231)( 24,230)
( 25,233)( 26,236)( 27,235)( 28,234)( 29,237)( 30,240)( 31,239)( 32,238)
( 33,241)( 34,244)( 35,243)( 36,242)( 37,245)( 38,248)( 39,247)( 40,246)
( 41,249)( 42,252)( 43,251)( 44,250)( 45,253)( 46,256)( 47,255)( 48,254)
( 49,257)( 50,260)( 51,259)( 52,258)( 53,157)( 54,160)( 55,159)( 56,158)
( 57,161)( 58,164)( 59,163)( 60,162)( 61,165)( 62,168)( 63,167)( 64,166)
( 65,169)( 66,172)( 67,171)( 68,170)( 69,173)( 70,176)( 71,175)( 72,174)
( 73,177)( 74,180)( 75,179)( 76,178)( 77,181)( 78,184)( 79,183)( 80,182)
( 81,185)( 82,188)( 83,187)( 84,186)( 85,189)( 86,192)( 87,191)( 88,190)
( 89,193)( 90,196)( 91,195)( 92,194)( 93,197)( 94,200)( 95,199)( 96,198)
( 97,201)( 98,204)( 99,203)(100,202)(101,205)(102,208)(103,207)(104,206)
(105,261)(106,264)(107,263)(108,262)(109,265)(110,268)(111,267)(112,266)
(113,269)(114,272)(115,271)(116,270)(117,273)(118,276)(119,275)(120,274)
(121,277)(122,280)(123,279)(124,278)(125,281)(126,284)(127,283)(128,282)
(129,285)(130,288)(131,287)(132,286)(133,289)(134,292)(135,291)(136,290)
(137,293)(138,296)(139,295)(140,294)(141,297)(142,300)(143,299)(144,298)
(145,301)(146,304)(147,303)(148,302)(149,305)(150,308)(151,307)(152,306)
(153,309)(154,312)(155,311)(156,310);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*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, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 49)( 10, 50)( 11, 52)
( 12, 51)( 13, 45)( 14, 46)( 15, 48)( 16, 47)( 17, 41)( 18, 42)( 19, 44)
( 20, 43)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 33)( 26, 34)( 27, 36)
( 28, 35)( 31, 32)( 53,109)( 54,110)( 55,112)( 56,111)( 57,105)( 58,106)
( 59,108)( 60,107)( 61,153)( 62,154)( 63,156)( 64,155)( 65,149)( 66,150)
( 67,152)( 68,151)( 69,145)( 70,146)( 71,148)( 72,147)( 73,141)( 74,142)
( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,133)( 82,134)
( 83,136)( 84,135)( 85,129)( 86,130)( 87,132)( 88,131)( 89,125)( 90,126)
( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)( 97,117)( 98,118)
( 99,120)(100,119)(101,113)(102,114)(103,116)(104,115)(157,161)(158,162)
(159,164)(160,163)(165,205)(166,206)(167,208)(168,207)(169,201)(170,202)
(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)(178,194)
(179,196)(180,195)(181,189)(182,190)(183,192)(184,191)(187,188)(209,265)
(210,266)(211,268)(212,267)(213,261)(214,262)(215,264)(216,263)(217,309)
(218,310)(219,312)(220,311)(221,305)(222,306)(223,308)(224,307)(225,301)
(226,302)(227,304)(228,303)(229,297)(230,298)(231,300)(232,299)(233,293)
(234,294)(235,296)(236,295)(237,289)(238,290)(239,292)(240,291)(241,285)
(242,286)(243,288)(244,287)(245,281)(246,282)(247,284)(248,283)(249,277)
(250,278)(251,280)(252,279)(253,273)(254,274)(255,276)(256,275)(257,269)
(258,270)(259,272)(260,271);
s2 := Sym(312)!( 1,209)( 2,212)( 3,211)( 4,210)( 5,213)( 6,216)( 7,215)
( 8,214)( 9,217)( 10,220)( 11,219)( 12,218)( 13,221)( 14,224)( 15,223)
( 16,222)( 17,225)( 18,228)( 19,227)( 20,226)( 21,229)( 22,232)( 23,231)
( 24,230)( 25,233)( 26,236)( 27,235)( 28,234)( 29,237)( 30,240)( 31,239)
( 32,238)( 33,241)( 34,244)( 35,243)( 36,242)( 37,245)( 38,248)( 39,247)
( 40,246)( 41,249)( 42,252)( 43,251)( 44,250)( 45,253)( 46,256)( 47,255)
( 48,254)( 49,257)( 50,260)( 51,259)( 52,258)( 53,157)( 54,160)( 55,159)
( 56,158)( 57,161)( 58,164)( 59,163)( 60,162)( 61,165)( 62,168)( 63,167)
( 64,166)( 65,169)( 66,172)( 67,171)( 68,170)( 69,173)( 70,176)( 71,175)
( 72,174)( 73,177)( 74,180)( 75,179)( 76,178)( 77,181)( 78,184)( 79,183)
( 80,182)( 81,185)( 82,188)( 83,187)( 84,186)( 85,189)( 86,192)( 87,191)
( 88,190)( 89,193)( 90,196)( 91,195)( 92,194)( 93,197)( 94,200)( 95,199)
( 96,198)( 97,201)( 98,204)( 99,203)(100,202)(101,205)(102,208)(103,207)
(104,206)(105,261)(106,264)(107,263)(108,262)(109,265)(110,268)(111,267)
(112,266)(113,269)(114,272)(115,271)(116,270)(117,273)(118,276)(119,275)
(120,274)(121,277)(122,280)(123,279)(124,278)(125,281)(126,284)(127,283)
(128,282)(129,285)(130,288)(131,287)(132,286)(133,289)(134,292)(135,291)
(136,290)(137,293)(138,296)(139,295)(140,294)(141,297)(142,300)(143,299)
(144,298)(145,301)(146,304)(147,303)(148,302)(149,305)(150,308)(151,307)
(152,306)(153,309)(154,312)(155,311)(156,310);
s3 := Sym(312)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312);
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,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*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