Polytope of Type {26,36}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,36}*1872
Also Known As : {26,36|2}. if this polytope has another name.
Group : SmallGroup(1872,188)
Rank : 3
Schlafli Type : {26,36}
Number of vertices, edges, etc : 26, 468, 36
Order of s0s1s2 : 468
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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) :
2-fold quotients : {26,18}*936
3-fold quotients : {26,12}*624
6-fold quotients : {26,6}*312
9-fold quotients : {26,4}*208
13-fold quotients : {2,36}*144
18-fold quotients : {26,2}*104
26-fold quotients : {2,18}*72
36-fold quotients : {13,2}*52
39-fold quotients : {2,12}*48
52-fold quotients : {2,9}*36
78-fold quotients : {2,6}*24
117-fold quotients : {2,4}*16
156-fold quotients : {2,3}*12
234-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 4, 37)( 5, 38)( 6, 39)( 7, 34)( 8, 35)( 9, 36)( 10, 31)( 11, 32)
( 12, 33)( 13, 28)( 14, 29)( 15, 30)( 16, 25)( 17, 26)( 18, 27)( 19, 22)
( 20, 23)( 21, 24)( 43, 76)( 44, 77)( 45, 78)( 46, 73)( 47, 74)( 48, 75)
( 49, 70)( 50, 71)( 51, 72)( 52, 67)( 53, 68)( 54, 69)( 55, 64)( 56, 65)
( 57, 66)( 58, 61)( 59, 62)( 60, 63)( 82,115)( 83,116)( 84,117)( 85,112)
( 86,113)( 87,114)( 88,109)( 89,110)( 90,111)( 91,106)( 92,107)( 93,108)
( 94,103)( 95,104)( 96,105)( 97,100)( 98,101)( 99,102)(121,154)(122,155)
(123,156)(124,151)(125,152)(126,153)(127,148)(128,149)(129,150)(130,145)
(131,146)(132,147)(133,142)(134,143)(135,144)(136,139)(137,140)(138,141)
(160,193)(161,194)(162,195)(163,190)(164,191)(165,192)(166,187)(167,188)
(168,189)(169,184)(170,185)(171,186)(172,181)(173,182)(174,183)(175,178)
(176,179)(177,180)(199,232)(200,233)(201,234)(202,229)(203,230)(204,231)
(205,226)(206,227)(207,228)(208,223)(209,224)(210,225)(211,220)(212,221)
(213,222)(214,217)(215,218)(216,219)(238,271)(239,272)(240,273)(241,268)
(242,269)(243,270)(244,265)(245,266)(246,267)(247,262)(248,263)(249,264)
(250,259)(251,260)(252,261)(253,256)(254,257)(255,258)(277,310)(278,311)
(279,312)(280,307)(281,308)(282,309)(283,304)(284,305)(285,306)(286,301)
(287,302)(288,303)(289,298)(290,299)(291,300)(292,295)(293,296)(294,297)
(316,349)(317,350)(318,351)(319,346)(320,347)(321,348)(322,343)(323,344)
(324,345)(325,340)(326,341)(327,342)(328,337)(329,338)(330,339)(331,334)
(332,335)(333,336)(355,388)(356,389)(357,390)(358,385)(359,386)(360,387)
(361,382)(362,383)(363,384)(364,379)(365,380)(366,381)(367,376)(368,377)
(369,378)(370,373)(371,374)(372,375)(394,427)(395,428)(396,429)(397,424)
(398,425)(399,426)(400,421)(401,422)(402,423)(403,418)(404,419)(405,420)
(406,415)(407,416)(408,417)(409,412)(410,413)(411,414)(433,466)(434,467)
(435,468)(436,463)(437,464)(438,465)(439,460)(440,461)(441,462)(442,457)
(443,458)(444,459)(445,454)(446,455)(447,456)(448,451)(449,452)(450,453);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 37)( 8, 39)( 9, 38)( 10, 34)( 11, 36)
( 12, 35)( 13, 31)( 14, 33)( 15, 32)( 16, 28)( 17, 30)( 18, 29)( 19, 25)
( 20, 27)( 21, 26)( 23, 24)( 40, 84)( 41, 83)( 42, 82)( 43, 81)( 44, 80)
( 45, 79)( 46,117)( 47,116)( 48,115)( 49,114)( 50,113)( 51,112)( 52,111)
( 53,110)( 54,109)( 55,108)( 56,107)( 57,106)( 58,105)( 59,104)( 60,103)
( 61,102)( 62,101)( 63,100)( 64, 99)( 65, 98)( 66, 97)( 67, 96)( 68, 95)
( 69, 94)( 70, 93)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)
( 77, 86)( 78, 85)(118,121)(119,123)(120,122)(124,154)(125,156)(126,155)
(127,151)(128,153)(129,152)(130,148)(131,150)(132,149)(133,145)(134,147)
(135,146)(136,142)(137,144)(138,143)(140,141)(157,201)(158,200)(159,199)
(160,198)(161,197)(162,196)(163,234)(164,233)(165,232)(166,231)(167,230)
(168,229)(169,228)(170,227)(171,226)(172,225)(173,224)(174,223)(175,222)
(176,221)(177,220)(178,219)(179,218)(180,217)(181,216)(182,215)(183,214)
(184,213)(185,212)(186,211)(187,210)(188,209)(189,208)(190,207)(191,206)
(192,205)(193,204)(194,203)(195,202)(235,355)(236,357)(237,356)(238,352)
(239,354)(240,353)(241,388)(242,390)(243,389)(244,385)(245,387)(246,386)
(247,382)(248,384)(249,383)(250,379)(251,381)(252,380)(253,376)(254,378)
(255,377)(256,373)(257,375)(258,374)(259,370)(260,372)(261,371)(262,367)
(263,369)(264,368)(265,364)(266,366)(267,365)(268,361)(269,363)(270,362)
(271,358)(272,360)(273,359)(274,435)(275,434)(276,433)(277,432)(278,431)
(279,430)(280,468)(281,467)(282,466)(283,465)(284,464)(285,463)(286,462)
(287,461)(288,460)(289,459)(290,458)(291,457)(292,456)(293,455)(294,454)
(295,453)(296,452)(297,451)(298,450)(299,449)(300,448)(301,447)(302,446)
(303,445)(304,444)(305,443)(306,442)(307,441)(308,440)(309,439)(310,438)
(311,437)(312,436)(313,396)(314,395)(315,394)(316,393)(317,392)(318,391)
(319,429)(320,428)(321,427)(322,426)(323,425)(324,424)(325,423)(326,422)
(327,421)(328,420)(329,419)(330,418)(331,417)(332,416)(333,415)(334,414)
(335,413)(336,412)(337,411)(338,410)(339,409)(340,408)(341,407)(342,406)
(343,405)(344,404)(345,403)(346,402)(347,401)(348,400)(349,399)(350,398)
(351,397);;
s2 := ( 1,274)( 2,276)( 3,275)( 4,277)( 5,279)( 6,278)( 7,280)( 8,282)
( 9,281)( 10,283)( 11,285)( 12,284)( 13,286)( 14,288)( 15,287)( 16,289)
( 17,291)( 18,290)( 19,292)( 20,294)( 21,293)( 22,295)( 23,297)( 24,296)
( 25,298)( 26,300)( 27,299)( 28,301)( 29,303)( 30,302)( 31,304)( 32,306)
( 33,305)( 34,307)( 35,309)( 36,308)( 37,310)( 38,312)( 39,311)( 40,235)
( 41,237)( 42,236)( 43,238)( 44,240)( 45,239)( 46,241)( 47,243)( 48,242)
( 49,244)( 50,246)( 51,245)( 52,247)( 53,249)( 54,248)( 55,250)( 56,252)
( 57,251)( 58,253)( 59,255)( 60,254)( 61,256)( 62,258)( 63,257)( 64,259)
( 65,261)( 66,260)( 67,262)( 68,264)( 69,263)( 70,265)( 71,267)( 72,266)
( 73,268)( 74,270)( 75,269)( 76,271)( 77,273)( 78,272)( 79,315)( 80,314)
( 81,313)( 82,318)( 83,317)( 84,316)( 85,321)( 86,320)( 87,319)( 88,324)
( 89,323)( 90,322)( 91,327)( 92,326)( 93,325)( 94,330)( 95,329)( 96,328)
( 97,333)( 98,332)( 99,331)(100,336)(101,335)(102,334)(103,339)(104,338)
(105,337)(106,342)(107,341)(108,340)(109,345)(110,344)(111,343)(112,348)
(113,347)(114,346)(115,351)(116,350)(117,349)(118,391)(119,393)(120,392)
(121,394)(122,396)(123,395)(124,397)(125,399)(126,398)(127,400)(128,402)
(129,401)(130,403)(131,405)(132,404)(133,406)(134,408)(135,407)(136,409)
(137,411)(138,410)(139,412)(140,414)(141,413)(142,415)(143,417)(144,416)
(145,418)(146,420)(147,419)(148,421)(149,423)(150,422)(151,424)(152,426)
(153,425)(154,427)(155,429)(156,428)(157,352)(158,354)(159,353)(160,355)
(161,357)(162,356)(163,358)(164,360)(165,359)(166,361)(167,363)(168,362)
(169,364)(170,366)(171,365)(172,367)(173,369)(174,368)(175,370)(176,372)
(177,371)(178,373)(179,375)(180,374)(181,376)(182,378)(183,377)(184,379)
(185,381)(186,380)(187,382)(188,384)(189,383)(190,385)(191,387)(192,386)
(193,388)(194,390)(195,389)(196,432)(197,431)(198,430)(199,435)(200,434)
(201,433)(202,438)(203,437)(204,436)(205,441)(206,440)(207,439)(208,444)
(209,443)(210,442)(211,447)(212,446)(213,445)(214,450)(215,449)(216,448)
(217,453)(218,452)(219,451)(220,456)(221,455)(222,454)(223,459)(224,458)
(225,457)(226,462)(227,461)(228,460)(229,465)(230,464)(231,463)(232,468)
(233,467)(234,466);;
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*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(468)!( 4, 37)( 5, 38)( 6, 39)( 7, 34)( 8, 35)( 9, 36)( 10, 31)
( 11, 32)( 12, 33)( 13, 28)( 14, 29)( 15, 30)( 16, 25)( 17, 26)( 18, 27)
( 19, 22)( 20, 23)( 21, 24)( 43, 76)( 44, 77)( 45, 78)( 46, 73)( 47, 74)
( 48, 75)( 49, 70)( 50, 71)( 51, 72)( 52, 67)( 53, 68)( 54, 69)( 55, 64)
( 56, 65)( 57, 66)( 58, 61)( 59, 62)( 60, 63)( 82,115)( 83,116)( 84,117)
( 85,112)( 86,113)( 87,114)( 88,109)( 89,110)( 90,111)( 91,106)( 92,107)
( 93,108)( 94,103)( 95,104)( 96,105)( 97,100)( 98,101)( 99,102)(121,154)
(122,155)(123,156)(124,151)(125,152)(126,153)(127,148)(128,149)(129,150)
(130,145)(131,146)(132,147)(133,142)(134,143)(135,144)(136,139)(137,140)
(138,141)(160,193)(161,194)(162,195)(163,190)(164,191)(165,192)(166,187)
(167,188)(168,189)(169,184)(170,185)(171,186)(172,181)(173,182)(174,183)
(175,178)(176,179)(177,180)(199,232)(200,233)(201,234)(202,229)(203,230)
(204,231)(205,226)(206,227)(207,228)(208,223)(209,224)(210,225)(211,220)
(212,221)(213,222)(214,217)(215,218)(216,219)(238,271)(239,272)(240,273)
(241,268)(242,269)(243,270)(244,265)(245,266)(246,267)(247,262)(248,263)
(249,264)(250,259)(251,260)(252,261)(253,256)(254,257)(255,258)(277,310)
(278,311)(279,312)(280,307)(281,308)(282,309)(283,304)(284,305)(285,306)
(286,301)(287,302)(288,303)(289,298)(290,299)(291,300)(292,295)(293,296)
(294,297)(316,349)(317,350)(318,351)(319,346)(320,347)(321,348)(322,343)
(323,344)(324,345)(325,340)(326,341)(327,342)(328,337)(329,338)(330,339)
(331,334)(332,335)(333,336)(355,388)(356,389)(357,390)(358,385)(359,386)
(360,387)(361,382)(362,383)(363,384)(364,379)(365,380)(366,381)(367,376)
(368,377)(369,378)(370,373)(371,374)(372,375)(394,427)(395,428)(396,429)
(397,424)(398,425)(399,426)(400,421)(401,422)(402,423)(403,418)(404,419)
(405,420)(406,415)(407,416)(408,417)(409,412)(410,413)(411,414)(433,466)
(434,467)(435,468)(436,463)(437,464)(438,465)(439,460)(440,461)(441,462)
(442,457)(443,458)(444,459)(445,454)(446,455)(447,456)(448,451)(449,452)
(450,453);
s1 := Sym(468)!( 1, 4)( 2, 6)( 3, 5)( 7, 37)( 8, 39)( 9, 38)( 10, 34)
( 11, 36)( 12, 35)( 13, 31)( 14, 33)( 15, 32)( 16, 28)( 17, 30)( 18, 29)
( 19, 25)( 20, 27)( 21, 26)( 23, 24)( 40, 84)( 41, 83)( 42, 82)( 43, 81)
( 44, 80)( 45, 79)( 46,117)( 47,116)( 48,115)( 49,114)( 50,113)( 51,112)
( 52,111)( 53,110)( 54,109)( 55,108)( 56,107)( 57,106)( 58,105)( 59,104)
( 60,103)( 61,102)( 62,101)( 63,100)( 64, 99)( 65, 98)( 66, 97)( 67, 96)
( 68, 95)( 69, 94)( 70, 93)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)
( 76, 87)( 77, 86)( 78, 85)(118,121)(119,123)(120,122)(124,154)(125,156)
(126,155)(127,151)(128,153)(129,152)(130,148)(131,150)(132,149)(133,145)
(134,147)(135,146)(136,142)(137,144)(138,143)(140,141)(157,201)(158,200)
(159,199)(160,198)(161,197)(162,196)(163,234)(164,233)(165,232)(166,231)
(167,230)(168,229)(169,228)(170,227)(171,226)(172,225)(173,224)(174,223)
(175,222)(176,221)(177,220)(178,219)(179,218)(180,217)(181,216)(182,215)
(183,214)(184,213)(185,212)(186,211)(187,210)(188,209)(189,208)(190,207)
(191,206)(192,205)(193,204)(194,203)(195,202)(235,355)(236,357)(237,356)
(238,352)(239,354)(240,353)(241,388)(242,390)(243,389)(244,385)(245,387)
(246,386)(247,382)(248,384)(249,383)(250,379)(251,381)(252,380)(253,376)
(254,378)(255,377)(256,373)(257,375)(258,374)(259,370)(260,372)(261,371)
(262,367)(263,369)(264,368)(265,364)(266,366)(267,365)(268,361)(269,363)
(270,362)(271,358)(272,360)(273,359)(274,435)(275,434)(276,433)(277,432)
(278,431)(279,430)(280,468)(281,467)(282,466)(283,465)(284,464)(285,463)
(286,462)(287,461)(288,460)(289,459)(290,458)(291,457)(292,456)(293,455)
(294,454)(295,453)(296,452)(297,451)(298,450)(299,449)(300,448)(301,447)
(302,446)(303,445)(304,444)(305,443)(306,442)(307,441)(308,440)(309,439)
(310,438)(311,437)(312,436)(313,396)(314,395)(315,394)(316,393)(317,392)
(318,391)(319,429)(320,428)(321,427)(322,426)(323,425)(324,424)(325,423)
(326,422)(327,421)(328,420)(329,419)(330,418)(331,417)(332,416)(333,415)
(334,414)(335,413)(336,412)(337,411)(338,410)(339,409)(340,408)(341,407)
(342,406)(343,405)(344,404)(345,403)(346,402)(347,401)(348,400)(349,399)
(350,398)(351,397);
s2 := Sym(468)!( 1,274)( 2,276)( 3,275)( 4,277)( 5,279)( 6,278)( 7,280)
( 8,282)( 9,281)( 10,283)( 11,285)( 12,284)( 13,286)( 14,288)( 15,287)
( 16,289)( 17,291)( 18,290)( 19,292)( 20,294)( 21,293)( 22,295)( 23,297)
( 24,296)( 25,298)( 26,300)( 27,299)( 28,301)( 29,303)( 30,302)( 31,304)
( 32,306)( 33,305)( 34,307)( 35,309)( 36,308)( 37,310)( 38,312)( 39,311)
( 40,235)( 41,237)( 42,236)( 43,238)( 44,240)( 45,239)( 46,241)( 47,243)
( 48,242)( 49,244)( 50,246)( 51,245)( 52,247)( 53,249)( 54,248)( 55,250)
( 56,252)( 57,251)( 58,253)( 59,255)( 60,254)( 61,256)( 62,258)( 63,257)
( 64,259)( 65,261)( 66,260)( 67,262)( 68,264)( 69,263)( 70,265)( 71,267)
( 72,266)( 73,268)( 74,270)( 75,269)( 76,271)( 77,273)( 78,272)( 79,315)
( 80,314)( 81,313)( 82,318)( 83,317)( 84,316)( 85,321)( 86,320)( 87,319)
( 88,324)( 89,323)( 90,322)( 91,327)( 92,326)( 93,325)( 94,330)( 95,329)
( 96,328)( 97,333)( 98,332)( 99,331)(100,336)(101,335)(102,334)(103,339)
(104,338)(105,337)(106,342)(107,341)(108,340)(109,345)(110,344)(111,343)
(112,348)(113,347)(114,346)(115,351)(116,350)(117,349)(118,391)(119,393)
(120,392)(121,394)(122,396)(123,395)(124,397)(125,399)(126,398)(127,400)
(128,402)(129,401)(130,403)(131,405)(132,404)(133,406)(134,408)(135,407)
(136,409)(137,411)(138,410)(139,412)(140,414)(141,413)(142,415)(143,417)
(144,416)(145,418)(146,420)(147,419)(148,421)(149,423)(150,422)(151,424)
(152,426)(153,425)(154,427)(155,429)(156,428)(157,352)(158,354)(159,353)
(160,355)(161,357)(162,356)(163,358)(164,360)(165,359)(166,361)(167,363)
(168,362)(169,364)(170,366)(171,365)(172,367)(173,369)(174,368)(175,370)
(176,372)(177,371)(178,373)(179,375)(180,374)(181,376)(182,378)(183,377)
(184,379)(185,381)(186,380)(187,382)(188,384)(189,383)(190,385)(191,387)
(192,386)(193,388)(194,390)(195,389)(196,432)(197,431)(198,430)(199,435)
(200,434)(201,433)(202,438)(203,437)(204,436)(205,441)(206,440)(207,439)
(208,444)(209,443)(210,442)(211,447)(212,446)(213,445)(214,450)(215,449)
(216,448)(217,453)(218,452)(219,451)(220,456)(221,455)(222,454)(223,459)
(224,458)(225,457)(226,462)(227,461)(228,460)(229,465)(230,464)(231,463)
(232,468)(233,467)(234,466);
poly := sub<Sym(468)|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*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