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