Polytope of Type {8,33}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,33}*1056
if this polytope has a name.
Group : SmallGroup(1056,888)
Rank : 3
Schlafli Type : {8,33}
Number of vertices, edges, etc : 16, 264, 66
Order of s0s1s2 : 132
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {4,33}*528
4-fold quotients : {4,33}*264
8-fold quotients : {2,33}*132
11-fold quotients : {8,3}*96
22-fold quotients : {4,3}*48
24-fold quotients : {2,11}*44
44-fold quotients : {4,3}*24
88-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,269)( 2,270)( 3,272)( 4,271)( 5,266)( 6,265)( 7,267)( 8,268)
( 9,277)( 10,278)( 11,280)( 12,279)( 13,274)( 14,273)( 15,275)( 16,276)
( 17,285)( 18,286)( 19,288)( 20,287)( 21,282)( 22,281)( 23,283)( 24,284)
( 25,293)( 26,294)( 27,296)( 28,295)( 29,290)( 30,289)( 31,291)( 32,292)
( 33,301)( 34,302)( 35,304)( 36,303)( 37,298)( 38,297)( 39,299)( 40,300)
( 41,309)( 42,310)( 43,312)( 44,311)( 45,306)( 46,305)( 47,307)( 48,308)
( 49,317)( 50,318)( 51,320)( 52,319)( 53,314)( 54,313)( 55,315)( 56,316)
( 57,325)( 58,326)( 59,328)( 60,327)( 61,322)( 62,321)( 63,323)( 64,324)
( 65,333)( 66,334)( 67,336)( 68,335)( 69,330)( 70,329)( 71,331)( 72,332)
( 73,341)( 74,342)( 75,344)( 76,343)( 77,338)( 78,337)( 79,339)( 80,340)
( 81,349)( 82,350)( 83,352)( 84,351)( 85,346)( 86,345)( 87,347)( 88,348)
( 89,357)( 90,358)( 91,360)( 92,359)( 93,354)( 94,353)( 95,355)( 96,356)
( 97,365)( 98,366)( 99,368)(100,367)(101,362)(102,361)(103,363)(104,364)
(105,373)(106,374)(107,376)(108,375)(109,370)(110,369)(111,371)(112,372)
(113,381)(114,382)(115,384)(116,383)(117,378)(118,377)(119,379)(120,380)
(121,389)(122,390)(123,392)(124,391)(125,386)(126,385)(127,387)(128,388)
(129,397)(130,398)(131,400)(132,399)(133,394)(134,393)(135,395)(136,396)
(137,405)(138,406)(139,408)(140,407)(141,402)(142,401)(143,403)(144,404)
(145,413)(146,414)(147,416)(148,415)(149,410)(150,409)(151,411)(152,412)
(153,421)(154,422)(155,424)(156,423)(157,418)(158,417)(159,419)(160,420)
(161,429)(162,430)(163,432)(164,431)(165,426)(166,425)(167,427)(168,428)
(169,437)(170,438)(171,440)(172,439)(173,434)(174,433)(175,435)(176,436)
(177,445)(178,446)(179,448)(180,447)(181,442)(182,441)(183,443)(184,444)
(185,453)(186,454)(187,456)(188,455)(189,450)(190,449)(191,451)(192,452)
(193,461)(194,462)(195,464)(196,463)(197,458)(198,457)(199,459)(200,460)
(201,469)(202,470)(203,472)(204,471)(205,466)(206,465)(207,467)(208,468)
(209,477)(210,478)(211,480)(212,479)(213,474)(214,473)(215,475)(216,476)
(217,485)(218,486)(219,488)(220,487)(221,482)(222,481)(223,483)(224,484)
(225,493)(226,494)(227,496)(228,495)(229,490)(230,489)(231,491)(232,492)
(233,501)(234,502)(235,504)(236,503)(237,498)(238,497)(239,499)(240,500)
(241,509)(242,510)(243,512)(244,511)(245,506)(246,505)(247,507)(248,508)
(249,517)(250,518)(251,520)(252,519)(253,514)(254,513)(255,515)(256,516)
(257,525)(258,526)(259,528)(260,527)(261,522)(262,521)(263,523)(264,524);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 9, 81)( 10, 82)( 11, 84)( 12, 83)( 13, 87)
( 14, 88)( 15, 85)( 16, 86)( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 79)
( 22, 80)( 23, 77)( 24, 78)( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 71)
( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)
( 38, 64)( 39, 61)( 40, 62)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 55)
( 46, 56)( 47, 53)( 48, 54)( 89,177)( 90,178)( 91,180)( 92,179)( 93,183)
( 94,184)( 95,181)( 96,182)( 97,257)( 98,258)( 99,260)(100,259)(101,263)
(102,264)(103,261)(104,262)(105,249)(106,250)(107,252)(108,251)(109,255)
(110,256)(111,253)(112,254)(113,241)(114,242)(115,244)(116,243)(117,247)
(118,248)(119,245)(120,246)(121,233)(122,234)(123,236)(124,235)(125,239)
(126,240)(127,237)(128,238)(129,225)(130,226)(131,228)(132,227)(133,231)
(134,232)(135,229)(136,230)(137,217)(138,218)(139,220)(140,219)(141,223)
(142,224)(143,221)(144,222)(145,209)(146,210)(147,212)(148,211)(149,215)
(150,216)(151,213)(152,214)(153,201)(154,202)(155,204)(156,203)(157,207)
(158,208)(159,205)(160,206)(161,193)(162,194)(163,196)(164,195)(165,199)
(166,200)(167,197)(168,198)(169,185)(170,186)(171,188)(172,187)(173,191)
(174,192)(175,189)(176,190)(265,266)(269,272)(270,271)(273,346)(274,345)
(275,347)(276,348)(277,352)(278,351)(279,350)(280,349)(281,338)(282,337)
(283,339)(284,340)(285,344)(286,343)(287,342)(288,341)(289,330)(290,329)
(291,331)(292,332)(293,336)(294,335)(295,334)(296,333)(297,322)(298,321)
(299,323)(300,324)(301,328)(302,327)(303,326)(304,325)(305,314)(306,313)
(307,315)(308,316)(309,320)(310,319)(311,318)(312,317)(353,442)(354,441)
(355,443)(356,444)(357,448)(358,447)(359,446)(360,445)(361,522)(362,521)
(363,523)(364,524)(365,528)(366,527)(367,526)(368,525)(369,514)(370,513)
(371,515)(372,516)(373,520)(374,519)(375,518)(376,517)(377,506)(378,505)
(379,507)(380,508)(381,512)(382,511)(383,510)(384,509)(385,498)(386,497)
(387,499)(388,500)(389,504)(390,503)(391,502)(392,501)(393,490)(394,489)
(395,491)(396,492)(397,496)(398,495)(399,494)(400,493)(401,482)(402,481)
(403,483)(404,484)(405,488)(406,487)(407,486)(408,485)(409,474)(410,473)
(411,475)(412,476)(413,480)(414,479)(415,478)(416,477)(417,466)(418,465)
(419,467)(420,468)(421,472)(422,471)(423,470)(424,469)(425,458)(426,457)
(427,459)(428,460)(429,464)(430,463)(431,462)(432,461)(433,450)(434,449)
(435,451)(436,452)(437,456)(438,455)(439,454)(440,453);;
s2 := ( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)( 8,100)
( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)( 16, 92)
( 17,169)( 18,170)( 19,175)( 20,176)( 21,174)( 22,173)( 23,171)( 24,172)
( 25,161)( 26,162)( 27,167)( 28,168)( 29,166)( 30,165)( 31,163)( 32,164)
( 33,153)( 34,154)( 35,159)( 36,160)( 37,158)( 38,157)( 39,155)( 40,156)
( 41,145)( 42,146)( 43,151)( 44,152)( 45,150)( 46,149)( 47,147)( 48,148)
( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)( 56,140)
( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)( 64,132)
( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)( 72,124)
( 73,113)( 74,114)( 75,119)( 76,120)( 77,118)( 78,117)( 79,115)( 80,116)
( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)( 87,107)( 88,108)
(177,185)(178,186)(179,191)(180,192)(181,190)(182,189)(183,187)(184,188)
(193,257)(194,258)(195,263)(196,264)(197,262)(198,261)(199,259)(200,260)
(201,249)(202,250)(203,255)(204,256)(205,254)(206,253)(207,251)(208,252)
(209,241)(210,242)(211,247)(212,248)(213,246)(214,245)(215,243)(216,244)
(217,233)(218,234)(219,239)(220,240)(221,238)(222,237)(223,235)(224,236)
(227,231)(228,232)(229,230)(265,362)(266,361)(267,368)(268,367)(269,365)
(270,366)(271,364)(272,363)(273,354)(274,353)(275,360)(276,359)(277,357)
(278,358)(279,356)(280,355)(281,434)(282,433)(283,440)(284,439)(285,437)
(286,438)(287,436)(288,435)(289,426)(290,425)(291,432)(292,431)(293,429)
(294,430)(295,428)(296,427)(297,418)(298,417)(299,424)(300,423)(301,421)
(302,422)(303,420)(304,419)(305,410)(306,409)(307,416)(308,415)(309,413)
(310,414)(311,412)(312,411)(313,402)(314,401)(315,408)(316,407)(317,405)
(318,406)(319,404)(320,403)(321,394)(322,393)(323,400)(324,399)(325,397)
(326,398)(327,396)(328,395)(329,386)(330,385)(331,392)(332,391)(333,389)
(334,390)(335,388)(336,387)(337,378)(338,377)(339,384)(340,383)(341,381)
(342,382)(343,380)(344,379)(345,370)(346,369)(347,376)(348,375)(349,373)
(350,374)(351,372)(352,371)(441,450)(442,449)(443,456)(444,455)(445,453)
(446,454)(447,452)(448,451)(457,522)(458,521)(459,528)(460,527)(461,525)
(462,526)(463,524)(464,523)(465,514)(466,513)(467,520)(468,519)(469,517)
(470,518)(471,516)(472,515)(473,506)(474,505)(475,512)(476,511)(477,509)
(478,510)(479,508)(480,507)(481,498)(482,497)(483,504)(484,503)(485,501)
(486,502)(487,500)(488,499)(489,490)(491,496)(492,495);;
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*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(528)!( 1,269)( 2,270)( 3,272)( 4,271)( 5,266)( 6,265)( 7,267)
( 8,268)( 9,277)( 10,278)( 11,280)( 12,279)( 13,274)( 14,273)( 15,275)
( 16,276)( 17,285)( 18,286)( 19,288)( 20,287)( 21,282)( 22,281)( 23,283)
( 24,284)( 25,293)( 26,294)( 27,296)( 28,295)( 29,290)( 30,289)( 31,291)
( 32,292)( 33,301)( 34,302)( 35,304)( 36,303)( 37,298)( 38,297)( 39,299)
( 40,300)( 41,309)( 42,310)( 43,312)( 44,311)( 45,306)( 46,305)( 47,307)
( 48,308)( 49,317)( 50,318)( 51,320)( 52,319)( 53,314)( 54,313)( 55,315)
( 56,316)( 57,325)( 58,326)( 59,328)( 60,327)( 61,322)( 62,321)( 63,323)
( 64,324)( 65,333)( 66,334)( 67,336)( 68,335)( 69,330)( 70,329)( 71,331)
( 72,332)( 73,341)( 74,342)( 75,344)( 76,343)( 77,338)( 78,337)( 79,339)
( 80,340)( 81,349)( 82,350)( 83,352)( 84,351)( 85,346)( 86,345)( 87,347)
( 88,348)( 89,357)( 90,358)( 91,360)( 92,359)( 93,354)( 94,353)( 95,355)
( 96,356)( 97,365)( 98,366)( 99,368)(100,367)(101,362)(102,361)(103,363)
(104,364)(105,373)(106,374)(107,376)(108,375)(109,370)(110,369)(111,371)
(112,372)(113,381)(114,382)(115,384)(116,383)(117,378)(118,377)(119,379)
(120,380)(121,389)(122,390)(123,392)(124,391)(125,386)(126,385)(127,387)
(128,388)(129,397)(130,398)(131,400)(132,399)(133,394)(134,393)(135,395)
(136,396)(137,405)(138,406)(139,408)(140,407)(141,402)(142,401)(143,403)
(144,404)(145,413)(146,414)(147,416)(148,415)(149,410)(150,409)(151,411)
(152,412)(153,421)(154,422)(155,424)(156,423)(157,418)(158,417)(159,419)
(160,420)(161,429)(162,430)(163,432)(164,431)(165,426)(166,425)(167,427)
(168,428)(169,437)(170,438)(171,440)(172,439)(173,434)(174,433)(175,435)
(176,436)(177,445)(178,446)(179,448)(180,447)(181,442)(182,441)(183,443)
(184,444)(185,453)(186,454)(187,456)(188,455)(189,450)(190,449)(191,451)
(192,452)(193,461)(194,462)(195,464)(196,463)(197,458)(198,457)(199,459)
(200,460)(201,469)(202,470)(203,472)(204,471)(205,466)(206,465)(207,467)
(208,468)(209,477)(210,478)(211,480)(212,479)(213,474)(214,473)(215,475)
(216,476)(217,485)(218,486)(219,488)(220,487)(221,482)(222,481)(223,483)
(224,484)(225,493)(226,494)(227,496)(228,495)(229,490)(230,489)(231,491)
(232,492)(233,501)(234,502)(235,504)(236,503)(237,498)(238,497)(239,499)
(240,500)(241,509)(242,510)(243,512)(244,511)(245,506)(246,505)(247,507)
(248,508)(249,517)(250,518)(251,520)(252,519)(253,514)(254,513)(255,515)
(256,516)(257,525)(258,526)(259,528)(260,527)(261,522)(262,521)(263,523)
(264,524);
s1 := Sym(528)!( 3, 4)( 5, 7)( 6, 8)( 9, 81)( 10, 82)( 11, 84)( 12, 83)
( 13, 87)( 14, 88)( 15, 85)( 16, 86)( 17, 73)( 18, 74)( 19, 76)( 20, 75)
( 21, 79)( 22, 80)( 23, 77)( 24, 78)( 25, 65)( 26, 66)( 27, 68)( 28, 67)
( 29, 71)( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)
( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 41, 49)( 42, 50)( 43, 52)( 44, 51)
( 45, 55)( 46, 56)( 47, 53)( 48, 54)( 89,177)( 90,178)( 91,180)( 92,179)
( 93,183)( 94,184)( 95,181)( 96,182)( 97,257)( 98,258)( 99,260)(100,259)
(101,263)(102,264)(103,261)(104,262)(105,249)(106,250)(107,252)(108,251)
(109,255)(110,256)(111,253)(112,254)(113,241)(114,242)(115,244)(116,243)
(117,247)(118,248)(119,245)(120,246)(121,233)(122,234)(123,236)(124,235)
(125,239)(126,240)(127,237)(128,238)(129,225)(130,226)(131,228)(132,227)
(133,231)(134,232)(135,229)(136,230)(137,217)(138,218)(139,220)(140,219)
(141,223)(142,224)(143,221)(144,222)(145,209)(146,210)(147,212)(148,211)
(149,215)(150,216)(151,213)(152,214)(153,201)(154,202)(155,204)(156,203)
(157,207)(158,208)(159,205)(160,206)(161,193)(162,194)(163,196)(164,195)
(165,199)(166,200)(167,197)(168,198)(169,185)(170,186)(171,188)(172,187)
(173,191)(174,192)(175,189)(176,190)(265,266)(269,272)(270,271)(273,346)
(274,345)(275,347)(276,348)(277,352)(278,351)(279,350)(280,349)(281,338)
(282,337)(283,339)(284,340)(285,344)(286,343)(287,342)(288,341)(289,330)
(290,329)(291,331)(292,332)(293,336)(294,335)(295,334)(296,333)(297,322)
(298,321)(299,323)(300,324)(301,328)(302,327)(303,326)(304,325)(305,314)
(306,313)(307,315)(308,316)(309,320)(310,319)(311,318)(312,317)(353,442)
(354,441)(355,443)(356,444)(357,448)(358,447)(359,446)(360,445)(361,522)
(362,521)(363,523)(364,524)(365,528)(366,527)(367,526)(368,525)(369,514)
(370,513)(371,515)(372,516)(373,520)(374,519)(375,518)(376,517)(377,506)
(378,505)(379,507)(380,508)(381,512)(382,511)(383,510)(384,509)(385,498)
(386,497)(387,499)(388,500)(389,504)(390,503)(391,502)(392,501)(393,490)
(394,489)(395,491)(396,492)(397,496)(398,495)(399,494)(400,493)(401,482)
(402,481)(403,483)(404,484)(405,488)(406,487)(407,486)(408,485)(409,474)
(410,473)(411,475)(412,476)(413,480)(414,479)(415,478)(416,477)(417,466)
(418,465)(419,467)(420,468)(421,472)(422,471)(423,470)(424,469)(425,458)
(426,457)(427,459)(428,460)(429,464)(430,463)(431,462)(432,461)(433,450)
(434,449)(435,451)(436,452)(437,456)(438,455)(439,454)(440,453);
s2 := Sym(528)!( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)
( 8,100)( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)
( 16, 92)( 17,169)( 18,170)( 19,175)( 20,176)( 21,174)( 22,173)( 23,171)
( 24,172)( 25,161)( 26,162)( 27,167)( 28,168)( 29,166)( 30,165)( 31,163)
( 32,164)( 33,153)( 34,154)( 35,159)( 36,160)( 37,158)( 38,157)( 39,155)
( 40,156)( 41,145)( 42,146)( 43,151)( 44,152)( 45,150)( 46,149)( 47,147)
( 48,148)( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)
( 56,140)( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)
( 64,132)( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)
( 72,124)( 73,113)( 74,114)( 75,119)( 76,120)( 77,118)( 78,117)( 79,115)
( 80,116)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)( 87,107)
( 88,108)(177,185)(178,186)(179,191)(180,192)(181,190)(182,189)(183,187)
(184,188)(193,257)(194,258)(195,263)(196,264)(197,262)(198,261)(199,259)
(200,260)(201,249)(202,250)(203,255)(204,256)(205,254)(206,253)(207,251)
(208,252)(209,241)(210,242)(211,247)(212,248)(213,246)(214,245)(215,243)
(216,244)(217,233)(218,234)(219,239)(220,240)(221,238)(222,237)(223,235)
(224,236)(227,231)(228,232)(229,230)(265,362)(266,361)(267,368)(268,367)
(269,365)(270,366)(271,364)(272,363)(273,354)(274,353)(275,360)(276,359)
(277,357)(278,358)(279,356)(280,355)(281,434)(282,433)(283,440)(284,439)
(285,437)(286,438)(287,436)(288,435)(289,426)(290,425)(291,432)(292,431)
(293,429)(294,430)(295,428)(296,427)(297,418)(298,417)(299,424)(300,423)
(301,421)(302,422)(303,420)(304,419)(305,410)(306,409)(307,416)(308,415)
(309,413)(310,414)(311,412)(312,411)(313,402)(314,401)(315,408)(316,407)
(317,405)(318,406)(319,404)(320,403)(321,394)(322,393)(323,400)(324,399)
(325,397)(326,398)(327,396)(328,395)(329,386)(330,385)(331,392)(332,391)
(333,389)(334,390)(335,388)(336,387)(337,378)(338,377)(339,384)(340,383)
(341,381)(342,382)(343,380)(344,379)(345,370)(346,369)(347,376)(348,375)
(349,373)(350,374)(351,372)(352,371)(441,450)(442,449)(443,456)(444,455)
(445,453)(446,454)(447,452)(448,451)(457,522)(458,521)(459,528)(460,527)
(461,525)(462,526)(463,524)(464,523)(465,514)(466,513)(467,520)(468,519)
(469,517)(470,518)(471,516)(472,515)(473,506)(474,505)(475,512)(476,511)
(477,509)(478,510)(479,508)(480,507)(481,498)(482,497)(483,504)(484,503)
(485,501)(486,502)(487,500)(488,499)(489,490)(491,496)(492,495);
poly := sub<Sym(528)|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*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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 >;
References : None.
to this polytope