Polytope of Type {4,6,33}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,33}*1584
if this polytope has a name.
Group : SmallGroup(1584,576)
Rank : 4
Schlafli Type : {4,6,33}
Number of vertices, edges, etc : 4, 12, 99, 33
Order of s0s1s2s3 : 132
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) :
2-fold quotients : {2,6,33}*792
3-fold quotients : {4,2,33}*528
6-fold quotients : {2,2,33}*264
9-fold quotients : {4,2,11}*176
11-fold quotients : {4,6,3}*144
18-fold quotients : {2,2,11}*88
22-fold quotients : {2,6,3}*72
33-fold quotients : {4,2,3}*48
66-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,199)( 2,200)( 3,201)( 4,202)( 5,203)( 6,204)( 7,205)( 8,206)
( 9,207)( 10,208)( 11,209)( 12,210)( 13,211)( 14,212)( 15,213)( 16,214)
( 17,215)( 18,216)( 19,217)( 20,218)( 21,219)( 22,220)( 23,221)( 24,222)
( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,229)( 32,230)
( 33,231)( 34,232)( 35,233)( 36,234)( 37,235)( 38,236)( 39,237)( 40,238)
( 41,239)( 42,240)( 43,241)( 44,242)( 45,243)( 46,244)( 47,245)( 48,246)
( 49,247)( 50,248)( 51,249)( 52,250)( 53,251)( 54,252)( 55,253)( 56,254)
( 57,255)( 58,256)( 59,257)( 60,258)( 61,259)( 62,260)( 63,261)( 64,262)
( 65,263)( 66,264)( 67,265)( 68,266)( 69,267)( 70,268)( 71,269)( 72,270)
( 73,271)( 74,272)( 75,273)( 76,274)( 77,275)( 78,276)( 79,277)( 80,278)
( 81,279)( 82,280)( 83,281)( 84,282)( 85,283)( 86,284)( 87,285)( 88,286)
( 89,287)( 90,288)( 91,289)( 92,290)( 93,291)( 94,292)( 95,293)( 96,294)
( 97,295)( 98,296)( 99,297)(100,298)(101,299)(102,300)(103,301)(104,302)
(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(111,309)(112,310)
(113,311)(114,312)(115,313)(116,314)(117,315)(118,316)(119,317)(120,318)
(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,325)(128,326)
(129,327)(130,328)(131,329)(132,330)(133,331)(134,332)(135,333)(136,334)
(137,335)(138,336)(139,337)(140,338)(141,339)(142,340)(143,341)(144,342)
(145,343)(146,344)(147,345)(148,346)(149,347)(150,348)(151,349)(152,350)
(153,351)(154,352)(155,353)(156,354)(157,355)(158,356)(159,357)(160,358)
(161,359)(162,360)(163,361)(164,362)(165,363)(166,364)(167,365)(168,366)
(169,367)(170,368)(171,369)(172,370)(173,371)(174,372)(175,373)(176,374)
(177,375)(178,376)(179,377)(180,378)(181,379)(182,380)(183,381)(184,382)
(185,383)(186,384)(187,385)(188,386)(189,387)(190,388)(191,389)(192,390)
(193,391)(194,392)(195,393)(196,394)(197,395)(198,396);;
s1 := ( 34, 67)( 35, 68)( 36, 69)( 37, 70)( 38, 71)( 39, 72)( 40, 73)( 41, 74)
( 42, 75)( 43, 76)( 44, 77)( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)
( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 89)( 57, 90)
( 58, 91)( 59, 92)( 60, 93)( 61, 94)( 62, 95)( 63, 96)( 64, 97)( 65, 98)
( 66, 99)(133,166)(134,167)(135,168)(136,169)(137,170)(138,171)(139,172)
(140,173)(141,174)(142,175)(143,176)(144,177)(145,178)(146,179)(147,180)
(148,181)(149,182)(150,183)(151,184)(152,185)(153,186)(154,187)(155,188)
(156,189)(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)(163,196)
(164,197)(165,198)(199,298)(200,299)(201,300)(202,301)(203,302)(204,303)
(205,304)(206,305)(207,306)(208,307)(209,308)(210,309)(211,310)(212,311)
(213,312)(214,313)(215,314)(216,315)(217,316)(218,317)(219,318)(220,319)
(221,320)(222,321)(223,322)(224,323)(225,324)(226,325)(227,326)(228,327)
(229,328)(230,329)(231,330)(232,364)(233,365)(234,366)(235,367)(236,368)
(237,369)(238,370)(239,371)(240,372)(241,373)(242,374)(243,375)(244,376)
(245,377)(246,378)(247,379)(248,380)(249,381)(250,382)(251,383)(252,384)
(253,385)(254,386)(255,387)(256,388)(257,389)(258,390)(259,391)(260,392)
(261,393)(262,394)(263,395)(264,396)(265,331)(266,332)(267,333)(268,334)
(269,335)(270,336)(271,337)(272,338)(273,339)(274,340)(275,341)(276,342)
(277,343)(278,344)(279,345)(280,346)(281,347)(282,348)(283,349)(284,350)
(285,351)(286,352)(287,353)(288,354)(289,355)(290,356)(291,357)(292,358)
(293,359)(294,360)(295,361)(296,362)(297,363);;
s2 := ( 1, 34)( 2, 44)( 3, 43)( 4, 42)( 5, 41)( 6, 40)( 7, 39)( 8, 38)
( 9, 37)( 10, 36)( 11, 35)( 12, 56)( 13, 66)( 14, 65)( 15, 64)( 16, 63)
( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 57)( 23, 45)( 24, 55)
( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 50)( 30, 49)( 31, 48)( 32, 47)
( 33, 46)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 78, 89)( 79, 99)
( 80, 98)( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)
( 88, 90)(100,133)(101,143)(102,142)(103,141)(104,140)(105,139)(106,138)
(107,137)(108,136)(109,135)(110,134)(111,155)(112,165)(113,164)(114,163)
(115,162)(116,161)(117,160)(118,159)(119,158)(120,157)(121,156)(122,144)
(123,154)(124,153)(125,152)(126,151)(127,150)(128,149)(129,148)(130,147)
(131,146)(132,145)(167,176)(168,175)(169,174)(170,173)(171,172)(177,188)
(178,198)(179,197)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)
(186,190)(187,189)(199,232)(200,242)(201,241)(202,240)(203,239)(204,238)
(205,237)(206,236)(207,235)(208,234)(209,233)(210,254)(211,264)(212,263)
(213,262)(214,261)(215,260)(216,259)(217,258)(218,257)(219,256)(220,255)
(221,243)(222,253)(223,252)(224,251)(225,250)(226,249)(227,248)(228,247)
(229,246)(230,245)(231,244)(266,275)(267,274)(268,273)(269,272)(270,271)
(276,287)(277,297)(278,296)(279,295)(280,294)(281,293)(282,292)(283,291)
(284,290)(285,289)(286,288)(298,331)(299,341)(300,340)(301,339)(302,338)
(303,337)(304,336)(305,335)(306,334)(307,333)(308,332)(309,353)(310,363)
(311,362)(312,361)(313,360)(314,359)(315,358)(316,357)(317,356)(318,355)
(319,354)(320,342)(321,352)(322,351)(323,350)(324,349)(325,348)(326,347)
(327,346)(328,345)(329,344)(330,343)(365,374)(366,373)(367,372)(368,371)
(369,370)(375,386)(376,396)(377,395)(378,394)(379,393)(380,392)(381,391)
(382,390)(383,389)(384,388)(385,387);;
s3 := ( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)
( 9, 16)( 10, 15)( 11, 14)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 34, 79)( 35, 78)( 36, 88)( 37, 87)( 38, 86)( 39, 85)( 40, 84)( 41, 83)
( 42, 82)( 43, 81)( 44, 80)( 45, 68)( 46, 67)( 47, 77)( 48, 76)( 49, 75)
( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)( 55, 69)( 56, 90)( 57, 89)
( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95)( 63, 94)( 64, 93)( 65, 92)
( 66, 91)(100,112)(101,111)(102,121)(103,120)(104,119)(105,118)(106,117)
(107,116)(108,115)(109,114)(110,113)(122,123)(124,132)(125,131)(126,130)
(127,129)(133,178)(134,177)(135,187)(136,186)(137,185)(138,184)(139,183)
(140,182)(141,181)(142,180)(143,179)(144,167)(145,166)(146,176)(147,175)
(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,189)
(156,188)(157,198)(158,197)(159,196)(160,195)(161,194)(162,193)(163,192)
(164,191)(165,190)(199,211)(200,210)(201,220)(202,219)(203,218)(204,217)
(205,216)(206,215)(207,214)(208,213)(209,212)(221,222)(223,231)(224,230)
(225,229)(226,228)(232,277)(233,276)(234,286)(235,285)(236,284)(237,283)
(238,282)(239,281)(240,280)(241,279)(242,278)(243,266)(244,265)(245,275)
(246,274)(247,273)(248,272)(249,271)(250,270)(251,269)(252,268)(253,267)
(254,288)(255,287)(256,297)(257,296)(258,295)(259,294)(260,293)(261,292)
(262,291)(263,290)(264,289)(298,310)(299,309)(300,319)(301,318)(302,317)
(303,316)(304,315)(305,314)(306,313)(307,312)(308,311)(320,321)(322,330)
(323,329)(324,328)(325,327)(331,376)(332,375)(333,385)(334,384)(335,383)
(336,382)(337,381)(338,380)(339,379)(340,378)(341,377)(342,365)(343,364)
(344,374)(345,373)(346,372)(347,371)(348,370)(349,369)(350,368)(351,367)
(352,366)(353,387)(354,386)(355,396)(356,395)(357,394)(358,393)(359,392)
(360,391)(361,390)(362,389)(363,388);;
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*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(396)!( 1,199)( 2,200)( 3,201)( 4,202)( 5,203)( 6,204)( 7,205)
( 8,206)( 9,207)( 10,208)( 11,209)( 12,210)( 13,211)( 14,212)( 15,213)
( 16,214)( 17,215)( 18,216)( 19,217)( 20,218)( 21,219)( 22,220)( 23,221)
( 24,222)( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,229)
( 32,230)( 33,231)( 34,232)( 35,233)( 36,234)( 37,235)( 38,236)( 39,237)
( 40,238)( 41,239)( 42,240)( 43,241)( 44,242)( 45,243)( 46,244)( 47,245)
( 48,246)( 49,247)( 50,248)( 51,249)( 52,250)( 53,251)( 54,252)( 55,253)
( 56,254)( 57,255)( 58,256)( 59,257)( 60,258)( 61,259)( 62,260)( 63,261)
( 64,262)( 65,263)( 66,264)( 67,265)( 68,266)( 69,267)( 70,268)( 71,269)
( 72,270)( 73,271)( 74,272)( 75,273)( 76,274)( 77,275)( 78,276)( 79,277)
( 80,278)( 81,279)( 82,280)( 83,281)( 84,282)( 85,283)( 86,284)( 87,285)
( 88,286)( 89,287)( 90,288)( 91,289)( 92,290)( 93,291)( 94,292)( 95,293)
( 96,294)( 97,295)( 98,296)( 99,297)(100,298)(101,299)(102,300)(103,301)
(104,302)(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(111,309)
(112,310)(113,311)(114,312)(115,313)(116,314)(117,315)(118,316)(119,317)
(120,318)(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,325)
(128,326)(129,327)(130,328)(131,329)(132,330)(133,331)(134,332)(135,333)
(136,334)(137,335)(138,336)(139,337)(140,338)(141,339)(142,340)(143,341)
(144,342)(145,343)(146,344)(147,345)(148,346)(149,347)(150,348)(151,349)
(152,350)(153,351)(154,352)(155,353)(156,354)(157,355)(158,356)(159,357)
(160,358)(161,359)(162,360)(163,361)(164,362)(165,363)(166,364)(167,365)
(168,366)(169,367)(170,368)(171,369)(172,370)(173,371)(174,372)(175,373)
(176,374)(177,375)(178,376)(179,377)(180,378)(181,379)(182,380)(183,381)
(184,382)(185,383)(186,384)(187,385)(188,386)(189,387)(190,388)(191,389)
(192,390)(193,391)(194,392)(195,393)(196,394)(197,395)(198,396);
s1 := Sym(396)!( 34, 67)( 35, 68)( 36, 69)( 37, 70)( 38, 71)( 39, 72)( 40, 73)
( 41, 74)( 42, 75)( 43, 76)( 44, 77)( 45, 78)( 46, 79)( 47, 80)( 48, 81)
( 49, 82)( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 89)
( 57, 90)( 58, 91)( 59, 92)( 60, 93)( 61, 94)( 62, 95)( 63, 96)( 64, 97)
( 65, 98)( 66, 99)(133,166)(134,167)(135,168)(136,169)(137,170)(138,171)
(139,172)(140,173)(141,174)(142,175)(143,176)(144,177)(145,178)(146,179)
(147,180)(148,181)(149,182)(150,183)(151,184)(152,185)(153,186)(154,187)
(155,188)(156,189)(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)
(163,196)(164,197)(165,198)(199,298)(200,299)(201,300)(202,301)(203,302)
(204,303)(205,304)(206,305)(207,306)(208,307)(209,308)(210,309)(211,310)
(212,311)(213,312)(214,313)(215,314)(216,315)(217,316)(218,317)(219,318)
(220,319)(221,320)(222,321)(223,322)(224,323)(225,324)(226,325)(227,326)
(228,327)(229,328)(230,329)(231,330)(232,364)(233,365)(234,366)(235,367)
(236,368)(237,369)(238,370)(239,371)(240,372)(241,373)(242,374)(243,375)
(244,376)(245,377)(246,378)(247,379)(248,380)(249,381)(250,382)(251,383)
(252,384)(253,385)(254,386)(255,387)(256,388)(257,389)(258,390)(259,391)
(260,392)(261,393)(262,394)(263,395)(264,396)(265,331)(266,332)(267,333)
(268,334)(269,335)(270,336)(271,337)(272,338)(273,339)(274,340)(275,341)
(276,342)(277,343)(278,344)(279,345)(280,346)(281,347)(282,348)(283,349)
(284,350)(285,351)(286,352)(287,353)(288,354)(289,355)(290,356)(291,357)
(292,358)(293,359)(294,360)(295,361)(296,362)(297,363);
s2 := Sym(396)!( 1, 34)( 2, 44)( 3, 43)( 4, 42)( 5, 41)( 6, 40)( 7, 39)
( 8, 38)( 9, 37)( 10, 36)( 11, 35)( 12, 56)( 13, 66)( 14, 65)( 15, 64)
( 16, 63)( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 57)( 23, 45)
( 24, 55)( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 50)( 30, 49)( 31, 48)
( 32, 47)( 33, 46)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 78, 89)
( 79, 99)( 80, 98)( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)
( 87, 91)( 88, 90)(100,133)(101,143)(102,142)(103,141)(104,140)(105,139)
(106,138)(107,137)(108,136)(109,135)(110,134)(111,155)(112,165)(113,164)
(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)(120,157)(121,156)
(122,144)(123,154)(124,153)(125,152)(126,151)(127,150)(128,149)(129,148)
(130,147)(131,146)(132,145)(167,176)(168,175)(169,174)(170,173)(171,172)
(177,188)(178,198)(179,197)(180,196)(181,195)(182,194)(183,193)(184,192)
(185,191)(186,190)(187,189)(199,232)(200,242)(201,241)(202,240)(203,239)
(204,238)(205,237)(206,236)(207,235)(208,234)(209,233)(210,254)(211,264)
(212,263)(213,262)(214,261)(215,260)(216,259)(217,258)(218,257)(219,256)
(220,255)(221,243)(222,253)(223,252)(224,251)(225,250)(226,249)(227,248)
(228,247)(229,246)(230,245)(231,244)(266,275)(267,274)(268,273)(269,272)
(270,271)(276,287)(277,297)(278,296)(279,295)(280,294)(281,293)(282,292)
(283,291)(284,290)(285,289)(286,288)(298,331)(299,341)(300,340)(301,339)
(302,338)(303,337)(304,336)(305,335)(306,334)(307,333)(308,332)(309,353)
(310,363)(311,362)(312,361)(313,360)(314,359)(315,358)(316,357)(317,356)
(318,355)(319,354)(320,342)(321,352)(322,351)(323,350)(324,349)(325,348)
(326,347)(327,346)(328,345)(329,344)(330,343)(365,374)(366,373)(367,372)
(368,371)(369,370)(375,386)(376,396)(377,395)(378,394)(379,393)(380,392)
(381,391)(382,390)(383,389)(384,388)(385,387);
s3 := Sym(396)!( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)
( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 23, 24)( 25, 33)( 26, 32)( 27, 31)
( 28, 30)( 34, 79)( 35, 78)( 36, 88)( 37, 87)( 38, 86)( 39, 85)( 40, 84)
( 41, 83)( 42, 82)( 43, 81)( 44, 80)( 45, 68)( 46, 67)( 47, 77)( 48, 76)
( 49, 75)( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)( 55, 69)( 56, 90)
( 57, 89)( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95)( 63, 94)( 64, 93)
( 65, 92)( 66, 91)(100,112)(101,111)(102,121)(103,120)(104,119)(105,118)
(106,117)(107,116)(108,115)(109,114)(110,113)(122,123)(124,132)(125,131)
(126,130)(127,129)(133,178)(134,177)(135,187)(136,186)(137,185)(138,184)
(139,183)(140,182)(141,181)(142,180)(143,179)(144,167)(145,166)(146,176)
(147,175)(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)
(155,189)(156,188)(157,198)(158,197)(159,196)(160,195)(161,194)(162,193)
(163,192)(164,191)(165,190)(199,211)(200,210)(201,220)(202,219)(203,218)
(204,217)(205,216)(206,215)(207,214)(208,213)(209,212)(221,222)(223,231)
(224,230)(225,229)(226,228)(232,277)(233,276)(234,286)(235,285)(236,284)
(237,283)(238,282)(239,281)(240,280)(241,279)(242,278)(243,266)(244,265)
(245,275)(246,274)(247,273)(248,272)(249,271)(250,270)(251,269)(252,268)
(253,267)(254,288)(255,287)(256,297)(257,296)(258,295)(259,294)(260,293)
(261,292)(262,291)(263,290)(264,289)(298,310)(299,309)(300,319)(301,318)
(302,317)(303,316)(304,315)(305,314)(306,313)(307,312)(308,311)(320,321)
(322,330)(323,329)(324,328)(325,327)(331,376)(332,375)(333,385)(334,384)
(335,383)(336,382)(337,381)(338,380)(339,379)(340,378)(341,377)(342,365)
(343,364)(344,374)(345,373)(346,372)(347,371)(348,370)(349,369)(350,368)
(351,367)(352,366)(353,387)(354,386)(355,396)(356,395)(357,394)(358,393)
(359,392)(360,391)(361,390)(362,389)(363,388);
poly := sub<Sym(396)|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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope