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Polytope of Type {33,6,4}

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