Polytope of Type {204,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {204,4}*1632a
Also Known As : {204,4|2}. if this polytope has another name.
Group : SmallGroup(1632,844)
Rank : 3
Schlafli Type : {204,4}
Number of vertices, edges, etc : 204, 408, 4
Order of s0s1s2 : 204
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {204,2}*816, {102,4}*816a
3-fold quotients : {68,4}*544
4-fold quotients : {102,2}*408
6-fold quotients : {68,2}*272, {34,4}*272
8-fold quotients : {51,2}*204
12-fold quotients : {34,2}*136
17-fold quotients : {12,4}*96a
24-fold quotients : {17,2}*68
34-fold quotients : {12,2}*48, {6,4}*48a
51-fold quotients : {4,4}*32
68-fold quotients : {6,2}*24
102-fold quotients : {2,4}*16, {4,2}*16
136-fold quotients : {3,2}*12
204-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)( 9, 10)
( 18, 35)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)( 25, 45)
( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)( 33, 37)
( 34, 36)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)( 75, 97)
( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)
(110,113)(111,112)(120,137)(121,153)(122,152)(123,151)(124,150)(125,149)
(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)(133,141)
(134,140)(135,139)(136,138)(155,170)(156,169)(157,168)(158,167)(159,166)
(160,165)(161,164)(162,163)(171,188)(172,204)(173,203)(174,202)(175,201)
(176,200)(177,199)(178,198)(179,197)(180,196)(181,195)(182,194)(183,193)
(184,192)(185,191)(186,190)(187,189)(205,256)(206,272)(207,271)(208,270)
(209,269)(210,268)(211,267)(212,266)(213,265)(214,264)(215,263)(216,262)
(217,261)(218,260)(219,259)(220,258)(221,257)(222,290)(223,306)(224,305)
(225,304)(226,303)(227,302)(228,301)(229,300)(230,299)(231,298)(232,297)
(233,296)(234,295)(235,294)(236,293)(237,292)(238,291)(239,273)(240,289)
(241,288)(242,287)(243,286)(244,285)(245,284)(246,283)(247,282)(248,281)
(249,280)(250,279)(251,278)(252,277)(253,276)(254,275)(255,274)(307,358)
(308,374)(309,373)(310,372)(311,371)(312,370)(313,369)(314,368)(315,367)
(316,366)(317,365)(318,364)(319,363)(320,362)(321,361)(322,360)(323,359)
(324,392)(325,408)(326,407)(327,406)(328,405)(329,404)(330,403)(331,402)
(332,401)(333,400)(334,399)(335,398)(336,397)(337,396)(338,395)(339,394)
(340,393)(341,375)(342,391)(343,390)(344,389)(345,388)(346,387)(347,386)
(348,385)(349,384)(350,383)(351,382)(352,381)(353,380)(354,379)(355,378)
(356,377)(357,376);;
s1 := ( 1,223)( 2,222)( 3,238)( 4,237)( 5,236)( 6,235)( 7,234)( 8,233)
( 9,232)( 10,231)( 11,230)( 12,229)( 13,228)( 14,227)( 15,226)( 16,225)
( 17,224)( 18,206)( 19,205)( 20,221)( 21,220)( 22,219)( 23,218)( 24,217)
( 25,216)( 26,215)( 27,214)( 28,213)( 29,212)( 30,211)( 31,210)( 32,209)
( 33,208)( 34,207)( 35,240)( 36,239)( 37,255)( 38,254)( 39,253)( 40,252)
( 41,251)( 42,250)( 43,249)( 44,248)( 45,247)( 46,246)( 47,245)( 48,244)
( 49,243)( 50,242)( 51,241)( 52,274)( 53,273)( 54,289)( 55,288)( 56,287)
( 57,286)( 58,285)( 59,284)( 60,283)( 61,282)( 62,281)( 63,280)( 64,279)
( 65,278)( 66,277)( 67,276)( 68,275)( 69,257)( 70,256)( 71,272)( 72,271)
( 73,270)( 74,269)( 75,268)( 76,267)( 77,266)( 78,265)( 79,264)( 80,263)
( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,291)( 87,290)( 88,306)
( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)( 96,298)
( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,325)(104,324)
(105,340)(106,339)(107,338)(108,337)(109,336)(110,335)(111,334)(112,333)
(113,332)(114,331)(115,330)(116,329)(117,328)(118,327)(119,326)(120,308)
(121,307)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)(128,317)
(129,316)(130,315)(131,314)(132,313)(133,312)(134,311)(135,310)(136,309)
(137,342)(138,341)(139,357)(140,356)(141,355)(142,354)(143,353)(144,352)
(145,351)(146,350)(147,349)(148,348)(149,347)(150,346)(151,345)(152,344)
(153,343)(154,376)(155,375)(156,391)(157,390)(158,389)(159,388)(160,387)
(161,386)(162,385)(163,384)(164,383)(165,382)(166,381)(167,380)(168,379)
(169,378)(170,377)(171,359)(172,358)(173,374)(174,373)(175,372)(176,371)
(177,370)(178,369)(179,368)(180,367)(181,366)(182,365)(183,364)(184,363)
(185,362)(186,361)(187,360)(188,393)(189,392)(190,408)(191,407)(192,406)
(193,405)(194,404)(195,403)(196,402)(197,401)(198,400)(199,399)(200,398)
(201,397)(202,396)(203,395)(204,394);;
s2 := (205,307)(206,308)(207,309)(208,310)(209,311)(210,312)(211,313)(212,314)
(213,315)(214,316)(215,317)(216,318)(217,319)(218,320)(219,321)(220,322)
(221,323)(222,324)(223,325)(224,326)(225,327)(226,328)(227,329)(228,330)
(229,331)(230,332)(231,333)(232,334)(233,335)(234,336)(235,337)(236,338)
(237,339)(238,340)(239,341)(240,342)(241,343)(242,344)(243,345)(244,346)
(245,347)(246,348)(247,349)(248,350)(249,351)(250,352)(251,353)(252,354)
(253,355)(254,356)(255,357)(256,358)(257,359)(258,360)(259,361)(260,362)
(261,363)(262,364)(263,365)(264,366)(265,367)(266,368)(267,369)(268,370)
(269,371)(270,372)(271,373)(272,374)(273,375)(274,376)(275,377)(276,378)
(277,379)(278,380)(279,381)(280,382)(281,383)(282,384)(283,385)(284,386)
(285,387)(286,388)(287,389)(288,390)(289,391)(290,392)(291,393)(292,394)
(293,395)(294,396)(295,397)(296,398)(297,399)(298,400)(299,401)(300,402)
(301,403)(302,404)(303,405)(304,406)(305,407)(306,408);;
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, 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*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*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*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*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*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(408)!( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)
( 9, 10)( 18, 35)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)
( 25, 45)( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)
( 33, 37)( 34, 36)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)
( 59, 62)( 60, 61)( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)
( 75, 97)( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)(104,119)(105,118)(106,117)(107,116)(108,115)
(109,114)(110,113)(111,112)(120,137)(121,153)(122,152)(123,151)(124,150)
(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)
(133,141)(134,140)(135,139)(136,138)(155,170)(156,169)(157,168)(158,167)
(159,166)(160,165)(161,164)(162,163)(171,188)(172,204)(173,203)(174,202)
(175,201)(176,200)(177,199)(178,198)(179,197)(180,196)(181,195)(182,194)
(183,193)(184,192)(185,191)(186,190)(187,189)(205,256)(206,272)(207,271)
(208,270)(209,269)(210,268)(211,267)(212,266)(213,265)(214,264)(215,263)
(216,262)(217,261)(218,260)(219,259)(220,258)(221,257)(222,290)(223,306)
(224,305)(225,304)(226,303)(227,302)(228,301)(229,300)(230,299)(231,298)
(232,297)(233,296)(234,295)(235,294)(236,293)(237,292)(238,291)(239,273)
(240,289)(241,288)(242,287)(243,286)(244,285)(245,284)(246,283)(247,282)
(248,281)(249,280)(250,279)(251,278)(252,277)(253,276)(254,275)(255,274)
(307,358)(308,374)(309,373)(310,372)(311,371)(312,370)(313,369)(314,368)
(315,367)(316,366)(317,365)(318,364)(319,363)(320,362)(321,361)(322,360)
(323,359)(324,392)(325,408)(326,407)(327,406)(328,405)(329,404)(330,403)
(331,402)(332,401)(333,400)(334,399)(335,398)(336,397)(337,396)(338,395)
(339,394)(340,393)(341,375)(342,391)(343,390)(344,389)(345,388)(346,387)
(347,386)(348,385)(349,384)(350,383)(351,382)(352,381)(353,380)(354,379)
(355,378)(356,377)(357,376);
s1 := Sym(408)!( 1,223)( 2,222)( 3,238)( 4,237)( 5,236)( 6,235)( 7,234)
( 8,233)( 9,232)( 10,231)( 11,230)( 12,229)( 13,228)( 14,227)( 15,226)
( 16,225)( 17,224)( 18,206)( 19,205)( 20,221)( 21,220)( 22,219)( 23,218)
( 24,217)( 25,216)( 26,215)( 27,214)( 28,213)( 29,212)( 30,211)( 31,210)
( 32,209)( 33,208)( 34,207)( 35,240)( 36,239)( 37,255)( 38,254)( 39,253)
( 40,252)( 41,251)( 42,250)( 43,249)( 44,248)( 45,247)( 46,246)( 47,245)
( 48,244)( 49,243)( 50,242)( 51,241)( 52,274)( 53,273)( 54,289)( 55,288)
( 56,287)( 57,286)( 58,285)( 59,284)( 60,283)( 61,282)( 62,281)( 63,280)
( 64,279)( 65,278)( 66,277)( 67,276)( 68,275)( 69,257)( 70,256)( 71,272)
( 72,271)( 73,270)( 74,269)( 75,268)( 76,267)( 77,266)( 78,265)( 79,264)
( 80,263)( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,291)( 87,290)
( 88,306)( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)
( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,325)
(104,324)(105,340)(106,339)(107,338)(108,337)(109,336)(110,335)(111,334)
(112,333)(113,332)(114,331)(115,330)(116,329)(117,328)(118,327)(119,326)
(120,308)(121,307)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)
(128,317)(129,316)(130,315)(131,314)(132,313)(133,312)(134,311)(135,310)
(136,309)(137,342)(138,341)(139,357)(140,356)(141,355)(142,354)(143,353)
(144,352)(145,351)(146,350)(147,349)(148,348)(149,347)(150,346)(151,345)
(152,344)(153,343)(154,376)(155,375)(156,391)(157,390)(158,389)(159,388)
(160,387)(161,386)(162,385)(163,384)(164,383)(165,382)(166,381)(167,380)
(168,379)(169,378)(170,377)(171,359)(172,358)(173,374)(174,373)(175,372)
(176,371)(177,370)(178,369)(179,368)(180,367)(181,366)(182,365)(183,364)
(184,363)(185,362)(186,361)(187,360)(188,393)(189,392)(190,408)(191,407)
(192,406)(193,405)(194,404)(195,403)(196,402)(197,401)(198,400)(199,399)
(200,398)(201,397)(202,396)(203,395)(204,394);
s2 := Sym(408)!(205,307)(206,308)(207,309)(208,310)(209,311)(210,312)(211,313)
(212,314)(213,315)(214,316)(215,317)(216,318)(217,319)(218,320)(219,321)
(220,322)(221,323)(222,324)(223,325)(224,326)(225,327)(226,328)(227,329)
(228,330)(229,331)(230,332)(231,333)(232,334)(233,335)(234,336)(235,337)
(236,338)(237,339)(238,340)(239,341)(240,342)(241,343)(242,344)(243,345)
(244,346)(245,347)(246,348)(247,349)(248,350)(249,351)(250,352)(251,353)
(252,354)(253,355)(254,356)(255,357)(256,358)(257,359)(258,360)(259,361)
(260,362)(261,363)(262,364)(263,365)(264,366)(265,367)(266,368)(267,369)
(268,370)(269,371)(270,372)(271,373)(272,374)(273,375)(274,376)(275,377)
(276,378)(277,379)(278,380)(279,381)(280,382)(281,383)(282,384)(283,385)
(284,386)(285,387)(286,388)(287,389)(288,390)(289,391)(290,392)(291,393)
(292,394)(293,395)(294,396)(295,397)(296,398)(297,399)(298,400)(299,401)
(300,402)(301,403)(302,404)(303,405)(304,406)(305,407)(306,408);
poly := sub<Sym(408)|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, 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*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*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*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*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*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