Polytope of Type {200,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {200,4}*1600a
Also Known As : {200,4|2}. if this polytope has another name.
Group : SmallGroup(1600,361)
Rank : 3
Schlafli Type : {200,4}
Number of vertices, edges, etc : 200, 400, 4
Order of s₀s₁s₂ : 200
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 : {100,4}*800, {200,2}*800
   4-fold quotients : {100,2}*400, {50,4}*400
   5-fold quotients : {40,4}*320a
   8-fold quotients : {50,2}*200
   10-fold quotients : {20,4}*160, {40,2}*160
   16-fold quotients : {25,2}*100
   20-fold quotients : {20,2}*80, {10,4}*80
   25-fold quotients : {8,4}*64a
   40-fold quotients : {10,2}*40
   50-fold quotients : {4,4}*32, {8,2}*32
   80-fold quotients : {5,2}*20
   100-fold quotients : {2,4}*16, {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)( 32, 49)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)
( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,100)( 57, 99)( 58, 98)
( 59, 97)( 60, 96)( 61, 95)( 62, 94)( 63, 93)( 64, 92)( 65, 91)( 66, 90)
( 67, 89)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)
( 75, 81)(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)
(111,120)(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)
(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)
(140,141)(151,176)(152,180)(153,179)(154,178)(155,177)(156,200)(157,199)
(158,198)(159,197)(160,196)(161,195)(162,194)(163,193)(164,192)(165,191)
(166,190)(167,189)(168,188)(169,187)(170,186)(171,185)(172,184)(173,183)
(174,182)(175,181)(201,251)(202,255)(203,254)(204,253)(205,252)(206,275)
(207,274)(208,273)(209,272)(210,271)(211,270)(212,269)(213,268)(214,267)
(215,266)(216,265)(217,264)(218,263)(219,262)(220,261)(221,260)(222,259)
(223,258)(224,257)(225,256)(226,276)(227,280)(228,279)(229,278)(230,277)
(231,300)(232,299)(233,298)(234,297)(235,296)(236,295)(237,294)(238,293)
(239,292)(240,291)(241,290)(242,289)(243,288)(244,287)(245,286)(246,285)
(247,284)(248,283)(249,282)(250,281)(301,351)(302,355)(303,354)(304,353)
(305,352)(306,375)(307,374)(308,373)(309,372)(310,371)(311,370)(312,369)
(313,368)(314,367)(315,366)(316,365)(317,364)(318,363)(319,362)(320,361)
(321,360)(322,359)(323,358)(324,357)(325,356)(326,376)(327,380)(328,379)
(329,378)(330,377)(331,400)(332,399)(333,398)(334,397)(335,396)(336,395)
(337,394)(338,393)(339,392)(340,391)(341,390)(342,389)(343,388)(344,387)
(345,386)(346,385)(347,384)(348,383)(349,382)(350,381);;
s1 := (  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)(  8,204)
(  9,203)( 10,202)( 11,225)( 12,224)( 13,223)( 14,222)( 15,221)( 16,220)
( 17,219)( 18,218)( 19,217)( 20,216)( 21,215)( 22,214)( 23,213)( 24,212)
( 25,211)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)( 32,230)
( 33,229)( 34,228)( 35,227)( 36,250)( 37,249)( 38,248)( 39,247)( 40,246)
( 41,245)( 42,244)( 43,243)( 44,242)( 45,241)( 46,240)( 47,239)( 48,238)
( 49,237)( 50,236)( 51,281)( 52,285)( 53,284)( 54,283)( 55,282)( 56,276)
( 57,280)( 58,279)( 59,278)( 60,277)( 61,300)( 62,299)( 63,298)( 64,297)
( 65,296)( 66,295)( 67,294)( 68,293)( 69,292)( 70,291)( 71,290)( 72,289)
( 73,288)( 74,287)( 75,286)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,275)( 87,274)( 88,273)
( 89,272)( 90,271)( 91,270)( 92,269)( 93,268)( 94,267)( 95,266)( 96,265)
( 97,264)( 98,263)( 99,262)(100,261)(101,306)(102,310)(103,309)(104,308)
(105,307)(106,301)(107,305)(108,304)(109,303)(110,302)(111,325)(112,324)
(113,323)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)(120,316)
(121,315)(122,314)(123,313)(124,312)(125,311)(126,331)(127,335)(128,334)
(129,333)(130,332)(131,326)(132,330)(133,329)(134,328)(135,327)(136,350)
(137,349)(138,348)(139,347)(140,346)(141,345)(142,344)(143,343)(144,342)
(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,381)(152,385)
(153,384)(154,383)(155,382)(156,376)(157,380)(158,379)(159,378)(160,377)
(161,400)(162,399)(163,398)(164,397)(165,396)(166,395)(167,394)(168,393)
(169,392)(170,391)(171,390)(172,389)(173,388)(174,387)(175,386)(176,356)
(177,360)(178,359)(179,358)(180,357)(181,351)(182,355)(183,354)(184,353)
(185,352)(186,375)(187,374)(188,373)(189,372)(190,371)(191,370)(192,369)
(193,368)(194,367)(195,366)(196,365)(197,364)(198,363)(199,362)(200,361);;
s2 := (201,301)(202,302)(203,303)(204,304)(205,305)(206,306)(207,307)(208,308)
(209,309)(210,310)(211,311)(212,312)(213,313)(214,314)(215,315)(216,316)
(217,317)(218,318)(219,319)(220,320)(221,321)(222,322)(223,323)(224,324)
(225,325)(226,326)(227,327)(228,328)(229,329)(230,330)(231,331)(232,332)
(233,333)(234,334)(235,335)(236,336)(237,337)(238,338)(239,339)(240,340)
(241,341)(242,342)(243,343)(244,344)(245,345)(246,346)(247,347)(248,348)
(249,349)(250,350)(251,351)(252,352)(253,353)(254,354)(255,355)(256,356)
(257,357)(258,358)(259,359)(260,360)(261,361)(262,362)(263,363)(264,364)
(265,365)(266,366)(267,367)(268,368)(269,369)(270,370)(271,371)(272,372)
(273,373)(274,374)(275,375)(276,376)(277,377)(278,378)(279,379)(280,380)
(281,381)(282,382)(283,383)(284,384)(285,385)(286,386)(287,387)(288,388)
(289,389)(290,390)(291,391)(292,392)(293,393)(294,394)(295,395)(296,396)
(297,397)(298,398)(299,399)(300,400);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(400)!(  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)
( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 40, 41)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,100)( 57, 99)
( 58, 98)( 59, 97)( 60, 96)( 61, 95)( 62, 94)( 63, 93)( 64, 92)( 65, 91)
( 66, 90)( 67, 89)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)
( 74, 82)( 75, 81)(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)
(110,121)(111,120)(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)
(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)
(139,142)(140,141)(151,176)(152,180)(153,179)(154,178)(155,177)(156,200)
(157,199)(158,198)(159,197)(160,196)(161,195)(162,194)(163,193)(164,192)
(165,191)(166,190)(167,189)(168,188)(169,187)(170,186)(171,185)(172,184)
(173,183)(174,182)(175,181)(201,251)(202,255)(203,254)(204,253)(205,252)
(206,275)(207,274)(208,273)(209,272)(210,271)(211,270)(212,269)(213,268)
(214,267)(215,266)(216,265)(217,264)(218,263)(219,262)(220,261)(221,260)
(222,259)(223,258)(224,257)(225,256)(226,276)(227,280)(228,279)(229,278)
(230,277)(231,300)(232,299)(233,298)(234,297)(235,296)(236,295)(237,294)
(238,293)(239,292)(240,291)(241,290)(242,289)(243,288)(244,287)(245,286)
(246,285)(247,284)(248,283)(249,282)(250,281)(301,351)(302,355)(303,354)
(304,353)(305,352)(306,375)(307,374)(308,373)(309,372)(310,371)(311,370)
(312,369)(313,368)(314,367)(315,366)(316,365)(317,364)(318,363)(319,362)
(320,361)(321,360)(322,359)(323,358)(324,357)(325,356)(326,376)(327,380)
(328,379)(329,378)(330,377)(331,400)(332,399)(333,398)(334,397)(335,396)
(336,395)(337,394)(338,393)(339,392)(340,391)(341,390)(342,389)(343,388)
(344,387)(345,386)(346,385)(347,384)(348,383)(349,382)(350,381);
s1 := Sym(400)!(  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)
(  8,204)(  9,203)( 10,202)( 11,225)( 12,224)( 13,223)( 14,222)( 15,221)
( 16,220)( 17,219)( 18,218)( 19,217)( 20,216)( 21,215)( 22,214)( 23,213)
( 24,212)( 25,211)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)
( 32,230)( 33,229)( 34,228)( 35,227)( 36,250)( 37,249)( 38,248)( 39,247)
( 40,246)( 41,245)( 42,244)( 43,243)( 44,242)( 45,241)( 46,240)( 47,239)
( 48,238)( 49,237)( 50,236)( 51,281)( 52,285)( 53,284)( 54,283)( 55,282)
( 56,276)( 57,280)( 58,279)( 59,278)( 60,277)( 61,300)( 62,299)( 63,298)
( 64,297)( 65,296)( 66,295)( 67,294)( 68,293)( 69,292)( 70,291)( 71,290)
( 72,289)( 73,288)( 74,287)( 75,286)( 76,256)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,275)( 87,274)
( 88,273)( 89,272)( 90,271)( 91,270)( 92,269)( 93,268)( 94,267)( 95,266)
( 96,265)( 97,264)( 98,263)( 99,262)(100,261)(101,306)(102,310)(103,309)
(104,308)(105,307)(106,301)(107,305)(108,304)(109,303)(110,302)(111,325)
(112,324)(113,323)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)
(120,316)(121,315)(122,314)(123,313)(124,312)(125,311)(126,331)(127,335)
(128,334)(129,333)(130,332)(131,326)(132,330)(133,329)(134,328)(135,327)
(136,350)(137,349)(138,348)(139,347)(140,346)(141,345)(142,344)(143,343)
(144,342)(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,381)
(152,385)(153,384)(154,383)(155,382)(156,376)(157,380)(158,379)(159,378)
(160,377)(161,400)(162,399)(163,398)(164,397)(165,396)(166,395)(167,394)
(168,393)(169,392)(170,391)(171,390)(172,389)(173,388)(174,387)(175,386)
(176,356)(177,360)(178,359)(179,358)(180,357)(181,351)(182,355)(183,354)
(184,353)(185,352)(186,375)(187,374)(188,373)(189,372)(190,371)(191,370)
(192,369)(193,368)(194,367)(195,366)(196,365)(197,364)(198,363)(199,362)
(200,361);
s2 := Sym(400)!(201,301)(202,302)(203,303)(204,304)(205,305)(206,306)(207,307)
(208,308)(209,309)(210,310)(211,311)(212,312)(213,313)(214,314)(215,315)
(216,316)(217,317)(218,318)(219,319)(220,320)(221,321)(222,322)(223,323)
(224,324)(225,325)(226,326)(227,327)(228,328)(229,329)(230,330)(231,331)
(232,332)(233,333)(234,334)(235,335)(236,336)(237,337)(238,338)(239,339)
(240,340)(241,341)(242,342)(243,343)(244,344)(245,345)(246,346)(247,347)
(248,348)(249,349)(250,350)(251,351)(252,352)(253,353)(254,354)(255,355)
(256,356)(257,357)(258,358)(259,359)(260,360)(261,361)(262,362)(263,363)
(264,364)(265,365)(266,366)(267,367)(268,368)(269,369)(270,370)(271,371)
(272,372)(273,373)(274,374)(275,375)(276,376)(277,377)(278,378)(279,379)
(280,380)(281,381)(282,382)(283,383)(284,384)(285,385)(286,386)(287,387)
(288,388)(289,389)(290,390)(291,391)(292,392)(293,393)(294,394)(295,395)
(296,396)(297,397)(298,398)(299,399)(300,400);
poly := sub<Sym(400)|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 >;

References : None.
to this polytope