Polytope of Type {2,99,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,99,4}*1584
if this polytope has a name.
Group : SmallGroup(1584,366)
Rank : 4
Schlafli Type : {2,99,4}
Number of vertices, edges, etc : 2, 99, 198, 4
Order of s₀s₁s₂s₃ : 198
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   3-fold quotients : {2,33,4}*528
   11-fold quotients : {2,9,4}*144
   33-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15,123)( 16,125)( 17,124)
( 18,126)( 19,131)( 20,133)( 21,132)( 22,134)( 23,127)( 24,129)( 25,128)
( 26,130)( 27,111)( 28,113)( 29,112)( 30,114)( 31,119)( 32,121)( 33,120)
( 34,122)( 35,115)( 36,117)( 37,116)( 38,118)( 39, 99)( 40,101)( 41,100)
( 42,102)( 43,107)( 44,109)( 45,108)( 46,110)( 47,103)( 48,105)( 49,104)
( 50,106)( 51, 87)( 52, 89)( 53, 88)( 54, 90)( 55, 95)( 56, 97)( 57, 96)
( 58, 98)( 59, 91)( 60, 93)( 61, 92)( 62, 94)( 63, 75)( 64, 77)( 65, 76)
( 66, 78)( 67, 83)( 68, 85)( 69, 84)( 70, 86)( 71, 79)( 72, 81)( 73, 80)
( 74, 82)(135,271)(136,273)(137,272)(138,274)(139,267)(140,269)(141,268)
(142,270)(143,275)(144,277)(145,276)(146,278)(147,391)(148,393)(149,392)
(150,394)(151,387)(152,389)(153,388)(154,390)(155,395)(156,397)(157,396)
(158,398)(159,379)(160,381)(161,380)(162,382)(163,375)(164,377)(165,376)
(166,378)(167,383)(168,385)(169,384)(170,386)(171,367)(172,369)(173,368)
(174,370)(175,363)(176,365)(177,364)(178,366)(179,371)(180,373)(181,372)
(182,374)(183,355)(184,357)(185,356)(186,358)(187,351)(188,353)(189,352)
(190,354)(191,359)(192,361)(193,360)(194,362)(195,343)(196,345)(197,344)
(198,346)(199,339)(200,341)(201,340)(202,342)(203,347)(204,349)(205,348)
(206,350)(207,331)(208,333)(209,332)(210,334)(211,327)(212,329)(213,328)
(214,330)(215,335)(216,337)(217,336)(218,338)(219,319)(220,321)(221,320)
(222,322)(223,315)(224,317)(225,316)(226,318)(227,323)(228,325)(229,324)
(230,326)(231,307)(232,309)(233,308)(234,310)(235,303)(236,305)(237,304)
(238,306)(239,311)(240,313)(241,312)(242,314)(243,295)(244,297)(245,296)
(246,298)(247,291)(248,293)(249,292)(250,294)(251,299)(252,301)(253,300)
(254,302)(255,283)(256,285)(257,284)(258,286)(259,279)(260,281)(261,280)
(262,282)(263,287)(264,289)(265,288)(266,290);;
s2 := (  3,147)(  4,148)(  5,150)(  6,149)(  7,155)(  8,156)(  9,158)( 10,157)
( 11,151)( 12,152)( 13,154)( 14,153)( 15,135)( 16,136)( 17,138)( 18,137)
( 19,143)( 20,144)( 21,146)( 22,145)( 23,139)( 24,140)( 25,142)( 26,141)
( 27,255)( 28,256)( 29,258)( 30,257)( 31,263)( 32,264)( 33,266)( 34,265)
( 35,259)( 36,260)( 37,262)( 38,261)( 39,243)( 40,244)( 41,246)( 42,245)
( 43,251)( 44,252)( 45,254)( 46,253)( 47,247)( 48,248)( 49,250)( 50,249)
( 51,231)( 52,232)( 53,234)( 54,233)( 55,239)( 56,240)( 57,242)( 58,241)
( 59,235)( 60,236)( 61,238)( 62,237)( 63,219)( 64,220)( 65,222)( 66,221)
( 67,227)( 68,228)( 69,230)( 70,229)( 71,223)( 72,224)( 73,226)( 74,225)
( 75,207)( 76,208)( 77,210)( 78,209)( 79,215)( 80,216)( 81,218)( 82,217)
( 83,211)( 84,212)( 85,214)( 86,213)( 87,195)( 88,196)( 89,198)( 90,197)
( 91,203)( 92,204)( 93,206)( 94,205)( 95,199)( 96,200)( 97,202)( 98,201)
( 99,183)(100,184)(101,186)(102,185)(103,191)(104,192)(105,194)(106,193)
(107,187)(108,188)(109,190)(110,189)(111,171)(112,172)(113,174)(114,173)
(115,179)(116,180)(117,182)(118,181)(119,175)(120,176)(121,178)(122,177)
(123,159)(124,160)(125,162)(126,161)(127,167)(128,168)(129,170)(130,169)
(131,163)(132,164)(133,166)(134,165)(267,283)(268,284)(269,286)(270,285)
(271,279)(272,280)(273,282)(274,281)(275,287)(276,288)(277,290)(278,289)
(291,391)(292,392)(293,394)(294,393)(295,387)(296,388)(297,390)(298,389)
(299,395)(300,396)(301,398)(302,397)(303,379)(304,380)(305,382)(306,381)
(307,375)(308,376)(309,378)(310,377)(311,383)(312,384)(313,386)(314,385)
(315,367)(316,368)(317,370)(318,369)(319,363)(320,364)(321,366)(322,365)
(323,371)(324,372)(325,374)(326,373)(327,355)(328,356)(329,358)(330,357)
(331,351)(332,352)(333,354)(334,353)(335,359)(336,360)(337,362)(338,361)
(339,343)(340,344)(341,346)(342,345)(349,350);;
s3 := (  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)
(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145)
(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)(160,161)
(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)(176,177)
(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)(192,193)
(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)(208,209)
(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)(224,225)
(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)(240,241)
(243,246)(244,245)(247,250)(248,249)(251,254)(252,253)(255,258)(256,257)
(259,262)(260,261)(263,266)(264,265)(267,270)(268,269)(271,274)(272,273)
(275,278)(276,277)(279,282)(280,281)(283,286)(284,285)(287,290)(288,289)
(291,294)(292,293)(295,298)(296,297)(299,302)(300,301)(303,306)(304,305)
(307,310)(308,309)(311,314)(312,313)(315,318)(316,317)(319,322)(320,321)
(323,326)(324,325)(327,330)(328,329)(331,334)(332,333)(335,338)(336,337)
(339,342)(340,341)(343,346)(344,345)(347,350)(348,349)(351,354)(352,353)
(355,358)(356,357)(359,362)(360,361)(363,366)(364,365)(367,370)(368,369)
(371,374)(372,373)(375,378)(376,377)(379,382)(380,381)(383,386)(384,385)
(387,390)(388,389)(391,394)(392,393)(395,398)(396,397);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*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*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*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(398)!(1,2);
s1 := Sym(398)!(  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15,123)( 16,125)
( 17,124)( 18,126)( 19,131)( 20,133)( 21,132)( 22,134)( 23,127)( 24,129)
( 25,128)( 26,130)( 27,111)( 28,113)( 29,112)( 30,114)( 31,119)( 32,121)
( 33,120)( 34,122)( 35,115)( 36,117)( 37,116)( 38,118)( 39, 99)( 40,101)
( 41,100)( 42,102)( 43,107)( 44,109)( 45,108)( 46,110)( 47,103)( 48,105)
( 49,104)( 50,106)( 51, 87)( 52, 89)( 53, 88)( 54, 90)( 55, 95)( 56, 97)
( 57, 96)( 58, 98)( 59, 91)( 60, 93)( 61, 92)( 62, 94)( 63, 75)( 64, 77)
( 65, 76)( 66, 78)( 67, 83)( 68, 85)( 69, 84)( 70, 86)( 71, 79)( 72, 81)
( 73, 80)( 74, 82)(135,271)(136,273)(137,272)(138,274)(139,267)(140,269)
(141,268)(142,270)(143,275)(144,277)(145,276)(146,278)(147,391)(148,393)
(149,392)(150,394)(151,387)(152,389)(153,388)(154,390)(155,395)(156,397)
(157,396)(158,398)(159,379)(160,381)(161,380)(162,382)(163,375)(164,377)
(165,376)(166,378)(167,383)(168,385)(169,384)(170,386)(171,367)(172,369)
(173,368)(174,370)(175,363)(176,365)(177,364)(178,366)(179,371)(180,373)
(181,372)(182,374)(183,355)(184,357)(185,356)(186,358)(187,351)(188,353)
(189,352)(190,354)(191,359)(192,361)(193,360)(194,362)(195,343)(196,345)
(197,344)(198,346)(199,339)(200,341)(201,340)(202,342)(203,347)(204,349)
(205,348)(206,350)(207,331)(208,333)(209,332)(210,334)(211,327)(212,329)
(213,328)(214,330)(215,335)(216,337)(217,336)(218,338)(219,319)(220,321)
(221,320)(222,322)(223,315)(224,317)(225,316)(226,318)(227,323)(228,325)
(229,324)(230,326)(231,307)(232,309)(233,308)(234,310)(235,303)(236,305)
(237,304)(238,306)(239,311)(240,313)(241,312)(242,314)(243,295)(244,297)
(245,296)(246,298)(247,291)(248,293)(249,292)(250,294)(251,299)(252,301)
(253,300)(254,302)(255,283)(256,285)(257,284)(258,286)(259,279)(260,281)
(261,280)(262,282)(263,287)(264,289)(265,288)(266,290);
s2 := Sym(398)!(  3,147)(  4,148)(  5,150)(  6,149)(  7,155)(  8,156)(  9,158)
( 10,157)( 11,151)( 12,152)( 13,154)( 14,153)( 15,135)( 16,136)( 17,138)
( 18,137)( 19,143)( 20,144)( 21,146)( 22,145)( 23,139)( 24,140)( 25,142)
( 26,141)( 27,255)( 28,256)( 29,258)( 30,257)( 31,263)( 32,264)( 33,266)
( 34,265)( 35,259)( 36,260)( 37,262)( 38,261)( 39,243)( 40,244)( 41,246)
( 42,245)( 43,251)( 44,252)( 45,254)( 46,253)( 47,247)( 48,248)( 49,250)
( 50,249)( 51,231)( 52,232)( 53,234)( 54,233)( 55,239)( 56,240)( 57,242)
( 58,241)( 59,235)( 60,236)( 61,238)( 62,237)( 63,219)( 64,220)( 65,222)
( 66,221)( 67,227)( 68,228)( 69,230)( 70,229)( 71,223)( 72,224)( 73,226)
( 74,225)( 75,207)( 76,208)( 77,210)( 78,209)( 79,215)( 80,216)( 81,218)
( 82,217)( 83,211)( 84,212)( 85,214)( 86,213)( 87,195)( 88,196)( 89,198)
( 90,197)( 91,203)( 92,204)( 93,206)( 94,205)( 95,199)( 96,200)( 97,202)
( 98,201)( 99,183)(100,184)(101,186)(102,185)(103,191)(104,192)(105,194)
(106,193)(107,187)(108,188)(109,190)(110,189)(111,171)(112,172)(113,174)
(114,173)(115,179)(116,180)(117,182)(118,181)(119,175)(120,176)(121,178)
(122,177)(123,159)(124,160)(125,162)(126,161)(127,167)(128,168)(129,170)
(130,169)(131,163)(132,164)(133,166)(134,165)(267,283)(268,284)(269,286)
(270,285)(271,279)(272,280)(273,282)(274,281)(275,287)(276,288)(277,290)
(278,289)(291,391)(292,392)(293,394)(294,393)(295,387)(296,388)(297,390)
(298,389)(299,395)(300,396)(301,398)(302,397)(303,379)(304,380)(305,382)
(306,381)(307,375)(308,376)(309,378)(310,377)(311,383)(312,384)(313,386)
(314,385)(315,367)(316,368)(317,370)(318,369)(319,363)(320,364)(321,366)
(322,365)(323,371)(324,372)(325,374)(326,373)(327,355)(328,356)(329,358)
(330,357)(331,351)(332,352)(333,354)(334,353)(335,359)(336,360)(337,362)
(338,361)(339,343)(340,344)(341,346)(342,345)(349,350);
s3 := Sym(398)!(  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)
(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)
(144,145)(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)
(160,161)(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)
(176,177)(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)
(192,193)(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)
(208,209)(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)
(224,225)(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)
(240,241)(243,246)(244,245)(247,250)(248,249)(251,254)(252,253)(255,258)
(256,257)(259,262)(260,261)(263,266)(264,265)(267,270)(268,269)(271,274)
(272,273)(275,278)(276,277)(279,282)(280,281)(283,286)(284,285)(287,290)
(288,289)(291,294)(292,293)(295,298)(296,297)(299,302)(300,301)(303,306)
(304,305)(307,310)(308,309)(311,314)(312,313)(315,318)(316,317)(319,322)
(320,321)(323,326)(324,325)(327,330)(328,329)(331,334)(332,333)(335,338)
(336,337)(339,342)(340,341)(343,346)(344,345)(347,350)(348,349)(351,354)
(352,353)(355,358)(356,357)(359,362)(360,361)(363,366)(364,365)(367,370)
(368,369)(371,374)(372,373)(375,378)(376,377)(379,382)(380,381)(383,386)
(384,385)(387,390)(388,389)(391,394)(392,393)(395,398)(396,397);
poly := sub<Sym(398)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*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*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*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*s1*s2*s1*s2 >;

to this polytope