Polytope of Type {2,4,99}

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

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

to this polytope