Polytope of Type {99,4,2}

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

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

to this polytope