Polytope of Type {198,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {198,4}*1584a
Also Known As : {198,4|2}. if this polytope has another name.
Group : SmallGroup(1584,156)
Rank : 3
Schlafli Type : {198,4}
Number of vertices, edges, etc : 198, 396, 4
Order of s₀s₁s₂ : 396
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   2-fold quotients : {198,2}*792
   3-fold quotients : {66,4}*528a
   4-fold quotients : {99,2}*396
   6-fold quotients : {66,2}*264
   9-fold quotients : {22,4}*176
   11-fold quotients : {18,4}*144a
   12-fold quotients : {33,2}*132
   18-fold quotients : {22,2}*88
   22-fold quotients : {18,2}*72
   33-fold quotients : {6,4}*48a
   36-fold quotients : {11,2}*44
   44-fold quotients : {9,2}*36
   66-fold quotients : {6,2}*24
   99-fold quotients : {2,4}*16
   132-fold quotients : {3,2}*12
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope