Polytope of Type {196,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {196,4}*1568
Also Known As : {196,4|2}. if this polytope has another name.
Group : SmallGroup(1568,78)
Rank : 3
Schlafli Type : {196,4}
Number of vertices, edges, etc : 196, 392, 4
Order of s₀s₁s₂ : 196
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 : {196,2}*784, {98,4}*784
   4-fold quotients : {98,2}*392
   7-fold quotients : {28,4}*224
   8-fold quotients : {49,2}*196
   14-fold quotients : {28,2}*112, {14,4}*112
   28-fold quotients : {14,2}*56
   49-fold quotients : {4,4}*32
   56-fold quotients : {7,2}*28
   98-fold quotients : {2,4}*16, {4,2}*16
   196-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope