Polytope of Type {4,196}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,196}*1568
Also Known As : {4,196|2}. if this polytope has another name.
Group : SmallGroup(1568,78)
Rank : 3
Schlafli Type : {4,196}
Number of vertices, edges, etc : 4, 392, 196
Order of s₀s₁s₂ : 196
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 : {2,196}*784, {4,98}*784
   4-fold quotients : {2,98}*392
   7-fold quotients : {4,28}*224
   8-fold quotients : {2,49}*196
   14-fold quotients : {2,28}*112, {4,14}*112
   28-fold quotients : {2,14}*56
   49-fold quotients : {4,4}*32
   56-fold quotients : {2,7}*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 := (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);;
s1 := (  1,197)(  2,203)(  3,202)(  4,201)(  5,200)(  6,199)(  7,198)(  8,245)
(  9,244)( 10,243)( 11,242)( 12,241)( 13,240)( 14,239)( 15,238)( 16,237)
( 17,236)( 18,235)( 19,234)( 20,233)( 21,232)( 22,231)( 23,230)( 24,229)
( 25,228)( 26,227)( 27,226)( 28,225)( 29,224)( 30,223)( 31,222)( 32,221)
( 33,220)( 34,219)( 35,218)( 36,217)( 37,216)( 38,215)( 39,214)( 40,213)
( 41,212)( 42,211)( 43,210)( 44,209)( 45,208)( 46,207)( 47,206)( 48,205)
( 49,204)( 50,246)( 51,252)( 52,251)( 53,250)( 54,249)( 55,248)( 56,247)
( 57,294)( 58,293)( 59,292)( 60,291)( 61,290)( 62,289)( 63,288)( 64,287)
( 65,286)( 66,285)( 67,284)( 68,283)( 69,282)( 70,281)( 71,280)( 72,279)
( 73,278)( 74,277)( 75,276)( 76,275)( 77,274)( 78,273)( 79,272)( 80,271)
( 81,270)( 82,269)( 83,268)( 84,267)( 85,266)( 86,265)( 87,264)( 88,263)
( 89,262)( 90,261)( 91,260)( 92,259)( 93,258)( 94,257)( 95,256)( 96,255)
( 97,254)( 98,253)( 99,295)(100,301)(101,300)(102,299)(103,298)(104,297)
(105,296)(106,343)(107,342)(108,341)(109,340)(110,339)(111,338)(112,337)
(113,336)(114,335)(115,334)(116,333)(117,332)(118,331)(119,330)(120,329)
(121,328)(122,327)(123,326)(124,325)(125,324)(126,323)(127,322)(128,321)
(129,320)(130,319)(131,318)(132,317)(133,316)(134,315)(135,314)(136,313)
(137,312)(138,311)(139,310)(140,309)(141,308)(142,307)(143,306)(144,305)
(145,304)(146,303)(147,302)(148,344)(149,350)(150,349)(151,348)(152,347)
(153,346)(154,345)(155,392)(156,391)(157,390)(158,389)(159,388)(160,387)
(161,386)(162,385)(163,384)(164,383)(165,382)(166,381)(167,380)(168,379)
(169,378)(170,377)(171,376)(172,375)(173,374)(174,373)(175,372)(176,371)
(177,370)(178,369)(179,368)(180,367)(181,366)(182,365)(183,364)(184,363)
(185,362)(186,361)(187,360)(188,359)(189,358)(190,357)(191,356)(192,355)
(193,354)(194,353)(195,352)(196,351);;
s2 := (  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 49)
( 16, 48)( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)
( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)
( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 98)
( 65, 97)( 66, 96)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 91)( 72, 90)
( 73, 89)( 74, 88)( 75, 87)( 76, 86)( 77, 85)( 78, 84)( 79, 83)( 80, 82)
( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,147)
(114,146)(115,145)(116,144)(117,143)(118,142)(119,141)(120,140)(121,139)
(122,138)(123,137)(124,136)(125,135)(126,134)(127,133)(128,132)(129,131)
(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(162,196)
(163,195)(164,194)(165,193)(166,192)(167,191)(168,190)(169,189)(170,188)
(171,187)(172,186)(173,185)(174,184)(175,183)(176,182)(177,181)(178,180)
(197,253)(198,259)(199,258)(200,257)(201,256)(202,255)(203,254)(204,246)
(205,252)(206,251)(207,250)(208,249)(209,248)(210,247)(211,294)(212,293)
(213,292)(214,291)(215,290)(216,289)(217,288)(218,287)(219,286)(220,285)
(221,284)(222,283)(223,282)(224,281)(225,280)(226,279)(227,278)(228,277)
(229,276)(230,275)(231,274)(232,273)(233,272)(234,271)(235,270)(236,269)
(237,268)(238,267)(239,266)(240,265)(241,264)(242,263)(243,262)(244,261)
(245,260)(295,351)(296,357)(297,356)(298,355)(299,354)(300,353)(301,352)
(302,344)(303,350)(304,349)(305,348)(306,347)(307,346)(308,345)(309,392)
(310,391)(311,390)(312,389)(313,388)(314,387)(315,386)(316,385)(317,384)
(318,383)(319,382)(320,381)(321,380)(322,379)(323,378)(324,377)(325,376)
(326,375)(327,374)(328,373)(329,372)(330,371)(331,370)(332,369)(333,368)
(334,367)(335,366)(336,365)(337,364)(338,363)(339,362)(340,361)(341,360)
(342,359)(343,358);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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*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(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);
s1 := Sym(392)!(  1,197)(  2,203)(  3,202)(  4,201)(  5,200)(  6,199)(  7,198)
(  8,245)(  9,244)( 10,243)( 11,242)( 12,241)( 13,240)( 14,239)( 15,238)
( 16,237)( 17,236)( 18,235)( 19,234)( 20,233)( 21,232)( 22,231)( 23,230)
( 24,229)( 25,228)( 26,227)( 27,226)( 28,225)( 29,224)( 30,223)( 31,222)
( 32,221)( 33,220)( 34,219)( 35,218)( 36,217)( 37,216)( 38,215)( 39,214)
( 40,213)( 41,212)( 42,211)( 43,210)( 44,209)( 45,208)( 46,207)( 47,206)
( 48,205)( 49,204)( 50,246)( 51,252)( 52,251)( 53,250)( 54,249)( 55,248)
( 56,247)( 57,294)( 58,293)( 59,292)( 60,291)( 61,290)( 62,289)( 63,288)
( 64,287)( 65,286)( 66,285)( 67,284)( 68,283)( 69,282)( 70,281)( 71,280)
( 72,279)( 73,278)( 74,277)( 75,276)( 76,275)( 77,274)( 78,273)( 79,272)
( 80,271)( 81,270)( 82,269)( 83,268)( 84,267)( 85,266)( 86,265)( 87,264)
( 88,263)( 89,262)( 90,261)( 91,260)( 92,259)( 93,258)( 94,257)( 95,256)
( 96,255)( 97,254)( 98,253)( 99,295)(100,301)(101,300)(102,299)(103,298)
(104,297)(105,296)(106,343)(107,342)(108,341)(109,340)(110,339)(111,338)
(112,337)(113,336)(114,335)(115,334)(116,333)(117,332)(118,331)(119,330)
(120,329)(121,328)(122,327)(123,326)(124,325)(125,324)(126,323)(127,322)
(128,321)(129,320)(130,319)(131,318)(132,317)(133,316)(134,315)(135,314)
(136,313)(137,312)(138,311)(139,310)(140,309)(141,308)(142,307)(143,306)
(144,305)(145,304)(146,303)(147,302)(148,344)(149,350)(150,349)(151,348)
(152,347)(153,346)(154,345)(155,392)(156,391)(157,390)(158,389)(159,388)
(160,387)(161,386)(162,385)(163,384)(164,383)(165,382)(166,381)(167,380)
(168,379)(169,378)(170,377)(171,376)(172,375)(173,374)(174,373)(175,372)
(176,371)(177,370)(178,369)(179,368)(180,367)(181,366)(182,365)(183,364)
(184,363)(185,362)(186,361)(187,360)(188,359)(189,358)(190,357)(191,356)
(192,355)(193,354)(194,353)(195,352)(196,351);
s2 := Sym(392)!(  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)
( 15, 49)( 16, 48)( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)
( 23, 41)( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)
( 31, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)
( 64, 98)( 65, 97)( 66, 96)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 91)
( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 76, 86)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(113,147)(114,146)(115,145)(116,144)(117,143)(118,142)(119,141)(120,140)
(121,139)(122,138)(123,137)(124,136)(125,135)(126,134)(127,133)(128,132)
(129,131)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)
(162,196)(163,195)(164,194)(165,193)(166,192)(167,191)(168,190)(169,189)
(170,188)(171,187)(172,186)(173,185)(174,184)(175,183)(176,182)(177,181)
(178,180)(197,253)(198,259)(199,258)(200,257)(201,256)(202,255)(203,254)
(204,246)(205,252)(206,251)(207,250)(208,249)(209,248)(210,247)(211,294)
(212,293)(213,292)(214,291)(215,290)(216,289)(217,288)(218,287)(219,286)
(220,285)(221,284)(222,283)(223,282)(224,281)(225,280)(226,279)(227,278)
(228,277)(229,276)(230,275)(231,274)(232,273)(233,272)(234,271)(235,270)
(236,269)(237,268)(238,267)(239,266)(240,265)(241,264)(242,263)(243,262)
(244,261)(245,260)(295,351)(296,357)(297,356)(298,355)(299,354)(300,353)
(301,352)(302,344)(303,350)(304,349)(305,348)(306,347)(307,346)(308,345)
(309,392)(310,391)(311,390)(312,389)(313,388)(314,387)(315,386)(316,385)
(317,384)(318,383)(319,382)(320,381)(321,380)(322,379)(323,378)(324,377)
(325,376)(326,375)(327,374)(328,373)(329,372)(330,371)(331,370)(332,369)
(333,368)(334,367)(335,366)(336,365)(337,364)(338,363)(339,362)(340,361)
(341,360)(342,359)(343,358);
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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*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 >;

References : None.
to this polytope