Polytope of Type {6,118}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,118}*1416
Also Known As : {6,118|2}. if this polytope has another name.
Group : SmallGroup(1416,34)
Rank : 3
Schlafli Type : {6,118}
Number of vertices, edges, etc : 6, 354, 118
Order of s₀s₁s₂ : 354
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) :
   3-fold quotients : {2,118}*472
   6-fold quotients : {2,59}*236
   59-fold quotients : {6,2}*24
   118-fold quotients : {3,2}*12
   177-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope