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Polytope of Type {6,122}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,122}*1464
Also Known As : {6,122|2}. if this polytope has another name.
Group : SmallGroup(1464,54)
Rank : 3
Schlafli Type : {6,122}
Number of vertices, edges, etc : 6, 366, 122
Order of s0s1s2 : 366
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 : {2,122}*488
   6-fold quotients : {2,61}*244
   61-fold quotients : {6,2}*24
   122-fold quotients : {3,2}*12
   183-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 62,123)( 63,124)( 64,125)( 65,126)( 66,127)( 67,128)( 68,129)( 69,130)
( 70,131)( 71,132)( 72,133)( 73,134)( 74,135)( 75,136)( 76,137)( 77,138)
( 78,139)( 79,140)( 80,141)( 81,142)( 82,143)( 83,144)( 84,145)( 85,146)
( 86,147)( 87,148)( 88,149)( 89,150)( 90,151)( 91,152)( 92,153)( 93,154)
( 94,155)( 95,156)( 96,157)( 97,158)( 98,159)( 99,160)(100,161)(101,162)
(102,163)(103,164)(104,165)(105,166)(106,167)(107,168)(108,169)(109,170)
(110,171)(111,172)(112,173)(113,174)(114,175)(115,176)(116,177)(117,178)
(118,179)(119,180)(120,181)(121,182)(122,183)(245,306)(246,307)(247,308)
(248,309)(249,310)(250,311)(251,312)(252,313)(253,314)(254,315)(255,316)
(256,317)(257,318)(258,319)(259,320)(260,321)(261,322)(262,323)(263,324)
(264,325)(265,326)(266,327)(267,328)(268,329)(269,330)(270,331)(271,332)
(272,333)(273,334)(274,335)(275,336)(276,337)(277,338)(278,339)(279,340)
(280,341)(281,342)(282,343)(283,344)(284,345)(285,346)(286,347)(287,348)
(288,349)(289,350)(290,351)(291,352)(292,353)(293,354)(294,355)(295,356)
(296,357)(297,358)(298,359)(299,360)(300,361)(301,362)(302,363)(303,364)
(304,365)(305,366);;
s1 := (  1, 62)(  2,122)(  3,121)(  4,120)(  5,119)(  6,118)(  7,117)(  8,116)
(  9,115)( 10,114)( 11,113)( 12,112)( 13,111)( 14,110)( 15,109)( 16,108)
( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,101)( 24,100)
( 25, 99)( 26, 98)( 27, 97)( 28, 96)( 29, 95)( 30, 94)( 31, 93)( 32, 92)
( 33, 91)( 34, 90)( 35, 89)( 36, 88)( 37, 87)( 38, 86)( 39, 85)( 40, 84)
( 41, 83)( 42, 82)( 43, 81)( 44, 80)( 45, 79)( 46, 78)( 47, 77)( 48, 76)
( 49, 75)( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)( 55, 69)( 56, 68)
( 57, 67)( 58, 66)( 59, 65)( 60, 64)( 61, 63)(124,183)(125,182)(126,181)
(127,180)(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)(134,173)
(135,172)(136,171)(137,170)(138,169)(139,168)(140,167)(141,166)(142,165)
(143,164)(144,163)(145,162)(146,161)(147,160)(148,159)(149,158)(150,157)
(151,156)(152,155)(153,154)(184,245)(185,305)(186,304)(187,303)(188,302)
(189,301)(190,300)(191,299)(192,298)(193,297)(194,296)(195,295)(196,294)
(197,293)(198,292)(199,291)(200,290)(201,289)(202,288)(203,287)(204,286)
(205,285)(206,284)(207,283)(208,282)(209,281)(210,280)(211,279)(212,278)
(213,277)(214,276)(215,275)(216,274)(217,273)(218,272)(219,271)(220,270)
(221,269)(222,268)(223,267)(224,266)(225,265)(226,264)(227,263)(228,262)
(229,261)(230,260)(231,259)(232,258)(233,257)(234,256)(235,255)(236,254)
(237,253)(238,252)(239,251)(240,250)(241,249)(242,248)(243,247)(244,246)
(307,366)(308,365)(309,364)(310,363)(311,362)(312,361)(313,360)(314,359)
(315,358)(316,357)(317,356)(318,355)(319,354)(320,353)(321,352)(322,351)
(323,350)(324,349)(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)
(331,342)(332,341)(333,340)(334,339)(335,338)(336,337);;
s2 := (  1,185)(  2,184)(  3,244)(  4,243)(  5,242)(  6,241)(  7,240)(  8,239)
(  9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,232)( 16,231)
( 17,230)( 18,229)( 19,228)( 20,227)( 21,226)( 22,225)( 23,224)( 24,223)
( 25,222)( 26,221)( 27,220)( 28,219)( 29,218)( 30,217)( 31,216)( 32,215)
( 33,214)( 34,213)( 35,212)( 36,211)( 37,210)( 38,209)( 39,208)( 40,207)
( 41,206)( 42,205)( 43,204)( 44,203)( 45,202)( 46,201)( 47,200)( 48,199)
( 49,198)( 50,197)( 51,196)( 52,195)( 53,194)( 54,193)( 55,192)( 56,191)
( 57,190)( 58,189)( 59,188)( 60,187)( 61,186)( 62,246)( 63,245)( 64,305)
( 65,304)( 66,303)( 67,302)( 68,301)( 69,300)( 70,299)( 71,298)( 72,297)
( 73,296)( 74,295)( 75,294)( 76,293)( 77,292)( 78,291)( 79,290)( 80,289)
( 81,288)( 82,287)( 83,286)( 84,285)( 85,284)( 86,283)( 87,282)( 88,281)
( 89,280)( 90,279)( 91,278)( 92,277)( 93,276)( 94,275)( 95,274)( 96,273)
( 97,272)( 98,271)( 99,270)(100,269)(101,268)(102,267)(103,266)(104,265)
(105,264)(106,263)(107,262)(108,261)(109,260)(110,259)(111,258)(112,257)
(113,256)(114,255)(115,254)(116,253)(117,252)(118,251)(119,250)(120,249)
(121,248)(122,247)(123,307)(124,306)(125,366)(126,365)(127,364)(128,363)
(129,362)(130,361)(131,360)(132,359)(133,358)(134,357)(135,356)(136,355)
(137,354)(138,353)(139,352)(140,351)(141,350)(142,349)(143,348)(144,347)
(145,346)(146,345)(147,344)(148,343)(149,342)(150,341)(151,340)(152,339)
(153,338)(154,337)(155,336)(156,335)(157,334)(158,333)(159,332)(160,331)
(161,330)(162,329)(163,328)(164,327)(165,326)(166,325)(167,324)(168,323)
(169,322)(170,321)(171,320)(172,319)(173,318)(174,317)(175,316)(176,315)
(177,314)(178,313)(179,312)(180,311)(181,310)(182,309)(183,308);;
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(366)!( 62,123)( 63,124)( 64,125)( 65,126)( 66,127)( 67,128)( 68,129)
( 69,130)( 70,131)( 71,132)( 72,133)( 73,134)( 74,135)( 75,136)( 76,137)
( 77,138)( 78,139)( 79,140)( 80,141)( 81,142)( 82,143)( 83,144)( 84,145)
( 85,146)( 86,147)( 87,148)( 88,149)( 89,150)( 90,151)( 91,152)( 92,153)
( 93,154)( 94,155)( 95,156)( 96,157)( 97,158)( 98,159)( 99,160)(100,161)
(101,162)(102,163)(103,164)(104,165)(105,166)(106,167)(107,168)(108,169)
(109,170)(110,171)(111,172)(112,173)(113,174)(114,175)(115,176)(116,177)
(117,178)(118,179)(119,180)(120,181)(121,182)(122,183)(245,306)(246,307)
(247,308)(248,309)(249,310)(250,311)(251,312)(252,313)(253,314)(254,315)
(255,316)(256,317)(257,318)(258,319)(259,320)(260,321)(261,322)(262,323)
(263,324)(264,325)(265,326)(266,327)(267,328)(268,329)(269,330)(270,331)
(271,332)(272,333)(273,334)(274,335)(275,336)(276,337)(277,338)(278,339)
(279,340)(280,341)(281,342)(282,343)(283,344)(284,345)(285,346)(286,347)
(287,348)(288,349)(289,350)(290,351)(291,352)(292,353)(293,354)(294,355)
(295,356)(296,357)(297,358)(298,359)(299,360)(300,361)(301,362)(302,363)
(303,364)(304,365)(305,366);
s1 := Sym(366)!(  1, 62)(  2,122)(  3,121)(  4,120)(  5,119)(  6,118)(  7,117)
(  8,116)(  9,115)( 10,114)( 11,113)( 12,112)( 13,111)( 14,110)( 15,109)
( 16,108)( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,101)
( 24,100)( 25, 99)( 26, 98)( 27, 97)( 28, 96)( 29, 95)( 30, 94)( 31, 93)
( 32, 92)( 33, 91)( 34, 90)( 35, 89)( 36, 88)( 37, 87)( 38, 86)( 39, 85)
( 40, 84)( 41, 83)( 42, 82)( 43, 81)( 44, 80)( 45, 79)( 46, 78)( 47, 77)
( 48, 76)( 49, 75)( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)( 55, 69)
( 56, 68)( 57, 67)( 58, 66)( 59, 65)( 60, 64)( 61, 63)(124,183)(125,182)
(126,181)(127,180)(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)
(134,173)(135,172)(136,171)(137,170)(138,169)(139,168)(140,167)(141,166)
(142,165)(143,164)(144,163)(145,162)(146,161)(147,160)(148,159)(149,158)
(150,157)(151,156)(152,155)(153,154)(184,245)(185,305)(186,304)(187,303)
(188,302)(189,301)(190,300)(191,299)(192,298)(193,297)(194,296)(195,295)
(196,294)(197,293)(198,292)(199,291)(200,290)(201,289)(202,288)(203,287)
(204,286)(205,285)(206,284)(207,283)(208,282)(209,281)(210,280)(211,279)
(212,278)(213,277)(214,276)(215,275)(216,274)(217,273)(218,272)(219,271)
(220,270)(221,269)(222,268)(223,267)(224,266)(225,265)(226,264)(227,263)
(228,262)(229,261)(230,260)(231,259)(232,258)(233,257)(234,256)(235,255)
(236,254)(237,253)(238,252)(239,251)(240,250)(241,249)(242,248)(243,247)
(244,246)(307,366)(308,365)(309,364)(310,363)(311,362)(312,361)(313,360)
(314,359)(315,358)(316,357)(317,356)(318,355)(319,354)(320,353)(321,352)
(322,351)(323,350)(324,349)(325,348)(326,347)(327,346)(328,345)(329,344)
(330,343)(331,342)(332,341)(333,340)(334,339)(335,338)(336,337);
s2 := Sym(366)!(  1,185)(  2,184)(  3,244)(  4,243)(  5,242)(  6,241)(  7,240)
(  8,239)(  9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,232)
( 16,231)( 17,230)( 18,229)( 19,228)( 20,227)( 21,226)( 22,225)( 23,224)
( 24,223)( 25,222)( 26,221)( 27,220)( 28,219)( 29,218)( 30,217)( 31,216)
( 32,215)( 33,214)( 34,213)( 35,212)( 36,211)( 37,210)( 38,209)( 39,208)
( 40,207)( 41,206)( 42,205)( 43,204)( 44,203)( 45,202)( 46,201)( 47,200)
( 48,199)( 49,198)( 50,197)( 51,196)( 52,195)( 53,194)( 54,193)( 55,192)
( 56,191)( 57,190)( 58,189)( 59,188)( 60,187)( 61,186)( 62,246)( 63,245)
( 64,305)( 65,304)( 66,303)( 67,302)( 68,301)( 69,300)( 70,299)( 71,298)
( 72,297)( 73,296)( 74,295)( 75,294)( 76,293)( 77,292)( 78,291)( 79,290)
( 80,289)( 81,288)( 82,287)( 83,286)( 84,285)( 85,284)( 86,283)( 87,282)
( 88,281)( 89,280)( 90,279)( 91,278)( 92,277)( 93,276)( 94,275)( 95,274)
( 96,273)( 97,272)( 98,271)( 99,270)(100,269)(101,268)(102,267)(103,266)
(104,265)(105,264)(106,263)(107,262)(108,261)(109,260)(110,259)(111,258)
(112,257)(113,256)(114,255)(115,254)(116,253)(117,252)(118,251)(119,250)
(120,249)(121,248)(122,247)(123,307)(124,306)(125,366)(126,365)(127,364)
(128,363)(129,362)(130,361)(131,360)(132,359)(133,358)(134,357)(135,356)
(136,355)(137,354)(138,353)(139,352)(140,351)(141,350)(142,349)(143,348)
(144,347)(145,346)(146,345)(147,344)(148,343)(149,342)(150,341)(151,340)
(152,339)(153,338)(154,337)(155,336)(156,335)(157,334)(158,333)(159,332)
(160,331)(161,330)(162,329)(163,328)(164,327)(165,326)(166,325)(167,324)
(168,323)(169,322)(170,321)(171,320)(172,319)(173,318)(174,317)(175,316)
(176,315)(177,314)(178,313)(179,312)(180,311)(181,310)(182,309)(183,308);
poly := sub<Sym(366)|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*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope