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