Polytope of Type {366,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {366,2}*1464
if this polytope has a name.
Group : SmallGroup(1464,60)
Rank : 3
Schlafli Type : {366,2}
Number of vertices, edges, etc : 366, 366, 2
Order of s₀s₁s₂ : 366
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {183,2}*732
   3-fold quotients : {122,2}*488
   6-fold quotients : {61,2}*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 := (  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)( 62,123)( 63,183)
( 64,182)( 65,181)( 66,180)( 67,179)( 68,178)( 69,177)( 70,176)( 71,175)
( 72,174)( 73,173)( 74,172)( 75,171)( 76,170)( 77,169)( 78,168)( 79,167)
( 80,166)( 81,165)( 82,164)( 83,163)( 84,162)( 85,161)( 86,160)( 87,159)
( 88,158)( 89,157)( 90,156)( 91,155)( 92,154)( 93,153)( 94,152)( 95,151)
( 96,150)( 97,149)( 98,148)( 99,147)(100,146)(101,145)(102,144)(103,143)
(104,142)(105,141)(106,140)(107,139)(108,138)(109,137)(110,136)(111,135)
(112,134)(113,133)(114,132)(115,131)(116,130)(117,129)(118,128)(119,127)
(120,126)(121,125)(122,124)(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)(245,306)(246,366)(247,365)(248,364)(249,363)(250,362)(251,361)
(252,360)(253,359)(254,358)(255,357)(256,356)(257,355)(258,354)(259,353)
(260,352)(261,351)(262,350)(263,349)(264,348)(265,347)(266,346)(267,345)
(268,344)(269,343)(270,342)(271,341)(272,340)(273,339)(274,338)(275,337)
(276,336)(277,335)(278,334)(279,333)(280,332)(281,331)(282,330)(283,329)
(284,328)(285,327)(286,326)(287,325)(288,324)(289,323)(290,322)(291,321)
(292,320)(293,319)(294,318)(295,317)(296,316)(297,315)(298,314)(299,313)
(300,312)(301,311)(302,310)(303,309)(304,308)(305,307);;
s1 := (  1,246)(  2,245)(  3,305)(  4,304)(  5,303)(  6,302)(  7,301)(  8,300)
(  9,299)( 10,298)( 11,297)( 12,296)( 13,295)( 14,294)( 15,293)( 16,292)
( 17,291)( 18,290)( 19,289)( 20,288)( 21,287)( 22,286)( 23,285)( 24,284)
( 25,283)( 26,282)( 27,281)( 28,280)( 29,279)( 30,278)( 31,277)( 32,276)
( 33,275)( 34,274)( 35,273)( 36,272)( 37,271)( 38,270)( 39,269)( 40,268)
( 41,267)( 42,266)( 43,265)( 44,264)( 45,263)( 46,262)( 47,261)( 48,260)
( 49,259)( 50,258)( 51,257)( 52,256)( 53,255)( 54,254)( 55,253)( 56,252)
( 57,251)( 58,250)( 59,249)( 60,248)( 61,247)( 62,185)( 63,184)( 64,244)
( 65,243)( 66,242)( 67,241)( 68,240)( 69,239)( 70,238)( 71,237)( 72,236)
( 73,235)( 74,234)( 75,233)( 76,232)( 77,231)( 78,230)( 79,229)( 80,228)
( 81,227)( 82,226)( 83,225)( 84,224)( 85,223)( 86,222)( 87,221)( 88,220)
( 89,219)( 90,218)( 91,217)( 92,216)( 93,215)( 94,214)( 95,213)( 96,212)
( 97,211)( 98,210)( 99,209)(100,208)(101,207)(102,206)(103,205)(104,204)
(105,203)(106,202)(107,201)(108,200)(109,199)(110,198)(111,197)(112,196)
(113,195)(114,194)(115,193)(116,192)(117,191)(118,190)(119,189)(120,188)
(121,187)(122,186)(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);;
s2 := (367,368);;
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, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(368)!(  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)( 62,123)
( 63,183)( 64,182)( 65,181)( 66,180)( 67,179)( 68,178)( 69,177)( 70,176)
( 71,175)( 72,174)( 73,173)( 74,172)( 75,171)( 76,170)( 77,169)( 78,168)
( 79,167)( 80,166)( 81,165)( 82,164)( 83,163)( 84,162)( 85,161)( 86,160)
( 87,159)( 88,158)( 89,157)( 90,156)( 91,155)( 92,154)( 93,153)( 94,152)
( 95,151)( 96,150)( 97,149)( 98,148)( 99,147)(100,146)(101,145)(102,144)
(103,143)(104,142)(105,141)(106,140)(107,139)(108,138)(109,137)(110,136)
(111,135)(112,134)(113,133)(114,132)(115,131)(116,130)(117,129)(118,128)
(119,127)(120,126)(121,125)(122,124)(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)(245,306)(246,366)(247,365)(248,364)(249,363)(250,362)
(251,361)(252,360)(253,359)(254,358)(255,357)(256,356)(257,355)(258,354)
(259,353)(260,352)(261,351)(262,350)(263,349)(264,348)(265,347)(266,346)
(267,345)(268,344)(269,343)(270,342)(271,341)(272,340)(273,339)(274,338)
(275,337)(276,336)(277,335)(278,334)(279,333)(280,332)(281,331)(282,330)
(283,329)(284,328)(285,327)(286,326)(287,325)(288,324)(289,323)(290,322)
(291,321)(292,320)(293,319)(294,318)(295,317)(296,316)(297,315)(298,314)
(299,313)(300,312)(301,311)(302,310)(303,309)(304,308)(305,307);
s1 := Sym(368)!(  1,246)(  2,245)(  3,305)(  4,304)(  5,303)(  6,302)(  7,301)
(  8,300)(  9,299)( 10,298)( 11,297)( 12,296)( 13,295)( 14,294)( 15,293)
( 16,292)( 17,291)( 18,290)( 19,289)( 20,288)( 21,287)( 22,286)( 23,285)
( 24,284)( 25,283)( 26,282)( 27,281)( 28,280)( 29,279)( 30,278)( 31,277)
( 32,276)( 33,275)( 34,274)( 35,273)( 36,272)( 37,271)( 38,270)( 39,269)
( 40,268)( 41,267)( 42,266)( 43,265)( 44,264)( 45,263)( 46,262)( 47,261)
( 48,260)( 49,259)( 50,258)( 51,257)( 52,256)( 53,255)( 54,254)( 55,253)
( 56,252)( 57,251)( 58,250)( 59,249)( 60,248)( 61,247)( 62,185)( 63,184)
( 64,244)( 65,243)( 66,242)( 67,241)( 68,240)( 69,239)( 70,238)( 71,237)
( 72,236)( 73,235)( 74,234)( 75,233)( 76,232)( 77,231)( 78,230)( 79,229)
( 80,228)( 81,227)( 82,226)( 83,225)( 84,224)( 85,223)( 86,222)( 87,221)
( 88,220)( 89,219)( 90,218)( 91,217)( 92,216)( 93,215)( 94,214)( 95,213)
( 96,212)( 97,211)( 98,210)( 99,209)(100,208)(101,207)(102,206)(103,205)
(104,204)(105,203)(106,202)(107,201)(108,200)(109,199)(110,198)(111,197)
(112,196)(113,195)(114,194)(115,193)(116,192)(117,191)(118,190)(119,189)
(120,188)(121,187)(122,186)(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);
s2 := Sym(368)!(367,368);
poly := sub<Sym(368)|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, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope