Polytope of Type {2,364}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,364}*1456
if this polytope has a name.
Group : SmallGroup(1456,158)
Rank : 3
Schlafli Type : {2,364}
Number of vertices, edges, etc : 2, 364, 364
Order of s₀s₁s₂ : 364
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,182}*728
   4-fold quotients : {2,91}*364
   7-fold quotients : {2,52}*208
   13-fold quotients : {2,28}*112
   14-fold quotients : {2,26}*104
   26-fold quotients : {2,14}*56
   28-fold quotients : {2,13}*52
   52-fold quotients : {2,7}*28
   91-fold quotients : {2,4}*16
   182-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope