Polytope of Type {2,360}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,360}*1440
if this polytope has a name.
Group : SmallGroup(1440,869)
Rank : 3
Schlafli Type : {2,360}
Number of vertices, edges, etc : 2, 360, 360
Order of s₀s₁s₂ : 360
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 : {2,180}*720
   3-fold quotients : {2,120}*480
   4-fold quotients : {2,90}*360
   5-fold quotients : {2,72}*288
   6-fold quotients : {2,60}*240
   8-fold quotients : {2,45}*180
   9-fold quotients : {2,40}*160
   10-fold quotients : {2,36}*144
   12-fold quotients : {2,30}*120
   15-fold quotients : {2,24}*96
   18-fold quotients : {2,20}*80
   20-fold quotients : {2,18}*72
   24-fold quotients : {2,15}*60
   30-fold quotients : {2,12}*48
   36-fold quotients : {2,10}*40
   40-fold quotients : {2,9}*36
   45-fold quotients : {2,8}*32
   60-fold quotients : {2,6}*24
   72-fold quotients : {2,5}*20
   90-fold quotients : {2,4}*16
   120-fold quotients : {2,3}*12
   180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope