Polytope of Type {36,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,20}*1440
Also Known As : {36,20|2}. if this polytope has another name.
Group : SmallGroup(1440,552)
Rank : 3
Schlafli Type : {36,20}
Number of vertices, edges, etc : 36, 360, 20
Order of s0s1s2 : 180
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) :
2-fold quotients : {36,10}*720, {18,20}*720a
3-fold quotients : {12,20}*480
4-fold quotients : {18,10}*360
5-fold quotients : {36,4}*288a
6-fold quotients : {12,10}*240, {6,20}*240a
9-fold quotients : {4,20}*160
10-fold quotients : {36,2}*144, {18,4}*144a
12-fold quotients : {6,10}*120
15-fold quotients : {12,4}*96a
18-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {18,2}*72
30-fold quotients : {12,2}*48, {6,4}*48a
36-fold quotients : {2,10}*40
40-fold quotients : {9,2}*36
45-fold quotients : {4,4}*32
60-fold quotients : {6,2}*24
72-fold quotients : {2,5}*20
90-fold quotients : {2,4}*16, {4,2}*16
120-fold quotients : {3,2}*12
180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 16, 33)( 17, 32)( 18, 31)
( 19, 36)( 20, 35)( 21, 34)( 22, 39)( 23, 38)( 24, 37)( 25, 42)( 26, 41)
( 27, 40)( 28, 45)( 29, 44)( 30, 43)( 47, 48)( 50, 51)( 53, 54)( 56, 57)
( 59, 60)( 61, 78)( 62, 77)( 63, 76)( 64, 81)( 65, 80)( 66, 79)( 67, 84)
( 68, 83)( 69, 82)( 70, 87)( 71, 86)( 72, 85)( 73, 90)( 74, 89)( 75, 88)
( 92, 93)( 95, 96)( 98, 99)(101,102)(104,105)(106,123)(107,122)(108,121)
(109,126)(110,125)(111,124)(112,129)(113,128)(114,127)(115,132)(116,131)
(117,130)(118,135)(119,134)(120,133)(137,138)(140,141)(143,144)(146,147)
(149,150)(151,168)(152,167)(153,166)(154,171)(155,170)(156,169)(157,174)
(158,173)(159,172)(160,177)(161,176)(162,175)(163,180)(164,179)(165,178)
(181,271)(182,273)(183,272)(184,274)(185,276)(186,275)(187,277)(188,279)
(189,278)(190,280)(191,282)(192,281)(193,283)(194,285)(195,284)(196,303)
(197,302)(198,301)(199,306)(200,305)(201,304)(202,309)(203,308)(204,307)
(205,312)(206,311)(207,310)(208,315)(209,314)(210,313)(211,288)(212,287)
(213,286)(214,291)(215,290)(216,289)(217,294)(218,293)(219,292)(220,297)
(221,296)(222,295)(223,300)(224,299)(225,298)(226,316)(227,318)(228,317)
(229,319)(230,321)(231,320)(232,322)(233,324)(234,323)(235,325)(236,327)
(237,326)(238,328)(239,330)(240,329)(241,348)(242,347)(243,346)(244,351)
(245,350)(246,349)(247,354)(248,353)(249,352)(250,357)(251,356)(252,355)
(253,360)(254,359)(255,358)(256,333)(257,332)(258,331)(259,336)(260,335)
(261,334)(262,339)(263,338)(264,337)(265,342)(266,341)(267,340)(268,345)
(269,344)(270,343);;
s1 := ( 1,196)( 2,198)( 3,197)( 4,208)( 5,210)( 6,209)( 7,205)( 8,207)
( 9,206)( 10,202)( 11,204)( 12,203)( 13,199)( 14,201)( 15,200)( 16,181)
( 17,183)( 18,182)( 19,193)( 20,195)( 21,194)( 22,190)( 23,192)( 24,191)
( 25,187)( 26,189)( 27,188)( 28,184)( 29,186)( 30,185)( 31,213)( 32,212)
( 33,211)( 34,225)( 35,224)( 36,223)( 37,222)( 38,221)( 39,220)( 40,219)
( 41,218)( 42,217)( 43,216)( 44,215)( 45,214)( 46,241)( 47,243)( 48,242)
( 49,253)( 50,255)( 51,254)( 52,250)( 53,252)( 54,251)( 55,247)( 56,249)
( 57,248)( 58,244)( 59,246)( 60,245)( 61,226)( 62,228)( 63,227)( 64,238)
( 65,240)( 66,239)( 67,235)( 68,237)( 69,236)( 70,232)( 71,234)( 72,233)
( 73,229)( 74,231)( 75,230)( 76,258)( 77,257)( 78,256)( 79,270)( 80,269)
( 81,268)( 82,267)( 83,266)( 84,265)( 85,264)( 86,263)( 87,262)( 88,261)
( 89,260)( 90,259)( 91,286)( 92,288)( 93,287)( 94,298)( 95,300)( 96,299)
( 97,295)( 98,297)( 99,296)(100,292)(101,294)(102,293)(103,289)(104,291)
(105,290)(106,271)(107,273)(108,272)(109,283)(110,285)(111,284)(112,280)
(113,282)(114,281)(115,277)(116,279)(117,278)(118,274)(119,276)(120,275)
(121,303)(122,302)(123,301)(124,315)(125,314)(126,313)(127,312)(128,311)
(129,310)(130,309)(131,308)(132,307)(133,306)(134,305)(135,304)(136,331)
(137,333)(138,332)(139,343)(140,345)(141,344)(142,340)(143,342)(144,341)
(145,337)(146,339)(147,338)(148,334)(149,336)(150,335)(151,316)(152,318)
(153,317)(154,328)(155,330)(156,329)(157,325)(158,327)(159,326)(160,322)
(161,324)(162,323)(163,319)(164,321)(165,320)(166,348)(167,347)(168,346)
(169,360)(170,359)(171,358)(172,357)(173,356)(174,355)(175,354)(176,353)
(177,352)(178,351)(179,350)(180,349);;
s2 := ( 1, 4)( 2, 5)( 3, 6)( 7, 13)( 8, 14)( 9, 15)( 16, 19)( 17, 20)
( 18, 21)( 22, 28)( 23, 29)( 24, 30)( 31, 34)( 32, 35)( 33, 36)( 37, 43)
( 38, 44)( 39, 45)( 46, 49)( 47, 50)( 48, 51)( 52, 58)( 53, 59)( 54, 60)
( 61, 64)( 62, 65)( 63, 66)( 67, 73)( 68, 74)( 69, 75)( 76, 79)( 77, 80)
( 78, 81)( 82, 88)( 83, 89)( 84, 90)( 91, 94)( 92, 95)( 93, 96)( 97,103)
( 98,104)( 99,105)(106,109)(107,110)(108,111)(112,118)(113,119)(114,120)
(121,124)(122,125)(123,126)(127,133)(128,134)(129,135)(136,139)(137,140)
(138,141)(142,148)(143,149)(144,150)(151,154)(152,155)(153,156)(157,163)
(158,164)(159,165)(166,169)(167,170)(168,171)(172,178)(173,179)(174,180)
(181,229)(182,230)(183,231)(184,226)(185,227)(186,228)(187,238)(188,239)
(189,240)(190,235)(191,236)(192,237)(193,232)(194,233)(195,234)(196,244)
(197,245)(198,246)(199,241)(200,242)(201,243)(202,253)(203,254)(204,255)
(205,250)(206,251)(207,252)(208,247)(209,248)(210,249)(211,259)(212,260)
(213,261)(214,256)(215,257)(216,258)(217,268)(218,269)(219,270)(220,265)
(221,266)(222,267)(223,262)(224,263)(225,264)(271,319)(272,320)(273,321)
(274,316)(275,317)(276,318)(277,328)(278,329)(279,330)(280,325)(281,326)
(282,327)(283,322)(284,323)(285,324)(286,334)(287,335)(288,336)(289,331)
(290,332)(291,333)(292,343)(293,344)(294,345)(295,340)(296,341)(297,342)
(298,337)(299,338)(300,339)(301,349)(302,350)(303,351)(304,346)(305,347)
(306,348)(307,358)(308,359)(309,360)(310,355)(311,356)(312,357)(313,352)
(314,353)(315,354);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(360)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 16, 33)( 17, 32)
( 18, 31)( 19, 36)( 20, 35)( 21, 34)( 22, 39)( 23, 38)( 24, 37)( 25, 42)
( 26, 41)( 27, 40)( 28, 45)( 29, 44)( 30, 43)( 47, 48)( 50, 51)( 53, 54)
( 56, 57)( 59, 60)( 61, 78)( 62, 77)( 63, 76)( 64, 81)( 65, 80)( 66, 79)
( 67, 84)( 68, 83)( 69, 82)( 70, 87)( 71, 86)( 72, 85)( 73, 90)( 74, 89)
( 75, 88)( 92, 93)( 95, 96)( 98, 99)(101,102)(104,105)(106,123)(107,122)
(108,121)(109,126)(110,125)(111,124)(112,129)(113,128)(114,127)(115,132)
(116,131)(117,130)(118,135)(119,134)(120,133)(137,138)(140,141)(143,144)
(146,147)(149,150)(151,168)(152,167)(153,166)(154,171)(155,170)(156,169)
(157,174)(158,173)(159,172)(160,177)(161,176)(162,175)(163,180)(164,179)
(165,178)(181,271)(182,273)(183,272)(184,274)(185,276)(186,275)(187,277)
(188,279)(189,278)(190,280)(191,282)(192,281)(193,283)(194,285)(195,284)
(196,303)(197,302)(198,301)(199,306)(200,305)(201,304)(202,309)(203,308)
(204,307)(205,312)(206,311)(207,310)(208,315)(209,314)(210,313)(211,288)
(212,287)(213,286)(214,291)(215,290)(216,289)(217,294)(218,293)(219,292)
(220,297)(221,296)(222,295)(223,300)(224,299)(225,298)(226,316)(227,318)
(228,317)(229,319)(230,321)(231,320)(232,322)(233,324)(234,323)(235,325)
(236,327)(237,326)(238,328)(239,330)(240,329)(241,348)(242,347)(243,346)
(244,351)(245,350)(246,349)(247,354)(248,353)(249,352)(250,357)(251,356)
(252,355)(253,360)(254,359)(255,358)(256,333)(257,332)(258,331)(259,336)
(260,335)(261,334)(262,339)(263,338)(264,337)(265,342)(266,341)(267,340)
(268,345)(269,344)(270,343);
s1 := Sym(360)!( 1,196)( 2,198)( 3,197)( 4,208)( 5,210)( 6,209)( 7,205)
( 8,207)( 9,206)( 10,202)( 11,204)( 12,203)( 13,199)( 14,201)( 15,200)
( 16,181)( 17,183)( 18,182)( 19,193)( 20,195)( 21,194)( 22,190)( 23,192)
( 24,191)( 25,187)( 26,189)( 27,188)( 28,184)( 29,186)( 30,185)( 31,213)
( 32,212)( 33,211)( 34,225)( 35,224)( 36,223)( 37,222)( 38,221)( 39,220)
( 40,219)( 41,218)( 42,217)( 43,216)( 44,215)( 45,214)( 46,241)( 47,243)
( 48,242)( 49,253)( 50,255)( 51,254)( 52,250)( 53,252)( 54,251)( 55,247)
( 56,249)( 57,248)( 58,244)( 59,246)( 60,245)( 61,226)( 62,228)( 63,227)
( 64,238)( 65,240)( 66,239)( 67,235)( 68,237)( 69,236)( 70,232)( 71,234)
( 72,233)( 73,229)( 74,231)( 75,230)( 76,258)( 77,257)( 78,256)( 79,270)
( 80,269)( 81,268)( 82,267)( 83,266)( 84,265)( 85,264)( 86,263)( 87,262)
( 88,261)( 89,260)( 90,259)( 91,286)( 92,288)( 93,287)( 94,298)( 95,300)
( 96,299)( 97,295)( 98,297)( 99,296)(100,292)(101,294)(102,293)(103,289)
(104,291)(105,290)(106,271)(107,273)(108,272)(109,283)(110,285)(111,284)
(112,280)(113,282)(114,281)(115,277)(116,279)(117,278)(118,274)(119,276)
(120,275)(121,303)(122,302)(123,301)(124,315)(125,314)(126,313)(127,312)
(128,311)(129,310)(130,309)(131,308)(132,307)(133,306)(134,305)(135,304)
(136,331)(137,333)(138,332)(139,343)(140,345)(141,344)(142,340)(143,342)
(144,341)(145,337)(146,339)(147,338)(148,334)(149,336)(150,335)(151,316)
(152,318)(153,317)(154,328)(155,330)(156,329)(157,325)(158,327)(159,326)
(160,322)(161,324)(162,323)(163,319)(164,321)(165,320)(166,348)(167,347)
(168,346)(169,360)(170,359)(171,358)(172,357)(173,356)(174,355)(175,354)
(176,353)(177,352)(178,351)(179,350)(180,349);
s2 := Sym(360)!( 1, 4)( 2, 5)( 3, 6)( 7, 13)( 8, 14)( 9, 15)( 16, 19)
( 17, 20)( 18, 21)( 22, 28)( 23, 29)( 24, 30)( 31, 34)( 32, 35)( 33, 36)
( 37, 43)( 38, 44)( 39, 45)( 46, 49)( 47, 50)( 48, 51)( 52, 58)( 53, 59)
( 54, 60)( 61, 64)( 62, 65)( 63, 66)( 67, 73)( 68, 74)( 69, 75)( 76, 79)
( 77, 80)( 78, 81)( 82, 88)( 83, 89)( 84, 90)( 91, 94)( 92, 95)( 93, 96)
( 97,103)( 98,104)( 99,105)(106,109)(107,110)(108,111)(112,118)(113,119)
(114,120)(121,124)(122,125)(123,126)(127,133)(128,134)(129,135)(136,139)
(137,140)(138,141)(142,148)(143,149)(144,150)(151,154)(152,155)(153,156)
(157,163)(158,164)(159,165)(166,169)(167,170)(168,171)(172,178)(173,179)
(174,180)(181,229)(182,230)(183,231)(184,226)(185,227)(186,228)(187,238)
(188,239)(189,240)(190,235)(191,236)(192,237)(193,232)(194,233)(195,234)
(196,244)(197,245)(198,246)(199,241)(200,242)(201,243)(202,253)(203,254)
(204,255)(205,250)(206,251)(207,252)(208,247)(209,248)(210,249)(211,259)
(212,260)(213,261)(214,256)(215,257)(216,258)(217,268)(218,269)(219,270)
(220,265)(221,266)(222,267)(223,262)(224,263)(225,264)(271,319)(272,320)
(273,321)(274,316)(275,317)(276,318)(277,328)(278,329)(279,330)(280,325)
(281,326)(282,327)(283,322)(284,323)(285,324)(286,334)(287,335)(288,336)
(289,331)(290,332)(291,333)(292,343)(293,344)(294,345)(295,340)(296,341)
(297,342)(298,337)(299,338)(300,339)(301,349)(302,350)(303,351)(304,346)
(305,347)(306,348)(307,358)(308,359)(309,360)(310,355)(311,356)(312,357)
(313,352)(314,353)(315,354);
poly := sub<Sym(360)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope