Polytope of Type {6,120}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,120}*1440c
if this polytope has a name.
Group : SmallGroup(1440,3583)
Rank : 3
Schlafli Type : {6,120}
Number of vertices, edges, etc : 6, 360, 120
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 6
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 : {6,60}*720c
   3-fold quotients : {2,120}*480
   4-fold quotients : {6,30}*360c
   5-fold quotients : {6,24}*288b
   6-fold quotients : {2,60}*240
   8-fold quotients : {6,15}*180
   9-fold quotients : {2,40}*160
   10-fold quotients : {6,12}*144b
   12-fold quotients : {2,30}*120
   15-fold quotients : {2,24}*96
   18-fold quotients : {2,20}*80
   20-fold quotients : {6,6}*72b
   24-fold quotients : {2,15}*60
   30-fold quotients : {2,12}*48
   36-fold quotients : {2,10}*40
   40-fold quotients : {6,3}*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 := ( 16, 31)( 17, 32)( 18, 33)( 19, 34)( 20, 35)( 21, 36)( 22, 37)( 23, 38)
( 24, 39)( 25, 40)( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)( 61, 76)
( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)
( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)(106,121)(107,122)
(108,123)(109,124)(110,125)(111,126)(112,127)(113,128)(114,129)(115,130)
(116,131)(117,132)(118,133)(119,134)(120,135)(151,166)(152,167)(153,168)
(154,169)(155,170)(156,171)(157,172)(158,173)(159,174)(160,175)(161,176)
(162,177)(163,178)(164,179)(165,180)(196,211)(197,212)(198,213)(199,214)
(200,215)(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)
(208,223)(209,224)(210,225)(241,256)(242,257)(243,258)(244,259)(245,260)
(246,261)(247,262)(248,263)(249,264)(250,265)(251,266)(252,267)(253,268)
(254,269)(255,270)(286,301)(287,302)(288,303)(289,304)(290,305)(291,306)
(292,307)(293,308)(294,309)(295,310)(296,311)(297,312)(298,313)(299,314)
(300,315)(331,346)(332,347)(333,348)(334,349)(335,350)(336,351)(337,352)
(338,353)(339,354)(340,355)(341,356)(342,357)(343,358)(344,359)(345,360);;
s1 := (  1, 16)(  2, 20)(  3, 19)(  4, 18)(  5, 17)(  6, 26)(  7, 30)(  8, 29)
(  9, 28)( 10, 27)( 11, 21)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 32, 35)
( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 46, 61)( 47, 65)
( 48, 64)( 49, 63)( 50, 62)( 51, 71)( 52, 75)( 53, 74)( 54, 73)( 55, 72)
( 56, 66)( 57, 70)( 58, 69)( 59, 68)( 60, 67)( 77, 80)( 78, 79)( 81, 86)
( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,151)( 92,155)( 93,154)( 94,153)
( 95,152)( 96,161)( 97,165)( 98,164)( 99,163)(100,162)(101,156)(102,160)
(103,159)(104,158)(105,157)(106,136)(107,140)(108,139)(109,138)(110,137)
(111,146)(112,150)(113,149)(114,148)(115,147)(116,141)(117,145)(118,144)
(119,143)(120,142)(121,166)(122,170)(123,169)(124,168)(125,167)(126,176)
(127,180)(128,179)(129,178)(130,177)(131,171)(132,175)(133,174)(134,173)
(135,172)(181,286)(182,290)(183,289)(184,288)(185,287)(186,296)(187,300)
(188,299)(189,298)(190,297)(191,291)(192,295)(193,294)(194,293)(195,292)
(196,271)(197,275)(198,274)(199,273)(200,272)(201,281)(202,285)(203,284)
(204,283)(205,282)(206,276)(207,280)(208,279)(209,278)(210,277)(211,301)
(212,305)(213,304)(214,303)(215,302)(216,311)(217,315)(218,314)(219,313)
(220,312)(221,306)(222,310)(223,309)(224,308)(225,307)(226,331)(227,335)
(228,334)(229,333)(230,332)(231,341)(232,345)(233,344)(234,343)(235,342)
(236,336)(237,340)(238,339)(239,338)(240,337)(241,316)(242,320)(243,319)
(244,318)(245,317)(246,326)(247,330)(248,329)(249,328)(250,327)(251,321)
(252,325)(253,324)(254,323)(255,322)(256,346)(257,350)(258,349)(259,348)
(260,347)(261,356)(262,360)(263,359)(264,358)(265,357)(266,351)(267,355)
(268,354)(269,353)(270,352);;
s2 := (  1,187)(  2,186)(  3,190)(  4,189)(  5,188)(  6,182)(  7,181)(  8,185)
(  9,184)( 10,183)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)( 16,217)
( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)( 24,214)
( 25,213)( 26,222)( 27,221)( 28,225)( 29,224)( 30,223)( 31,202)( 32,201)
( 33,205)( 34,204)( 35,203)( 36,197)( 37,196)( 38,200)( 39,199)( 40,198)
( 41,207)( 42,206)( 43,210)( 44,209)( 45,208)( 46,232)( 47,231)( 48,235)
( 49,234)( 50,233)( 51,227)( 52,226)( 53,230)( 54,229)( 55,228)( 56,237)
( 57,236)( 58,240)( 59,239)( 60,238)( 61,262)( 62,261)( 63,265)( 64,264)
( 65,263)( 66,257)( 67,256)( 68,260)( 69,259)( 70,258)( 71,267)( 72,266)
( 73,270)( 74,269)( 75,268)( 76,247)( 77,246)( 78,250)( 79,249)( 80,248)
( 81,242)( 82,241)( 83,245)( 84,244)( 85,243)( 86,252)( 87,251)( 88,255)
( 89,254)( 90,253)( 91,322)( 92,321)( 93,325)( 94,324)( 95,323)( 96,317)
( 97,316)( 98,320)( 99,319)(100,318)(101,327)(102,326)(103,330)(104,329)
(105,328)(106,352)(107,351)(108,355)(109,354)(110,353)(111,347)(112,346)
(113,350)(114,349)(115,348)(116,357)(117,356)(118,360)(119,359)(120,358)
(121,337)(122,336)(123,340)(124,339)(125,338)(126,332)(127,331)(128,335)
(129,334)(130,333)(131,342)(132,341)(133,345)(134,344)(135,343)(136,277)
(137,276)(138,280)(139,279)(140,278)(141,272)(142,271)(143,275)(144,274)
(145,273)(146,282)(147,281)(148,285)(149,284)(150,283)(151,307)(152,306)
(153,310)(154,309)(155,308)(156,302)(157,301)(158,305)(159,304)(160,303)
(161,312)(162,311)(163,315)(164,314)(165,313)(166,292)(167,291)(168,295)
(169,294)(170,293)(171,287)(172,286)(173,290)(174,289)(175,288)(176,297)
(177,296)(178,300)(179,299)(180,298);;
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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(360)!( 16, 31)( 17, 32)( 18, 33)( 19, 34)( 20, 35)( 21, 36)( 22, 37)
( 23, 38)( 24, 39)( 25, 40)( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)
( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)
( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)(106,121)
(107,122)(108,123)(109,124)(110,125)(111,126)(112,127)(113,128)(114,129)
(115,130)(116,131)(117,132)(118,133)(119,134)(120,135)(151,166)(152,167)
(153,168)(154,169)(155,170)(156,171)(157,172)(158,173)(159,174)(160,175)
(161,176)(162,177)(163,178)(164,179)(165,180)(196,211)(197,212)(198,213)
(199,214)(200,215)(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)
(207,222)(208,223)(209,224)(210,225)(241,256)(242,257)(243,258)(244,259)
(245,260)(246,261)(247,262)(248,263)(249,264)(250,265)(251,266)(252,267)
(253,268)(254,269)(255,270)(286,301)(287,302)(288,303)(289,304)(290,305)
(291,306)(292,307)(293,308)(294,309)(295,310)(296,311)(297,312)(298,313)
(299,314)(300,315)(331,346)(332,347)(333,348)(334,349)(335,350)(336,351)
(337,352)(338,353)(339,354)(340,355)(341,356)(342,357)(343,358)(344,359)
(345,360);
s1 := Sym(360)!(  1, 16)(  2, 20)(  3, 19)(  4, 18)(  5, 17)(  6, 26)(  7, 30)
(  8, 29)(  9, 28)( 10, 27)( 11, 21)( 12, 25)( 13, 24)( 14, 23)( 15, 22)
( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 46, 61)
( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 71)( 52, 75)( 53, 74)( 54, 73)
( 55, 72)( 56, 66)( 57, 70)( 58, 69)( 59, 68)( 60, 67)( 77, 80)( 78, 79)
( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,151)( 92,155)( 93,154)
( 94,153)( 95,152)( 96,161)( 97,165)( 98,164)( 99,163)(100,162)(101,156)
(102,160)(103,159)(104,158)(105,157)(106,136)(107,140)(108,139)(109,138)
(110,137)(111,146)(112,150)(113,149)(114,148)(115,147)(116,141)(117,145)
(118,144)(119,143)(120,142)(121,166)(122,170)(123,169)(124,168)(125,167)
(126,176)(127,180)(128,179)(129,178)(130,177)(131,171)(132,175)(133,174)
(134,173)(135,172)(181,286)(182,290)(183,289)(184,288)(185,287)(186,296)
(187,300)(188,299)(189,298)(190,297)(191,291)(192,295)(193,294)(194,293)
(195,292)(196,271)(197,275)(198,274)(199,273)(200,272)(201,281)(202,285)
(203,284)(204,283)(205,282)(206,276)(207,280)(208,279)(209,278)(210,277)
(211,301)(212,305)(213,304)(214,303)(215,302)(216,311)(217,315)(218,314)
(219,313)(220,312)(221,306)(222,310)(223,309)(224,308)(225,307)(226,331)
(227,335)(228,334)(229,333)(230,332)(231,341)(232,345)(233,344)(234,343)
(235,342)(236,336)(237,340)(238,339)(239,338)(240,337)(241,316)(242,320)
(243,319)(244,318)(245,317)(246,326)(247,330)(248,329)(249,328)(250,327)
(251,321)(252,325)(253,324)(254,323)(255,322)(256,346)(257,350)(258,349)
(259,348)(260,347)(261,356)(262,360)(263,359)(264,358)(265,357)(266,351)
(267,355)(268,354)(269,353)(270,352);
s2 := Sym(360)!(  1,187)(  2,186)(  3,190)(  4,189)(  5,188)(  6,182)(  7,181)
(  8,185)(  9,184)( 10,183)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)
( 16,217)( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)
( 24,214)( 25,213)( 26,222)( 27,221)( 28,225)( 29,224)( 30,223)( 31,202)
( 32,201)( 33,205)( 34,204)( 35,203)( 36,197)( 37,196)( 38,200)( 39,199)
( 40,198)( 41,207)( 42,206)( 43,210)( 44,209)( 45,208)( 46,232)( 47,231)
( 48,235)( 49,234)( 50,233)( 51,227)( 52,226)( 53,230)( 54,229)( 55,228)
( 56,237)( 57,236)( 58,240)( 59,239)( 60,238)( 61,262)( 62,261)( 63,265)
( 64,264)( 65,263)( 66,257)( 67,256)( 68,260)( 69,259)( 70,258)( 71,267)
( 72,266)( 73,270)( 74,269)( 75,268)( 76,247)( 77,246)( 78,250)( 79,249)
( 80,248)( 81,242)( 82,241)( 83,245)( 84,244)( 85,243)( 86,252)( 87,251)
( 88,255)( 89,254)( 90,253)( 91,322)( 92,321)( 93,325)( 94,324)( 95,323)
( 96,317)( 97,316)( 98,320)( 99,319)(100,318)(101,327)(102,326)(103,330)
(104,329)(105,328)(106,352)(107,351)(108,355)(109,354)(110,353)(111,347)
(112,346)(113,350)(114,349)(115,348)(116,357)(117,356)(118,360)(119,359)
(120,358)(121,337)(122,336)(123,340)(124,339)(125,338)(126,332)(127,331)
(128,335)(129,334)(130,333)(131,342)(132,341)(133,345)(134,344)(135,343)
(136,277)(137,276)(138,280)(139,279)(140,278)(141,272)(142,271)(143,275)
(144,274)(145,273)(146,282)(147,281)(148,285)(149,284)(150,283)(151,307)
(152,306)(153,310)(154,309)(155,308)(156,302)(157,301)(158,305)(159,304)
(160,303)(161,312)(162,311)(163,315)(164,314)(165,313)(166,292)(167,291)
(168,295)(169,294)(170,293)(171,287)(172,286)(173,290)(174,289)(175,288)
(176,297)(177,296)(178,300)(179,299)(180,298);
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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope