Polytope of Type {120,6}

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