Polytope of Type {120,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,6}*1440b
Also Known As : {120,6|2}. if this polytope has another 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 : 2
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}*720b
   3-fold quotients : {40,6}*480, {120,2}*480
   4-fold quotients : {30,6}*360b
   5-fold quotients : {24,6}*288a
   6-fold quotients : {20,6}*240a, {60,2}*240
   9-fold quotients : {40,2}*160
   10-fold quotients : {12,6}*144a
   12-fold quotients : {10,6}*120, {30,2}*120
   15-fold quotients : {24,2}*96, {8,6}*96
   18-fold quotients : {20,2}*80
   20-fold quotients : {6,6}*72a
   24-fold quotients : {15,2}*60
   30-fold quotients : {12,2}*48, {4,6}*48a
   36-fold quotients : {10,2}*40
   45-fold quotients : {8,2}*32
   60-fold quotients : {2,6}*24, {6,2}*24
   72-fold quotients : {5,2}*20
   90-fold quotients : {4,2}*16
   120-fold quotients : {2,3}*12, {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)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)
( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)
( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)( 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)(106,151)(107,155)(108,154)(109,153)(110,152)(111,161)(112,165)
(113,164)(114,163)(115,162)(116,156)(117,160)(118,159)(119,158)(120,157)
(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)(181,271)
(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)(196,286)(197,290)
(198,289)(199,288)(200,287)(201,296)(202,300)(203,299)(204,298)(205,297)
(206,291)(207,295)(208,294)(209,293)(210,292)(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)(226,316)(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)(241,331)(242,335)(243,334)(244,333)(245,332)
(246,341)(247,345)(248,344)(249,343)(250,342)(251,336)(252,340)(253,339)
(254,338)(255,337)(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);;
s1 := (  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);;
s2 := (  1, 16)(  2, 17)(  3, 18)(  4, 19)(  5, 20)(  6, 21)(  7, 22)(  8, 23)
(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)( 46, 61)
( 47, 62)( 48, 63)( 49, 64)( 50, 65)( 51, 66)( 52, 67)( 53, 68)( 54, 69)
( 55, 70)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 91,106)( 92,107)
( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)
(101,116)(102,117)(103,118)(104,119)(105,120)(136,151)(137,152)(138,153)
(139,154)(140,155)(141,156)(142,157)(143,158)(144,159)(145,160)(146,161)
(147,162)(148,163)(149,164)(150,165)(181,196)(182,197)(183,198)(184,199)
(185,200)(186,201)(187,202)(188,203)(189,204)(190,205)(191,206)(192,207)
(193,208)(194,209)(195,210)(226,241)(227,242)(228,243)(229,244)(230,245)
(231,246)(232,247)(233,248)(234,249)(235,250)(236,251)(237,252)(238,253)
(239,254)(240,255)(271,286)(272,287)(273,288)(274,289)(275,290)(276,291)
(277,292)(278,293)(279,294)(280,295)(281,296)(282,297)(283,298)(284,299)
(285,300)(316,331)(317,332)(318,333)(319,334)(320,335)(321,336)(322,337)
(323,338)(324,339)(325,340)(326,341)(327,342)(328,343)(329,344)(330,345);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)
( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)
( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)
( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 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)(106,151)(107,155)(108,154)(109,153)(110,152)(111,161)
(112,165)(113,164)(114,163)(115,162)(116,156)(117,160)(118,159)(119,158)
(120,157)(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)
(181,271)(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)(196,286)
(197,290)(198,289)(199,288)(200,287)(201,296)(202,300)(203,299)(204,298)
(205,297)(206,291)(207,295)(208,294)(209,293)(210,292)(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)(226,316)(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)(241,331)(242,335)(243,334)(244,333)
(245,332)(246,341)(247,345)(248,344)(249,343)(250,342)(251,336)(252,340)
(253,339)(254,338)(255,337)(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);
s1 := 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);
s2 := Sym(360)!(  1, 16)(  2, 17)(  3, 18)(  4, 19)(  5, 20)(  6, 21)(  7, 22)
(  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)
( 46, 61)( 47, 62)( 48, 63)( 49, 64)( 50, 65)( 51, 66)( 52, 67)( 53, 68)
( 54, 69)( 55, 70)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 91,106)
( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)
(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(136,151)(137,152)
(138,153)(139,154)(140,155)(141,156)(142,157)(143,158)(144,159)(145,160)
(146,161)(147,162)(148,163)(149,164)(150,165)(181,196)(182,197)(183,198)
(184,199)(185,200)(186,201)(187,202)(188,203)(189,204)(190,205)(191,206)
(192,207)(193,208)(194,209)(195,210)(226,241)(227,242)(228,243)(229,244)
(230,245)(231,246)(232,247)(233,248)(234,249)(235,250)(236,251)(237,252)
(238,253)(239,254)(240,255)(271,286)(272,287)(273,288)(274,289)(275,290)
(276,291)(277,292)(278,293)(279,294)(280,295)(281,296)(282,297)(283,298)
(284,299)(285,300)(316,331)(317,332)(318,333)(319,334)(320,335)(321,336)
(322,337)(323,338)(324,339)(325,340)(326,341)(327,342)(328,343)(329,344)
(330,345);
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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