Polytope of Type {30,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,24}*1440b
Also Known As : {30,24|2}. if this polytope has another name.
Group : SmallGroup(1440,3578)
Rank : 3
Schlafli Type : {30,24}
Number of vertices, edges, etc : 30, 360, 24
Order of s0s1s2 : 120
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 : {30,12}*720b
3-fold quotients : {10,24}*480, {30,8}*480
4-fold quotients : {30,6}*360b
5-fold quotients : {6,24}*288a
6-fold quotients : {10,12}*240, {30,4}*240a
9-fold quotients : {10,8}*160
10-fold quotients : {6,12}*144a
12-fold quotients : {10,6}*120, {30,2}*120
15-fold quotients : {2,24}*96, {6,8}*96
18-fold quotients : {10,4}*80
20-fold quotients : {6,6}*72a
24-fold quotients : {15,2}*60
30-fold quotients : {2,12}*48, {6,4}*48a
36-fold quotients : {10,2}*40
45-fold quotients : {2,8}*32
60-fold quotients : {2,6}*24, {6,2}*24
72-fold quotients : {5,2}*20
90-fold quotients : {2,4}*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)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)( 99,103)
(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)(115,117)
(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)(137,140)
(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)(153,154)
(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)(171,176)
(172,180)(173,179)(174,178)(175,177)(182,185)(183,184)(186,191)(187,195)
(188,194)(189,193)(190,192)(197,200)(198,199)(201,206)(202,210)(203,209)
(204,208)(205,207)(212,215)(213,214)(216,221)(217,225)(218,224)(219,223)
(220,222)(227,230)(228,229)(231,236)(232,240)(233,239)(234,238)(235,237)
(242,245)(243,244)(246,251)(247,255)(248,254)(249,253)(250,252)(257,260)
(258,259)(261,266)(262,270)(263,269)(264,268)(265,267)(272,275)(273,274)
(276,281)(277,285)(278,284)(279,283)(280,282)(287,290)(288,289)(291,296)
(292,300)(293,299)(294,298)(295,297)(302,305)(303,304)(306,311)(307,315)
(308,314)(309,313)(310,312)(317,320)(318,319)(321,326)(322,330)(323,329)
(324,328)(325,327)(332,335)(333,334)(336,341)(337,345)(338,344)(339,343)
(340,342)(347,350)(348,349)(351,356)(352,360)(353,359)(354,358)(355,357);;
s1 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 37)
( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)
( 25, 33)( 26, 42)( 27, 41)( 28, 45)( 29, 44)( 30, 43)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)( 63, 85)
( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)
( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91,142)( 92,141)( 93,145)( 94,144)
( 95,143)( 96,137)( 97,136)( 98,140)( 99,139)(100,138)(101,147)(102,146)
(103,150)(104,149)(105,148)(106,172)(107,171)(108,175)(109,174)(110,173)
(111,167)(112,166)(113,170)(114,169)(115,168)(116,177)(117,176)(118,180)
(119,179)(120,178)(121,157)(122,156)(123,160)(124,159)(125,158)(126,152)
(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)(134,164)
(135,163)(181,277)(182,276)(183,280)(184,279)(185,278)(186,272)(187,271)
(188,275)(189,274)(190,273)(191,282)(192,281)(193,285)(194,284)(195,283)
(196,307)(197,306)(198,310)(199,309)(200,308)(201,302)(202,301)(203,305)
(204,304)(205,303)(206,312)(207,311)(208,315)(209,314)(210,313)(211,292)
(212,291)(213,295)(214,294)(215,293)(216,287)(217,286)(218,290)(219,289)
(220,288)(221,297)(222,296)(223,300)(224,299)(225,298)(226,322)(227,321)
(228,325)(229,324)(230,323)(231,317)(232,316)(233,320)(234,319)(235,318)
(236,327)(237,326)(238,330)(239,329)(240,328)(241,352)(242,351)(243,355)
(244,354)(245,353)(246,347)(247,346)(248,350)(249,349)(250,348)(251,357)
(252,356)(253,360)(254,359)(255,358)(256,337)(257,336)(258,340)(259,339)
(260,338)(261,332)(262,331)(263,335)(264,334)(265,333)(266,342)(267,341)
(268,345)(269,344)(270,343);;
s2 := ( 1,196)( 2,197)( 3,198)( 4,199)( 5,200)( 6,201)( 7,202)( 8,203)
( 9,204)( 10,205)( 11,206)( 12,207)( 13,208)( 14,209)( 15,210)( 16,181)
( 17,182)( 18,183)( 19,184)( 20,185)( 21,186)( 22,187)( 23,188)( 24,189)
( 25,190)( 26,191)( 27,192)( 28,193)( 29,194)( 30,195)( 31,211)( 32,212)
( 33,213)( 34,214)( 35,215)( 36,216)( 37,217)( 38,218)( 39,219)( 40,220)
( 41,221)( 42,222)( 43,223)( 44,224)( 45,225)( 46,241)( 47,242)( 48,243)
( 49,244)( 50,245)( 51,246)( 52,247)( 53,248)( 54,249)( 55,250)( 56,251)
( 57,252)( 58,253)( 59,254)( 60,255)( 61,226)( 62,227)( 63,228)( 64,229)
( 65,230)( 66,231)( 67,232)( 68,233)( 69,234)( 70,235)( 71,236)( 72,237)
( 73,238)( 74,239)( 75,240)( 76,256)( 77,257)( 78,258)( 79,259)( 80,260)
( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)(112,322)
(113,323)(114,324)(115,325)(116,326)(117,327)(118,328)(119,329)(120,330)
(121,346)(122,347)(123,348)(124,349)(125,350)(126,351)(127,352)(128,353)
(129,354)(130,355)(131,356)(132,357)(133,358)(134,359)(135,360)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,291)(142,292)(143,293)(144,294)
(145,295)(146,296)(147,297)(148,298)(149,299)(150,300)(151,271)(152,272)
(153,273)(154,274)(155,275)(156,276)(157,277)(158,278)(159,279)(160,280)
(161,281)(162,282)(163,283)(164,284)(165,285)(166,301)(167,302)(168,303)
(169,304)(170,305)(171,306)(172,307)(173,308)(174,309)(175,310)(176,311)
(177,312)(178,313)(179,314)(180,315);;
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*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 ];;
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)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)
( 99,103)(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)
(115,117)(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)
(137,140)(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)
(153,154)(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)
(171,176)(172,180)(173,179)(174,178)(175,177)(182,185)(183,184)(186,191)
(187,195)(188,194)(189,193)(190,192)(197,200)(198,199)(201,206)(202,210)
(203,209)(204,208)(205,207)(212,215)(213,214)(216,221)(217,225)(218,224)
(219,223)(220,222)(227,230)(228,229)(231,236)(232,240)(233,239)(234,238)
(235,237)(242,245)(243,244)(246,251)(247,255)(248,254)(249,253)(250,252)
(257,260)(258,259)(261,266)(262,270)(263,269)(264,268)(265,267)(272,275)
(273,274)(276,281)(277,285)(278,284)(279,283)(280,282)(287,290)(288,289)
(291,296)(292,300)(293,299)(294,298)(295,297)(302,305)(303,304)(306,311)
(307,315)(308,314)(309,313)(310,312)(317,320)(318,319)(321,326)(322,330)
(323,329)(324,328)(325,327)(332,335)(333,334)(336,341)(337,345)(338,344)
(339,343)(340,342)(347,350)(348,349)(351,356)(352,360)(353,359)(354,358)
(355,357);
s1 := Sym(360)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)
( 16, 37)( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)
( 24, 34)( 25, 33)( 26, 42)( 27, 41)( 28, 45)( 29, 44)( 30, 43)( 46, 52)
( 47, 51)( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)
( 63, 85)( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)
( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91,142)( 92,141)( 93,145)
( 94,144)( 95,143)( 96,137)( 97,136)( 98,140)( 99,139)(100,138)(101,147)
(102,146)(103,150)(104,149)(105,148)(106,172)(107,171)(108,175)(109,174)
(110,173)(111,167)(112,166)(113,170)(114,169)(115,168)(116,177)(117,176)
(118,180)(119,179)(120,178)(121,157)(122,156)(123,160)(124,159)(125,158)
(126,152)(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)
(134,164)(135,163)(181,277)(182,276)(183,280)(184,279)(185,278)(186,272)
(187,271)(188,275)(189,274)(190,273)(191,282)(192,281)(193,285)(194,284)
(195,283)(196,307)(197,306)(198,310)(199,309)(200,308)(201,302)(202,301)
(203,305)(204,304)(205,303)(206,312)(207,311)(208,315)(209,314)(210,313)
(211,292)(212,291)(213,295)(214,294)(215,293)(216,287)(217,286)(218,290)
(219,289)(220,288)(221,297)(222,296)(223,300)(224,299)(225,298)(226,322)
(227,321)(228,325)(229,324)(230,323)(231,317)(232,316)(233,320)(234,319)
(235,318)(236,327)(237,326)(238,330)(239,329)(240,328)(241,352)(242,351)
(243,355)(244,354)(245,353)(246,347)(247,346)(248,350)(249,349)(250,348)
(251,357)(252,356)(253,360)(254,359)(255,358)(256,337)(257,336)(258,340)
(259,339)(260,338)(261,332)(262,331)(263,335)(264,334)(265,333)(266,342)
(267,341)(268,345)(269,344)(270,343);
s2 := Sym(360)!( 1,196)( 2,197)( 3,198)( 4,199)( 5,200)( 6,201)( 7,202)
( 8,203)( 9,204)( 10,205)( 11,206)( 12,207)( 13,208)( 14,209)( 15,210)
( 16,181)( 17,182)( 18,183)( 19,184)( 20,185)( 21,186)( 22,187)( 23,188)
( 24,189)( 25,190)( 26,191)( 27,192)( 28,193)( 29,194)( 30,195)( 31,211)
( 32,212)( 33,213)( 34,214)( 35,215)( 36,216)( 37,217)( 38,218)( 39,219)
( 40,220)( 41,221)( 42,222)( 43,223)( 44,224)( 45,225)( 46,241)( 47,242)
( 48,243)( 49,244)( 50,245)( 51,246)( 52,247)( 53,248)( 54,249)( 55,250)
( 56,251)( 57,252)( 58,253)( 59,254)( 60,255)( 61,226)( 62,227)( 63,228)
( 64,229)( 65,230)( 66,231)( 67,232)( 68,233)( 69,234)( 70,235)( 71,236)
( 72,237)( 73,238)( 74,239)( 75,240)( 76,256)( 77,257)( 78,258)( 79,259)
( 80,260)( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)
(112,322)(113,323)(114,324)(115,325)(116,326)(117,327)(118,328)(119,329)
(120,330)(121,346)(122,347)(123,348)(124,349)(125,350)(126,351)(127,352)
(128,353)(129,354)(130,355)(131,356)(132,357)(133,358)(134,359)(135,360)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,291)(142,292)(143,293)
(144,294)(145,295)(146,296)(147,297)(148,298)(149,299)(150,300)(151,271)
(152,272)(153,273)(154,274)(155,275)(156,276)(157,277)(158,278)(159,279)
(160,280)(161,281)(162,282)(163,283)(164,284)(165,285)(166,301)(167,302)
(168,303)(169,304)(170,305)(171,306)(172,307)(173,308)(174,309)(175,310)
(176,311)(177,312)(178,313)(179,314)(180,315);
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*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 >;
References : None.
to this polytope