Polytope of Type {30,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,24}*1440c
if this polytope has a name.
Group : SmallGroup(1440,3811)
Rank : 3
Schlafli Type : {30,24}
Number of vertices, edges, etc : 30, 360, 24
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 : {30,12}*720c
   3-fold quotients : {30,8}*480
   4-fold quotients : {30,6}*360c
   5-fold quotients : {6,24}*288c
   6-fold quotients : {30,4}*240a
   8-fold quotients : {15,6}*180
   9-fold quotients : {10,8}*160
   10-fold quotients : {6,12}*144c
   12-fold quotients : {30,2}*120
   15-fold quotients : {6,8}*96
   18-fold quotients : {10,4}*80
   20-fold quotients : {6,6}*72c
   24-fold quotients : {15,2}*60
   30-fold quotients : {6,4}*48a
   36-fold quotients : {10,2}*40
   40-fold quotients : {3,6}*36
   45-fold quotients : {2,8}*32
   60-fold quotients : {6,2}*24
   72-fold quotients : {5,2}*20
   90-fold quotients : {2,4}*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)( 92, 95)( 93, 94)( 96,101)( 97,105)
( 98,104)( 99,103)(100,102)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,131)(112,135)(113,134)(114,133)(115,132)(116,126)(117,130)(118,129)
(119,128)(120,127)(137,140)(138,139)(141,146)(142,150)(143,149)(144,148)
(145,147)(151,166)(152,170)(153,169)(154,168)(155,167)(156,176)(157,180)
(158,179)(159,178)(160,177)(161,171)(162,175)(163,174)(164,173)(165,172)
(182,185)(183,184)(186,191)(187,195)(188,194)(189,193)(190,192)(196,211)
(197,215)(198,214)(199,213)(200,212)(201,221)(202,225)(203,224)(204,223)
(205,222)(206,216)(207,220)(208,219)(209,218)(210,217)(227,230)(228,229)
(231,236)(232,240)(233,239)(234,238)(235,237)(241,256)(242,260)(243,259)
(244,258)(245,257)(246,266)(247,270)(248,269)(249,268)(250,267)(251,261)
(252,265)(253,264)(254,263)(255,262)(272,275)(273,274)(276,281)(277,285)
(278,284)(279,283)(280,282)(286,301)(287,305)(288,304)(289,303)(290,302)
(291,311)(292,315)(293,314)(294,313)(295,312)(296,306)(297,310)(298,309)
(299,308)(300,307)(317,320)(318,319)(321,326)(322,330)(323,329)(324,328)
(325,327)(331,346)(332,350)(333,349)(334,348)(335,347)(336,356)(337,360)
(338,359)(339,358)(340,357)(341,351)(342,355)(343,354)(344,353)(345,352);;
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)( 91,136)( 92,137)
( 93,138)( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)
(101,146)(102,147)(103,148)(104,149)(105,150)(106,166)(107,167)(108,168)
(109,169)(110,170)(111,171)(112,172)(113,173)(114,174)(115,175)(116,176)
(117,177)(118,178)(119,179)(120,180)(121,151)(122,152)(123,153)(124,154)
(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)
(133,163)(134,164)(135,165)(181,271)(182,272)(183,273)(184,274)(185,275)
(186,276)(187,277)(188,278)(189,279)(190,280)(191,281)(192,282)(193,283)
(194,284)(195,285)(196,301)(197,302)(198,303)(199,304)(200,305)(201,306)
(202,307)(203,308)(204,309)(205,310)(206,311)(207,312)(208,313)(209,314)
(210,315)(211,286)(212,287)(213,288)(214,289)(215,290)(216,291)(217,292)
(218,293)(219,294)(220,295)(221,296)(222,297)(223,298)(224,299)(225,300)
(226,316)(227,317)(228,318)(229,319)(230,320)(231,321)(232,322)(233,323)
(234,324)(235,325)(236,326)(237,327)(238,328)(239,329)(240,330)(241,346)
(242,347)(243,348)(244,349)(245,350)(246,351)(247,352)(248,353)(249,354)
(250,355)(251,356)(252,357)(253,358)(254,359)(255,360)(256,331)(257,332)
(258,333)(259,334)(260,335)(261,336)(262,337)(263,338)(264,339)(265,340)
(266,341)(267,342)(268,343)(269,344)(270,345);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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 ];;
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)( 92, 95)( 93, 94)( 96,101)
( 97,105)( 98,104)( 99,103)(100,102)(106,121)(107,125)(108,124)(109,123)
(110,122)(111,131)(112,135)(113,134)(114,133)(115,132)(116,126)(117,130)
(118,129)(119,128)(120,127)(137,140)(138,139)(141,146)(142,150)(143,149)
(144,148)(145,147)(151,166)(152,170)(153,169)(154,168)(155,167)(156,176)
(157,180)(158,179)(159,178)(160,177)(161,171)(162,175)(163,174)(164,173)
(165,172)(182,185)(183,184)(186,191)(187,195)(188,194)(189,193)(190,192)
(196,211)(197,215)(198,214)(199,213)(200,212)(201,221)(202,225)(203,224)
(204,223)(205,222)(206,216)(207,220)(208,219)(209,218)(210,217)(227,230)
(228,229)(231,236)(232,240)(233,239)(234,238)(235,237)(241,256)(242,260)
(243,259)(244,258)(245,257)(246,266)(247,270)(248,269)(249,268)(250,267)
(251,261)(252,265)(253,264)(254,263)(255,262)(272,275)(273,274)(276,281)
(277,285)(278,284)(279,283)(280,282)(286,301)(287,305)(288,304)(289,303)
(290,302)(291,311)(292,315)(293,314)(294,313)(295,312)(296,306)(297,310)
(298,309)(299,308)(300,307)(317,320)(318,319)(321,326)(322,330)(323,329)
(324,328)(325,327)(331,346)(332,350)(333,349)(334,348)(335,347)(336,356)
(337,360)(338,359)(339,358)(340,357)(341,351)(342,355)(343,354)(344,353)
(345,352);
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)( 91,136)
( 92,137)( 93,138)( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)
(100,145)(101,146)(102,147)(103,148)(104,149)(105,150)(106,166)(107,167)
(108,168)(109,169)(110,170)(111,171)(112,172)(113,173)(114,174)(115,175)
(116,176)(117,177)(118,178)(119,179)(120,180)(121,151)(122,152)(123,153)
(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)
(132,162)(133,163)(134,164)(135,165)(181,271)(182,272)(183,273)(184,274)
(185,275)(186,276)(187,277)(188,278)(189,279)(190,280)(191,281)(192,282)
(193,283)(194,284)(195,285)(196,301)(197,302)(198,303)(199,304)(200,305)
(201,306)(202,307)(203,308)(204,309)(205,310)(206,311)(207,312)(208,313)
(209,314)(210,315)(211,286)(212,287)(213,288)(214,289)(215,290)(216,291)
(217,292)(218,293)(219,294)(220,295)(221,296)(222,297)(223,298)(224,299)
(225,300)(226,316)(227,317)(228,318)(229,319)(230,320)(231,321)(232,322)
(233,323)(234,324)(235,325)(236,326)(237,327)(238,328)(239,329)(240,330)
(241,346)(242,347)(243,348)(244,349)(245,350)(246,351)(247,352)(248,353)
(249,354)(250,355)(251,356)(252,357)(253,358)(254,359)(255,360)(256,331)
(257,332)(258,333)(259,334)(260,335)(261,336)(262,337)(263,338)(264,339)
(265,340)(266,341)(267,342)(268,343)(269,344)(270,345);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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 >;

References : None.
to this polytope