Polytope of Type {24,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,30}*1440b
Also Known As : {24,30|2}. if this polytope has another name.
Group : SmallGroup(1440,3578)
Rank : 3
Schlafli Type : {24,30}
Number of vertices, edges, etc : 24, 360, 30
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 : {12,30}*720b
   3-fold quotients : {24,10}*480, {8,30}*480
   4-fold quotients : {6,30}*360b
   5-fold quotients : {24,6}*288a
   6-fold quotients : {12,10}*240, {4,30}*240a
   9-fold quotients : {8,10}*160
   10-fold quotients : {12,6}*144a
   12-fold quotients : {6,10}*120, {2,30}*120
   15-fold quotients : {24,2}*96, {8,6}*96
   18-fold quotients : {4,10}*80
   20-fold quotients : {6,6}*72a
   24-fold quotients : {2,15}*60
   30-fold quotients : {12,2}*48, {4,6}*48a
   36-fold quotients : {2,10}*40
   45-fold quotients : {8,2}*32
   60-fold quotients : {2,6}*24, {6,2}*24
   72-fold quotients : {2,5}*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 := ( 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);;
s1 := (  1,196)(  2,200)(  3,199)(  4,198)(  5,197)(  6,206)(  7,210)(  8,209)
(  9,208)( 10,207)( 11,201)( 12,205)( 13,204)( 14,203)( 15,202)( 16,181)
( 17,185)( 18,184)( 19,183)( 20,182)( 21,191)( 22,195)( 23,194)( 24,193)
( 25,192)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,211)( 32,215)
( 33,214)( 34,213)( 35,212)( 36,221)( 37,225)( 38,224)( 39,223)( 40,222)
( 41,216)( 42,220)( 43,219)( 44,218)( 45,217)( 46,241)( 47,245)( 48,244)
( 49,243)( 50,242)( 51,251)( 52,255)( 53,254)( 54,253)( 55,252)( 56,246)
( 57,250)( 58,249)( 59,248)( 60,247)( 61,226)( 62,230)( 63,229)( 64,228)
( 65,227)( 66,236)( 67,240)( 68,239)( 69,238)( 70,237)( 71,231)( 72,235)
( 73,234)( 74,233)( 75,232)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,266)( 82,270)( 83,269)( 84,268)( 85,267)( 86,261)( 87,265)( 88,264)
( 89,263)( 90,262)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,341)
( 97,345)( 98,344)( 99,343)(100,342)(101,336)(102,340)(103,339)(104,338)
(105,337)(106,316)(107,320)(108,319)(109,318)(110,317)(111,326)(112,330)
(113,329)(114,328)(115,327)(116,321)(117,325)(118,324)(119,323)(120,322)
(121,346)(122,350)(123,349)(124,348)(125,347)(126,356)(127,360)(128,359)
(129,358)(130,357)(131,351)(132,355)(133,354)(134,353)(135,352)(136,286)
(137,290)(138,289)(139,288)(140,287)(141,296)(142,300)(143,299)(144,298)
(145,297)(146,291)(147,295)(148,294)(149,293)(150,292)(151,271)(152,275)
(153,274)(154,273)(155,272)(156,281)(157,285)(158,284)(159,283)(160,282)
(161,276)(162,280)(163,279)(164,278)(165,277)(166,301)(167,305)(168,304)
(169,303)(170,302)(171,311)(172,315)(173,314)(174,313)(175,312)(176,306)
(177,310)(178,309)(179,308)(180,307);;
s2 := (  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 67)( 62, 66)( 63, 70)( 64, 69)
( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)( 80, 83)
( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,102)
(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)(118,120)
(121,127)(122,126)(123,130)(124,129)(125,128)(131,132)(133,135)(136,142)
(137,141)(138,145)(139,144)(140,143)(146,147)(148,150)(151,157)(152,156)
(153,160)(154,159)(155,158)(161,162)(163,165)(166,172)(167,171)(168,175)
(169,174)(170,173)(176,177)(178,180)(181,187)(182,186)(183,190)(184,189)
(185,188)(191,192)(193,195)(196,202)(197,201)(198,205)(199,204)(200,203)
(206,207)(208,210)(211,217)(212,216)(213,220)(214,219)(215,218)(221,222)
(223,225)(226,232)(227,231)(228,235)(229,234)(230,233)(236,237)(238,240)
(241,247)(242,246)(243,250)(244,249)(245,248)(251,252)(253,255)(256,262)
(257,261)(258,265)(259,264)(260,263)(266,267)(268,270)(271,277)(272,276)
(273,280)(274,279)(275,278)(281,282)(283,285)(286,292)(287,291)(288,295)
(289,294)(290,293)(296,297)(298,300)(301,307)(302,306)(303,310)(304,309)
(305,308)(311,312)(313,315)(316,322)(317,321)(318,325)(319,324)(320,323)
(326,327)(328,330)(331,337)(332,336)(333,340)(334,339)(335,338)(341,342)
(343,345)(346,352)(347,351)(348,355)(349,354)(350,353)(356,357)(358,360);;
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, s0*s1*s2*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, 
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)( 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);
s1 := Sym(360)!(  1,196)(  2,200)(  3,199)(  4,198)(  5,197)(  6,206)(  7,210)
(  8,209)(  9,208)( 10,207)( 11,201)( 12,205)( 13,204)( 14,203)( 15,202)
( 16,181)( 17,185)( 18,184)( 19,183)( 20,182)( 21,191)( 22,195)( 23,194)
( 24,193)( 25,192)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,211)
( 32,215)( 33,214)( 34,213)( 35,212)( 36,221)( 37,225)( 38,224)( 39,223)
( 40,222)( 41,216)( 42,220)( 43,219)( 44,218)( 45,217)( 46,241)( 47,245)
( 48,244)( 49,243)( 50,242)( 51,251)( 52,255)( 53,254)( 54,253)( 55,252)
( 56,246)( 57,250)( 58,249)( 59,248)( 60,247)( 61,226)( 62,230)( 63,229)
( 64,228)( 65,227)( 66,236)( 67,240)( 68,239)( 69,238)( 70,237)( 71,231)
( 72,235)( 73,234)( 74,233)( 75,232)( 76,256)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,266)( 82,270)( 83,269)( 84,268)( 85,267)( 86,261)( 87,265)
( 88,264)( 89,263)( 90,262)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)
( 96,341)( 97,345)( 98,344)( 99,343)(100,342)(101,336)(102,340)(103,339)
(104,338)(105,337)(106,316)(107,320)(108,319)(109,318)(110,317)(111,326)
(112,330)(113,329)(114,328)(115,327)(116,321)(117,325)(118,324)(119,323)
(120,322)(121,346)(122,350)(123,349)(124,348)(125,347)(126,356)(127,360)
(128,359)(129,358)(130,357)(131,351)(132,355)(133,354)(134,353)(135,352)
(136,286)(137,290)(138,289)(139,288)(140,287)(141,296)(142,300)(143,299)
(144,298)(145,297)(146,291)(147,295)(148,294)(149,293)(150,292)(151,271)
(152,275)(153,274)(154,273)(155,272)(156,281)(157,285)(158,284)(159,283)
(160,282)(161,276)(162,280)(163,279)(164,278)(165,277)(166,301)(167,305)
(168,304)(169,303)(170,302)(171,311)(172,315)(173,314)(174,313)(175,312)
(176,306)(177,310)(178,309)(179,308)(180,307);
s2 := Sym(360)!(  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 67)( 62, 66)( 63, 70)
( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)
(101,102)(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)
(118,120)(121,127)(122,126)(123,130)(124,129)(125,128)(131,132)(133,135)
(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)(148,150)(151,157)
(152,156)(153,160)(154,159)(155,158)(161,162)(163,165)(166,172)(167,171)
(168,175)(169,174)(170,173)(176,177)(178,180)(181,187)(182,186)(183,190)
(184,189)(185,188)(191,192)(193,195)(196,202)(197,201)(198,205)(199,204)
(200,203)(206,207)(208,210)(211,217)(212,216)(213,220)(214,219)(215,218)
(221,222)(223,225)(226,232)(227,231)(228,235)(229,234)(230,233)(236,237)
(238,240)(241,247)(242,246)(243,250)(244,249)(245,248)(251,252)(253,255)
(256,262)(257,261)(258,265)(259,264)(260,263)(266,267)(268,270)(271,277)
(272,276)(273,280)(274,279)(275,278)(281,282)(283,285)(286,292)(287,291)
(288,295)(289,294)(290,293)(296,297)(298,300)(301,307)(302,306)(303,310)
(304,309)(305,308)(311,312)(313,315)(316,322)(317,321)(318,325)(319,324)
(320,323)(326,327)(328,330)(331,337)(332,336)(333,340)(334,339)(335,338)
(341,342)(343,345)(346,352)(347,351)(348,355)(349,354)(350,353)(356,357)
(358,360);
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, s0*s1*s2*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, 
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