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# Polytope of Type {24,30}

Atlas Canonical Name : {24,30}*1440c
if this polytope has a name.
Group : SmallGroup(1440,3811)
Rank : 3
Schlafli Type : {24,30}
Number of vertices, edges, etc : 24, 360, 30
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 : {12,30}*720c
3-fold quotients : {8,30}*480
4-fold quotients : {6,30}*360c
5-fold quotients : {24,6}*288c
6-fold quotients : {4,30}*240a
8-fold quotients : {6,15}*180
9-fold quotients : {8,10}*160
10-fold quotients : {12,6}*144c
12-fold quotients : {2,30}*120
15-fold quotients : {8,6}*96
18-fold quotients : {4,10}*80
20-fold quotients : {6,6}*72b
24-fold quotients : {2,15}*60
30-fold quotients : {4,6}*48a
36-fold quotients : {2,10}*40
40-fold quotients : {6,3}*36
45-fold quotients : {8,2}*32
60-fold quotients : {2,6}*24
72-fold quotients : {2,5}*20
90-fold quotients : {4,2}*16
120-fold quotients : {2,3}*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, 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, 97)( 92, 96)( 93,100)( 94, 99)
( 95, 98)(101,102)(103,105)(106,127)(107,126)(108,130)(109,129)(110,128)
(111,122)(112,121)(113,125)(114,124)(115,123)(116,132)(117,131)(118,135)
(119,134)(120,133)(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)
(148,150)(151,172)(152,171)(153,175)(154,174)(155,173)(156,167)(157,166)
(158,170)(159,169)(160,168)(161,177)(162,176)(163,180)(164,179)(165,178)
(181,187)(182,186)(183,190)(184,189)(185,188)(191,192)(193,195)(196,217)
(197,216)(198,220)(199,219)(200,218)(201,212)(202,211)(203,215)(204,214)
(205,213)(206,222)(207,221)(208,225)(209,224)(210,223)(226,232)(227,231)
(228,235)(229,234)(230,233)(236,237)(238,240)(241,262)(242,261)(243,265)
(244,264)(245,263)(246,257)(247,256)(248,260)(249,259)(250,258)(251,267)
(252,266)(253,270)(254,269)(255,268)(271,277)(272,276)(273,280)(274,279)
(275,278)(281,282)(283,285)(286,307)(287,306)(288,310)(289,309)(290,308)
(291,302)(292,301)(293,305)(294,304)(295,303)(296,312)(297,311)(298,315)
(299,314)(300,313)(316,322)(317,321)(318,325)(319,324)(320,323)(326,327)
(328,330)(331,352)(332,351)(333,355)(334,354)(335,353)(336,347)(337,346)
(338,350)(339,349)(340,348)(341,357)(342,356)(343,360)(344,359)(345,358);;
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*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*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,
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, 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, 97)( 92, 96)( 93,100)
( 94, 99)( 95, 98)(101,102)(103,105)(106,127)(107,126)(108,130)(109,129)
(110,128)(111,122)(112,121)(113,125)(114,124)(115,123)(116,132)(117,131)
(118,135)(119,134)(120,133)(136,142)(137,141)(138,145)(139,144)(140,143)
(146,147)(148,150)(151,172)(152,171)(153,175)(154,174)(155,173)(156,167)
(157,166)(158,170)(159,169)(160,168)(161,177)(162,176)(163,180)(164,179)
(165,178)(181,187)(182,186)(183,190)(184,189)(185,188)(191,192)(193,195)
(196,217)(197,216)(198,220)(199,219)(200,218)(201,212)(202,211)(203,215)
(204,214)(205,213)(206,222)(207,221)(208,225)(209,224)(210,223)(226,232)
(227,231)(228,235)(229,234)(230,233)(236,237)(238,240)(241,262)(242,261)
(243,265)(244,264)(245,263)(246,257)(247,256)(248,260)(249,259)(250,258)
(251,267)(252,266)(253,270)(254,269)(255,268)(271,277)(272,276)(273,280)
(274,279)(275,278)(281,282)(283,285)(286,307)(287,306)(288,310)(289,309)
(290,308)(291,302)(292,301)(293,305)(294,304)(295,303)(296,312)(297,311)
(298,315)(299,314)(300,313)(316,322)(317,321)(318,325)(319,324)(320,323)
(326,327)(328,330)(331,352)(332,351)(333,355)(334,354)(335,353)(336,347)
(337,346)(338,350)(339,349)(340,348)(341,357)(342,356)(343,360)(344,359)
(345,358);
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*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*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,
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