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# Polytope of Type {30,12}

Atlas Canonical Name : {30,12}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 3
Schlafli Type : {30,12}
Number of vertices, edges, etc : 60, 360, 24
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {30,12}*720d
3-fold quotients : {30,4}*480
4-fold quotients : {30,6}*360b
5-fold quotients : {6,12}*288a
6-fold quotients : {15,4}*240, {30,4}*240b, {30,4}*240c
10-fold quotients : {6,12}*144d
12-fold quotients : {15,4}*120, {10,6}*120, {30,2}*120
15-fold quotients : {6,4}*96
20-fold quotients : {6,6}*72a
24-fold quotients : {15,2}*60
30-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
36-fold quotients : {10,2}*40
60-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
72-fold quotients : {5,2}*20
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 := (  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)
( 12, 15)( 23, 24)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 33)( 30, 34)
( 31, 36)( 32, 35)( 43, 44)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 49, 53)
( 50, 54)( 51, 56)( 52, 55)( 61,121)( 62,122)( 63,124)( 64,123)( 65,137)
( 66,138)( 67,140)( 68,139)( 69,133)( 70,134)( 71,136)( 72,135)( 73,129)
( 74,130)( 75,132)( 76,131)( 77,125)( 78,126)( 79,128)( 80,127)( 81,141)
( 82,142)( 83,144)( 84,143)( 85,157)( 86,158)( 87,160)( 88,159)( 89,153)
( 90,154)( 91,156)( 92,155)( 93,149)( 94,150)( 95,152)( 96,151)( 97,145)
( 98,146)( 99,148)(100,147)(101,161)(102,162)(103,164)(104,163)(105,177)
(106,178)(107,180)(108,179)(109,173)(110,174)(111,176)(112,175)(113,169)
(114,170)(115,172)(116,171)(117,165)(118,166)(119,168)(120,167)(183,184)
(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)
(203,204)(205,217)(206,218)(207,220)(208,219)(209,213)(210,214)(211,216)
(212,215)(223,224)(225,237)(226,238)(227,240)(228,239)(229,233)(230,234)
(231,236)(232,235)(241,301)(242,302)(243,304)(244,303)(245,317)(246,318)
(247,320)(248,319)(249,313)(250,314)(251,316)(252,315)(253,309)(254,310)
(255,312)(256,311)(257,305)(258,306)(259,308)(260,307)(261,321)(262,322)
(263,324)(264,323)(265,337)(266,338)(267,340)(268,339)(269,333)(270,334)
(271,336)(272,335)(273,329)(274,330)(275,332)(276,331)(277,325)(278,326)
(279,328)(280,327)(281,341)(282,342)(283,344)(284,343)(285,357)(286,358)
(287,360)(288,359)(289,353)(290,354)(291,356)(292,355)(293,349)(294,350)
(295,352)(296,351)(297,345)(298,346)(299,348)(300,347);;
s1 := (  1, 65)(  2, 68)(  3, 67)(  4, 66)(  5, 61)(  6, 64)(  7, 63)(  8, 62)
(  9, 77)( 10, 80)( 11, 79)( 12, 78)( 13, 73)( 14, 76)( 15, 75)( 16, 74)
( 17, 69)( 18, 72)( 19, 71)( 20, 70)( 21,105)( 22,108)( 23,107)( 24,106)
( 25,101)( 26,104)( 27,103)( 28,102)( 29,117)( 30,120)( 31,119)( 32,118)
( 33,113)( 34,116)( 35,115)( 36,114)( 37,109)( 38,112)( 39,111)( 40,110)
( 41, 85)( 42, 88)( 43, 87)( 44, 86)( 45, 81)( 46, 84)( 47, 83)( 48, 82)
( 49, 97)( 50,100)( 51, 99)( 52, 98)( 53, 93)( 54, 96)( 55, 95)( 56, 94)
( 57, 89)( 58, 92)( 59, 91)( 60, 90)(121,125)(122,128)(123,127)(124,126)
(129,137)(130,140)(131,139)(132,138)(134,136)(141,165)(142,168)(143,167)
(144,166)(145,161)(146,164)(147,163)(148,162)(149,177)(150,180)(151,179)
(152,178)(153,173)(154,176)(155,175)(156,174)(157,169)(158,172)(159,171)
(160,170)(181,245)(182,248)(183,247)(184,246)(185,241)(186,244)(187,243)
(188,242)(189,257)(190,260)(191,259)(192,258)(193,253)(194,256)(195,255)
(196,254)(197,249)(198,252)(199,251)(200,250)(201,285)(202,288)(203,287)
(204,286)(205,281)(206,284)(207,283)(208,282)(209,297)(210,300)(211,299)
(212,298)(213,293)(214,296)(215,295)(216,294)(217,289)(218,292)(219,291)
(220,290)(221,265)(222,268)(223,267)(224,266)(225,261)(226,264)(227,263)
(228,262)(229,277)(230,280)(231,279)(232,278)(233,273)(234,276)(235,275)
(236,274)(237,269)(238,272)(239,271)(240,270)(301,305)(302,308)(303,307)
(304,306)(309,317)(310,320)(311,319)(312,318)(314,316)(321,345)(322,348)
(323,347)(324,346)(325,341)(326,344)(327,343)(328,342)(329,357)(330,360)
(331,359)(332,358)(333,353)(334,356)(335,355)(336,354)(337,349)(338,352)
(339,351)(340,350);;
s2 := (  1,202)(  2,201)(  3,204)(  4,203)(  5,206)(  6,205)(  7,208)(  8,207)
(  9,210)( 10,209)( 11,212)( 12,211)( 13,214)( 14,213)( 15,216)( 16,215)
( 17,218)( 18,217)( 19,220)( 20,219)( 21,182)( 22,181)( 23,184)( 24,183)
( 25,186)( 26,185)( 27,188)( 28,187)( 29,190)( 30,189)( 31,192)( 32,191)
( 33,194)( 34,193)( 35,196)( 36,195)( 37,198)( 38,197)( 39,200)( 40,199)
( 41,222)( 42,221)( 43,224)( 44,223)( 45,226)( 46,225)( 47,228)( 48,227)
( 49,230)( 50,229)( 51,232)( 52,231)( 53,234)( 54,233)( 55,236)( 56,235)
( 57,238)( 58,237)( 59,240)( 60,239)( 61,262)( 62,261)( 63,264)( 64,263)
( 65,266)( 66,265)( 67,268)( 68,267)( 69,270)( 70,269)( 71,272)( 72,271)
( 73,274)( 74,273)( 75,276)( 76,275)( 77,278)( 78,277)( 79,280)( 80,279)
( 81,242)( 82,241)( 83,244)( 84,243)( 85,246)( 86,245)( 87,248)( 88,247)
( 89,250)( 90,249)( 91,252)( 92,251)( 93,254)( 94,253)( 95,256)( 96,255)
( 97,258)( 98,257)( 99,260)(100,259)(101,282)(102,281)(103,284)(104,283)
(105,286)(106,285)(107,288)(108,287)(109,290)(110,289)(111,292)(112,291)
(113,294)(114,293)(115,296)(116,295)(117,298)(118,297)(119,300)(120,299)
(121,322)(122,321)(123,324)(124,323)(125,326)(126,325)(127,328)(128,327)
(129,330)(130,329)(131,332)(132,331)(133,334)(134,333)(135,336)(136,335)
(137,338)(138,337)(139,340)(140,339)(141,302)(142,301)(143,304)(144,303)
(145,306)(146,305)(147,308)(148,307)(149,310)(150,309)(151,312)(152,311)
(153,314)(154,313)(155,316)(156,315)(157,318)(158,317)(159,320)(160,319)
(161,342)(162,341)(163,344)(164,343)(165,346)(166,345)(167,348)(168,347)
(169,350)(170,349)(171,352)(172,351)(173,354)(174,353)(175,356)(176,355)
(177,358)(178,357)(179,360)(180,359);;
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*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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 ];;
poly := F / rels;;

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

```
References : None.
to this polytope