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Polytope of Type {30,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6,4}*1440e
if this polytope has a name.
Group : SmallGroup(1440,5901)
Rank : 4
Schlafli Type : {30,6,4}
Number of vertices, edges, etc : 30, 90, 12, 4
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Non-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) :
   3-fold quotients : {10,6,4}*480b
   5-fold quotients : {6,6,4}*288d
   15-fold quotients : {2,6,4}*96c
   30-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)
( 21, 41)( 22, 42)( 23, 43)( 24, 44)( 25, 57)( 26, 58)( 27, 59)( 28, 60)
( 29, 53)( 30, 54)( 31, 55)( 32, 56)( 33, 49)( 34, 50)( 35, 51)( 36, 52)
( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 65, 77)( 66, 78)( 67, 79)( 68, 80)
( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 81,101)( 82,102)( 83,103)( 84,104)
( 85,117)( 86,118)( 87,119)( 88,120)( 89,113)( 90,114)( 91,115)( 92,116)
( 93,109)( 94,110)( 95,111)( 96,112)( 97,105)( 98,106)( 99,107)(100,108)
(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)
(141,161)(142,162)(143,163)(144,164)(145,177)(146,178)(147,179)(148,180)
(149,173)(150,174)(151,175)(152,176)(153,169)(154,170)(155,171)(156,172)
(157,165)(158,166)(159,167)(160,168)(185,197)(186,198)(187,199)(188,200)
(189,193)(190,194)(191,195)(192,196)(201,221)(202,222)(203,223)(204,224)
(205,237)(206,238)(207,239)(208,240)(209,233)(210,234)(211,235)(212,236)
(213,229)(214,230)(215,231)(216,232)(217,225)(218,226)(219,227)(220,228)
(245,257)(246,258)(247,259)(248,260)(249,253)(250,254)(251,255)(252,256)
(261,281)(262,282)(263,283)(264,284)(265,297)(266,298)(267,299)(268,300)
(269,293)(270,294)(271,295)(272,296)(273,289)(274,290)(275,291)(276,292)
(277,285)(278,286)(279,287)(280,288)(305,317)(306,318)(307,319)(308,320)
(309,313)(310,314)(311,315)(312,316)(321,341)(322,342)(323,343)(324,344)
(325,357)(326,358)(327,359)(328,360)(329,353)(330,354)(331,355)(332,356)
(333,349)(334,350)(335,351)(336,352)(337,345)(338,346)(339,347)(340,348);;
s1 := (  1, 25)(  2, 26)(  3, 28)(  4, 27)(  5, 21)(  6, 22)(  7, 24)(  8, 23)
(  9, 37)( 10, 38)( 11, 40)( 12, 39)( 13, 33)( 14, 34)( 15, 36)( 16, 35)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 41, 45)( 42, 46)( 43, 48)( 44, 47)
( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 55, 56)( 61,145)( 62,146)( 63,148)
( 64,147)( 65,141)( 66,142)( 67,144)( 68,143)( 69,157)( 70,158)( 71,160)
( 72,159)( 73,153)( 74,154)( 75,156)( 76,155)( 77,149)( 78,150)( 79,152)
( 80,151)( 81,125)( 82,126)( 83,128)( 84,127)( 85,121)( 86,122)( 87,124)
( 88,123)( 89,137)( 90,138)( 91,140)( 92,139)( 93,133)( 94,134)( 95,136)
( 96,135)( 97,129)( 98,130)( 99,132)(100,131)(101,165)(102,166)(103,168)
(104,167)(105,161)(106,162)(107,164)(108,163)(109,177)(110,178)(111,180)
(112,179)(113,173)(114,174)(115,176)(116,175)(117,169)(118,170)(119,172)
(120,171)(181,205)(182,206)(183,208)(184,207)(185,201)(186,202)(187,204)
(188,203)(189,217)(190,218)(191,220)(192,219)(193,213)(194,214)(195,216)
(196,215)(197,209)(198,210)(199,212)(200,211)(221,225)(222,226)(223,228)
(224,227)(229,237)(230,238)(231,240)(232,239)(235,236)(241,325)(242,326)
(243,328)(244,327)(245,321)(246,322)(247,324)(248,323)(249,337)(250,338)
(251,340)(252,339)(253,333)(254,334)(255,336)(256,335)(257,329)(258,330)
(259,332)(260,331)(261,305)(262,306)(263,308)(264,307)(265,301)(266,302)
(267,304)(268,303)(269,317)(270,318)(271,320)(272,319)(273,313)(274,314)
(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)(281,345)(282,346)
(283,348)(284,347)(285,341)(286,342)(287,344)(288,343)(289,357)(290,358)
(291,360)(292,359)(293,353)(294,354)(295,356)(296,355)(297,349)(298,350)
(299,352)(300,351);;
s2 := (  1,241)(  2,244)(  3,243)(  4,242)(  5,245)(  6,248)(  7,247)(  8,246)
(  9,249)( 10,252)( 11,251)( 12,250)( 13,253)( 14,256)( 15,255)( 16,254)
( 17,257)( 18,260)( 19,259)( 20,258)( 21,261)( 22,264)( 23,263)( 24,262)
( 25,265)( 26,268)( 27,267)( 28,266)( 29,269)( 30,272)( 31,271)( 32,270)
( 33,273)( 34,276)( 35,275)( 36,274)( 37,277)( 38,280)( 39,279)( 40,278)
( 41,281)( 42,284)( 43,283)( 44,282)( 45,285)( 46,288)( 47,287)( 48,286)
( 49,289)( 50,292)( 51,291)( 52,290)( 53,293)( 54,296)( 55,295)( 56,294)
( 57,297)( 58,300)( 59,299)( 60,298)( 61,181)( 62,184)( 63,183)( 64,182)
( 65,185)( 66,188)( 67,187)( 68,186)( 69,189)( 70,192)( 71,191)( 72,190)
( 73,193)( 74,196)( 75,195)( 76,194)( 77,197)( 78,200)( 79,199)( 80,198)
( 81,201)( 82,204)( 83,203)( 84,202)( 85,205)( 86,208)( 87,207)( 88,206)
( 89,209)( 90,212)( 91,211)( 92,210)( 93,213)( 94,216)( 95,215)( 96,214)
( 97,217)( 98,220)( 99,219)(100,218)(101,221)(102,224)(103,223)(104,222)
(105,225)(106,228)(107,227)(108,226)(109,229)(110,232)(111,231)(112,230)
(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)(120,238)
(121,301)(122,304)(123,303)(124,302)(125,305)(126,308)(127,307)(128,306)
(129,309)(130,312)(131,311)(132,310)(133,313)(134,316)(135,315)(136,314)
(137,317)(138,320)(139,319)(140,318)(141,321)(142,324)(143,323)(144,322)
(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)(152,330)
(153,333)(154,336)(155,335)(156,334)(157,337)(158,340)(159,339)(160,338)
(161,341)(162,344)(163,343)(164,342)(165,345)(166,348)(167,347)(168,346)
(169,349)(170,352)(171,351)(172,350)(173,353)(174,356)(175,355)(176,354)
(177,357)(178,360)(179,359)(180,358);;
s3 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*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)!(  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)
( 12, 16)( 21, 41)( 22, 42)( 23, 43)( 24, 44)( 25, 57)( 26, 58)( 27, 59)
( 28, 60)( 29, 53)( 30, 54)( 31, 55)( 32, 56)( 33, 49)( 34, 50)( 35, 51)
( 36, 52)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 65, 77)( 66, 78)( 67, 79)
( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 81,101)( 82,102)( 83,103)
( 84,104)( 85,117)( 86,118)( 87,119)( 88,120)( 89,113)( 90,114)( 91,115)
( 92,116)( 93,109)( 94,110)( 95,111)( 96,112)( 97,105)( 98,106)( 99,107)
(100,108)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)
(132,136)(141,161)(142,162)(143,163)(144,164)(145,177)(146,178)(147,179)
(148,180)(149,173)(150,174)(151,175)(152,176)(153,169)(154,170)(155,171)
(156,172)(157,165)(158,166)(159,167)(160,168)(185,197)(186,198)(187,199)
(188,200)(189,193)(190,194)(191,195)(192,196)(201,221)(202,222)(203,223)
(204,224)(205,237)(206,238)(207,239)(208,240)(209,233)(210,234)(211,235)
(212,236)(213,229)(214,230)(215,231)(216,232)(217,225)(218,226)(219,227)
(220,228)(245,257)(246,258)(247,259)(248,260)(249,253)(250,254)(251,255)
(252,256)(261,281)(262,282)(263,283)(264,284)(265,297)(266,298)(267,299)
(268,300)(269,293)(270,294)(271,295)(272,296)(273,289)(274,290)(275,291)
(276,292)(277,285)(278,286)(279,287)(280,288)(305,317)(306,318)(307,319)
(308,320)(309,313)(310,314)(311,315)(312,316)(321,341)(322,342)(323,343)
(324,344)(325,357)(326,358)(327,359)(328,360)(329,353)(330,354)(331,355)
(332,356)(333,349)(334,350)(335,351)(336,352)(337,345)(338,346)(339,347)
(340,348);
s1 := Sym(360)!(  1, 25)(  2, 26)(  3, 28)(  4, 27)(  5, 21)(  6, 22)(  7, 24)
(  8, 23)(  9, 37)( 10, 38)( 11, 40)( 12, 39)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 41, 45)( 42, 46)( 43, 48)
( 44, 47)( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 55, 56)( 61,145)( 62,146)
( 63,148)( 64,147)( 65,141)( 66,142)( 67,144)( 68,143)( 69,157)( 70,158)
( 71,160)( 72,159)( 73,153)( 74,154)( 75,156)( 76,155)( 77,149)( 78,150)
( 79,152)( 80,151)( 81,125)( 82,126)( 83,128)( 84,127)( 85,121)( 86,122)
( 87,124)( 88,123)( 89,137)( 90,138)( 91,140)( 92,139)( 93,133)( 94,134)
( 95,136)( 96,135)( 97,129)( 98,130)( 99,132)(100,131)(101,165)(102,166)
(103,168)(104,167)(105,161)(106,162)(107,164)(108,163)(109,177)(110,178)
(111,180)(112,179)(113,173)(114,174)(115,176)(116,175)(117,169)(118,170)
(119,172)(120,171)(181,205)(182,206)(183,208)(184,207)(185,201)(186,202)
(187,204)(188,203)(189,217)(190,218)(191,220)(192,219)(193,213)(194,214)
(195,216)(196,215)(197,209)(198,210)(199,212)(200,211)(221,225)(222,226)
(223,228)(224,227)(229,237)(230,238)(231,240)(232,239)(235,236)(241,325)
(242,326)(243,328)(244,327)(245,321)(246,322)(247,324)(248,323)(249,337)
(250,338)(251,340)(252,339)(253,333)(254,334)(255,336)(256,335)(257,329)
(258,330)(259,332)(260,331)(261,305)(262,306)(263,308)(264,307)(265,301)
(266,302)(267,304)(268,303)(269,317)(270,318)(271,320)(272,319)(273,313)
(274,314)(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)(281,345)
(282,346)(283,348)(284,347)(285,341)(286,342)(287,344)(288,343)(289,357)
(290,358)(291,360)(292,359)(293,353)(294,354)(295,356)(296,355)(297,349)
(298,350)(299,352)(300,351);
s2 := Sym(360)!(  1,241)(  2,244)(  3,243)(  4,242)(  5,245)(  6,248)(  7,247)
(  8,246)(  9,249)( 10,252)( 11,251)( 12,250)( 13,253)( 14,256)( 15,255)
( 16,254)( 17,257)( 18,260)( 19,259)( 20,258)( 21,261)( 22,264)( 23,263)
( 24,262)( 25,265)( 26,268)( 27,267)( 28,266)( 29,269)( 30,272)( 31,271)
( 32,270)( 33,273)( 34,276)( 35,275)( 36,274)( 37,277)( 38,280)( 39,279)
( 40,278)( 41,281)( 42,284)( 43,283)( 44,282)( 45,285)( 46,288)( 47,287)
( 48,286)( 49,289)( 50,292)( 51,291)( 52,290)( 53,293)( 54,296)( 55,295)
( 56,294)( 57,297)( 58,300)( 59,299)( 60,298)( 61,181)( 62,184)( 63,183)
( 64,182)( 65,185)( 66,188)( 67,187)( 68,186)( 69,189)( 70,192)( 71,191)
( 72,190)( 73,193)( 74,196)( 75,195)( 76,194)( 77,197)( 78,200)( 79,199)
( 80,198)( 81,201)( 82,204)( 83,203)( 84,202)( 85,205)( 86,208)( 87,207)
( 88,206)( 89,209)( 90,212)( 91,211)( 92,210)( 93,213)( 94,216)( 95,215)
( 96,214)( 97,217)( 98,220)( 99,219)(100,218)(101,221)(102,224)(103,223)
(104,222)(105,225)(106,228)(107,227)(108,226)(109,229)(110,232)(111,231)
(112,230)(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)
(120,238)(121,301)(122,304)(123,303)(124,302)(125,305)(126,308)(127,307)
(128,306)(129,309)(130,312)(131,311)(132,310)(133,313)(134,316)(135,315)
(136,314)(137,317)(138,320)(139,319)(140,318)(141,321)(142,324)(143,323)
(144,322)(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)
(152,330)(153,333)(154,336)(155,335)(156,334)(157,337)(158,340)(159,339)
(160,338)(161,341)(162,344)(163,343)(164,342)(165,345)(166,348)(167,347)
(168,346)(169,349)(170,352)(171,351)(172,350)(173,353)(174,356)(175,355)
(176,354)(177,357)(178,360)(179,359)(180,358);
s3 := Sym(360)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360);
poly := sub<Sym(360)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*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