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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}*1440c
if this polytope has a name.
Group : SmallGroup(1440,5712)
Rank : 4
Schlafli Type : {30,6,4}
Number of vertices, edges, etc : 30, 90, 12, 4
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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 : {15,6,4}*720, {30,6,2}*720c
   3-fold quotients : {30,2,4}*480
   4-fold quotients : {15,6,2}*360
   5-fold quotients : {6,6,4}*288c
   6-fold quotients : {15,2,4}*240, {30,2,2}*240
   9-fold quotients : {10,2,4}*160
   10-fold quotients : {3,6,4}*144, {6,6,2}*144c
   12-fold quotients : {15,2,2}*120
   15-fold quotients : {6,2,4}*96
   18-fold quotients : {5,2,4}*80, {10,2,2}*80
   20-fold quotients : {3,6,2}*72
   30-fold quotients : {3,2,4}*48, {6,2,2}*48
   36-fold quotients : {5,2,2}*40
   45-fold quotients : {2,2,4}*32
   60-fold quotients : {3,2,2}*24
   90-fold quotients : {2,2,2}*16
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)( 91,292)( 92,291)( 93,295)( 94,294)( 95,293)( 96,287)
( 97,286)( 98,290)( 99,289)(100,288)(101,297)(102,296)(103,300)(104,299)
(105,298)(106,277)(107,276)(108,280)(109,279)(110,278)(111,272)(112,271)
(113,275)(114,274)(115,273)(116,282)(117,281)(118,285)(119,284)(120,283)
(121,307)(122,306)(123,310)(124,309)(125,308)(126,302)(127,301)(128,305)
(129,304)(130,303)(131,312)(132,311)(133,315)(134,314)(135,313)(136,337)
(137,336)(138,340)(139,339)(140,338)(141,332)(142,331)(143,335)(144,334)
(145,333)(146,342)(147,341)(148,345)(149,344)(150,343)(151,322)(152,321)
(153,325)(154,324)(155,323)(156,317)(157,316)(158,320)(159,319)(160,318)
(161,327)(162,326)(163,330)(164,329)(165,328)(166,352)(167,351)(168,355)
(169,354)(170,353)(171,347)(172,346)(173,350)(174,349)(175,348)(176,357)
(177,356)(178,360)(179,359)(180,358);;
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)(196,211)(197,212)(198,213)(199,214)(200,215)
(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)(208,223)
(209,224)(210,225)(241,256)(242,257)(243,258)(244,259)(245,260)(246,261)
(247,262)(248,263)(249,264)(250,265)(251,266)(252,267)(253,268)(254,269)
(255,270)(271,316)(272,317)(273,318)(274,319)(275,320)(276,321)(277,322)
(278,323)(279,324)(280,325)(281,326)(282,327)(283,328)(284,329)(285,330)
(286,346)(287,347)(288,348)(289,349)(290,350)(291,351)(292,352)(293,353)
(294,354)(295,355)(296,356)(297,357)(298,358)(299,359)(300,360)(301,331)
(302,332)(303,333)(304,334)(305,335)(306,336)(307,337)(308,338)(309,339)
(310,340)(311,341)(312,342)(313,343)(314,344)(315,345);;
s3 := (  1, 91)(  2, 92)(  3, 93)(  4, 94)(  5, 95)(  6, 96)(  7, 97)(  8, 98)
(  9, 99)( 10,100)( 11,101)( 12,102)( 13,103)( 14,104)( 15,105)( 16,106)
( 17,107)( 18,108)( 19,109)( 20,110)( 21,111)( 22,112)( 23,113)( 24,114)
( 25,115)( 26,116)( 27,117)( 28,118)( 29,119)( 30,120)( 31,121)( 32,122)
( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)( 40,130)
( 41,131)( 42,132)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)
( 49,139)( 50,140)( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)( 56,146)
( 57,147)( 58,148)( 59,149)( 60,150)( 61,151)( 62,152)( 63,153)( 64,154)
( 65,155)( 66,156)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)( 72,162)
( 73,163)( 74,164)( 75,165)( 76,166)( 77,167)( 78,168)( 79,169)( 80,170)
( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)( 88,178)
( 89,179)( 90,180)(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)(196,286)(197,287)(198,288)(199,289)(200,290)(201,291)(202,292)
(203,293)(204,294)(205,295)(206,296)(207,297)(208,298)(209,299)(210,300)
(211,301)(212,302)(213,303)(214,304)(215,305)(216,306)(217,307)(218,308)
(219,309)(220,310)(221,311)(222,312)(223,313)(224,314)(225,315)(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)(241,331)(242,332)
(243,333)(244,334)(245,335)(246,336)(247,337)(248,338)(249,339)(250,340)
(251,341)(252,342)(253,343)(254,344)(255,345)(256,346)(257,347)(258,348)
(259,349)(260,350)(261,351)(262,352)(263,353)(264,354)(265,355)(266,356)
(267,357)(268,358)(269,359)(270,360);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*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 ];;
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)( 91,292)( 92,291)( 93,295)( 94,294)( 95,293)
( 96,287)( 97,286)( 98,290)( 99,289)(100,288)(101,297)(102,296)(103,300)
(104,299)(105,298)(106,277)(107,276)(108,280)(109,279)(110,278)(111,272)
(112,271)(113,275)(114,274)(115,273)(116,282)(117,281)(118,285)(119,284)
(120,283)(121,307)(122,306)(123,310)(124,309)(125,308)(126,302)(127,301)
(128,305)(129,304)(130,303)(131,312)(132,311)(133,315)(134,314)(135,313)
(136,337)(137,336)(138,340)(139,339)(140,338)(141,332)(142,331)(143,335)
(144,334)(145,333)(146,342)(147,341)(148,345)(149,344)(150,343)(151,322)
(152,321)(153,325)(154,324)(155,323)(156,317)(157,316)(158,320)(159,319)
(160,318)(161,327)(162,326)(163,330)(164,329)(165,328)(166,352)(167,351)
(168,355)(169,354)(170,353)(171,347)(172,346)(173,350)(174,349)(175,348)
(176,357)(177,356)(178,360)(179,359)(180,358);
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)(196,211)(197,212)(198,213)(199,214)
(200,215)(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)
(208,223)(209,224)(210,225)(241,256)(242,257)(243,258)(244,259)(245,260)
(246,261)(247,262)(248,263)(249,264)(250,265)(251,266)(252,267)(253,268)
(254,269)(255,270)(271,316)(272,317)(273,318)(274,319)(275,320)(276,321)
(277,322)(278,323)(279,324)(280,325)(281,326)(282,327)(283,328)(284,329)
(285,330)(286,346)(287,347)(288,348)(289,349)(290,350)(291,351)(292,352)
(293,353)(294,354)(295,355)(296,356)(297,357)(298,358)(299,359)(300,360)
(301,331)(302,332)(303,333)(304,334)(305,335)(306,336)(307,337)(308,338)
(309,339)(310,340)(311,341)(312,342)(313,343)(314,344)(315,345);
s3 := Sym(360)!(  1, 91)(  2, 92)(  3, 93)(  4, 94)(  5, 95)(  6, 96)(  7, 97)
(  8, 98)(  9, 99)( 10,100)( 11,101)( 12,102)( 13,103)( 14,104)( 15,105)
( 16,106)( 17,107)( 18,108)( 19,109)( 20,110)( 21,111)( 22,112)( 23,113)
( 24,114)( 25,115)( 26,116)( 27,117)( 28,118)( 29,119)( 30,120)( 31,121)
( 32,122)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)
( 40,130)( 41,131)( 42,132)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)
( 48,138)( 49,139)( 50,140)( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)
( 56,146)( 57,147)( 58,148)( 59,149)( 60,150)( 61,151)( 62,152)( 63,153)
( 64,154)( 65,155)( 66,156)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)
( 72,162)( 73,163)( 74,164)( 75,165)( 76,166)( 77,167)( 78,168)( 79,169)
( 80,170)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)
( 88,178)( 89,179)( 90,180)(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)(196,286)(197,287)(198,288)(199,289)(200,290)(201,291)
(202,292)(203,293)(204,294)(205,295)(206,296)(207,297)(208,298)(209,299)
(210,300)(211,301)(212,302)(213,303)(214,304)(215,305)(216,306)(217,307)
(218,308)(219,309)(220,310)(221,311)(222,312)(223,313)(224,314)(225,315)
(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)(241,331)
(242,332)(243,333)(244,334)(245,335)(246,336)(247,337)(248,338)(249,339)
(250,340)(251,341)(252,342)(253,343)(254,344)(255,345)(256,346)(257,347)
(258,348)(259,349)(260,350)(261,351)(262,352)(263,353)(264,354)(265,355)
(266,356)(267,357)(268,358)(269,359)(270,360);
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*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 >; 
 
References : None.
to this polytope