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