Polytope of Type {4,30,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,8}*1920b
if this polytope has a name.
Group : SmallGroup(1920,239556)
Rank : 4
Schlafli Type : {4,30,8}
Number of vertices, edges, etc : 4, 60, 120, 8
Order of s0s1s2s3 : 120
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) :
2-fold quotients : {4,30,4}*960c
4-fold quotients : {4,30,2}*480b
5-fold quotients : {4,6,8}*384b
8-fold quotients : {4,15,2}*240
10-fold quotients : {4,6,4}*192c
20-fold quotients : {4,6,2}*96c
40-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480);;
s1 := ( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)(247,260)(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)(263,284)(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)(271,296)(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)(279,288)(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)(365,377)(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)(381,401)(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)(397,405)(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)(428,439)(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)(444,463)(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)(460,467);;
s2 := ( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)( 8, 22)( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)(112,118)(114,116)(121,205)(122,208)(123,207)(124,206)(125,201)(126,204)(127,203)(128,202)(129,217)(130,220)(131,219)(132,218)(133,213)(134,216)(135,215)(136,214)(137,209)(138,212)(139,211)(140,210)(141,185)(142,188)(143,187)(144,186)(145,181)(146,184)(147,183)(148,182)(149,197)(150,200)(151,199)(152,198)(153,193)(154,196)(155,195)(156,194)(157,189)(158,192)(159,191)(160,190)(161,225)(162,228)(163,227)(164,226)(165,221)(166,224)(167,223)(168,222)(169,237)(170,240)(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,229)(178,232)(179,231)(180,230)(241,385)(242,388)(243,387)(244,386)(245,381)(246,384)(247,383)(248,382)(249,397)(250,400)(251,399)(252,398)(253,393)(254,396)(255,395)(256,394)(257,389)(258,392)(259,391)(260,390)(261,365)(262,368)(263,367)(264,366)(265,361)(266,364)(267,363)(268,362)(269,377)(270,380)(271,379)(272,378)(273,373)(274,376)(275,375)(276,374)(277,369)(278,372)(279,371)(280,370)(281,405)(282,408)(283,407)(284,406)(285,401)(286,404)(287,403)(288,402)(289,417)(290,420)(291,419)(292,418)(293,413)(294,416)(295,415)(296,414)(297,409)(298,412)(299,411)(300,410)(301,445)(302,448)(303,447)(304,446)(305,441)(306,444)(307,443)(308,442)(309,457)(310,460)(311,459)(312,458)(313,453)(314,456)(315,455)(316,454)(317,449)(318,452)(319,451)(320,450)(321,425)(322,428)(323,427)(324,426)(325,421)(326,424)(327,423)(328,422)(329,437)(330,440)(331,439)(332,438)(333,433)(334,436)(335,435)(336,434)(337,429)(338,432)(339,431)(340,430)(341,465)(342,468)(343,467)(344,466)(345,461)(346,464)(347,463)(348,462)(349,477)(350,480)(351,479)(352,478)(353,473)(354,476)(355,475)(356,474)(357,469)(358,472)(359,471)(360,470);;
s3 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)(121,421)(122,422)(123,423)(124,424)(125,425)(126,426)(127,427)(128,428)(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,435)(136,436)(137,437)(138,438)(139,439)(140,440)(141,441)(142,442)(143,443)(144,444)(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,451)(152,452)(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)(160,460)(161,461)(162,462)(163,463)(164,464)(165,465)(166,466)(167,467)(168,468)(169,469)(170,470)(171,471)(172,472)(173,473)(174,474)(175,475)(176,476)(177,477)(178,478)(179,479)(180,480)(181,361)(182,362)(183,363)(184,364)(185,365)(186,366)(187,367)(188,368)(189,369)(190,370)(191,371)(192,372)(193,373)(194,374)(195,375)(196,376)(197,377)(198,378)(199,379)(200,380)(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)(208,388)(209,389)(210,390)(211,391)(212,392)(213,393)(214,394)(215,395)(216,396)(217,397)(218,398)(219,399)(220,400)(221,401)(222,402)(223,403)(224,404)(225,405)(226,406)(227,407)(228,408)(229,409)(230,410)(231,411)(232,412)(233,413)(234,414)(235,415)(236,416)(237,417)(238,418)(239,419)(240,420);;
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*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(480)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480);
s1 := Sym(480)!( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)(247,260)(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)(263,284)(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)(271,296)(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)(279,288)(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)(365,377)(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)(381,401)(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)(397,405)(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)(428,439)(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)(444,463)(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)(460,467);
s2 := Sym(480)!( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)( 8, 22)( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)(112,118)(114,116)(121,205)(122,208)(123,207)(124,206)(125,201)(126,204)(127,203)(128,202)(129,217)(130,220)(131,219)(132,218)(133,213)(134,216)(135,215)(136,214)(137,209)(138,212)(139,211)(140,210)(141,185)(142,188)(143,187)(144,186)(145,181)(146,184)(147,183)(148,182)(149,197)(150,200)(151,199)(152,198)(153,193)(154,196)(155,195)(156,194)(157,189)(158,192)(159,191)(160,190)(161,225)(162,228)(163,227)(164,226)(165,221)(166,224)(167,223)(168,222)(169,237)(170,240)(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,229)(178,232)(179,231)(180,230)(241,385)(242,388)(243,387)(244,386)(245,381)(246,384)(247,383)(248,382)(249,397)(250,400)(251,399)(252,398)(253,393)(254,396)(255,395)(256,394)(257,389)(258,392)(259,391)(260,390)(261,365)(262,368)(263,367)(264,366)(265,361)(266,364)(267,363)(268,362)(269,377)(270,380)(271,379)(272,378)(273,373)(274,376)(275,375)(276,374)(277,369)(278,372)(279,371)(280,370)(281,405)(282,408)(283,407)(284,406)(285,401)(286,404)(287,403)(288,402)(289,417)(290,420)(291,419)(292,418)(293,413)(294,416)(295,415)(296,414)(297,409)(298,412)(299,411)(300,410)(301,445)(302,448)(303,447)(304,446)(305,441)(306,444)(307,443)(308,442)(309,457)(310,460)(311,459)(312,458)(313,453)(314,456)(315,455)(316,454)(317,449)(318,452)(319,451)(320,450)(321,425)(322,428)(323,427)(324,426)(325,421)(326,424)(327,423)(328,422)(329,437)(330,440)(331,439)(332,438)(333,433)(334,436)(335,435)(336,434)(337,429)(338,432)(339,431)(340,430)(341,465)(342,468)(343,467)(344,466)(345,461)(346,464)(347,463)(348,462)(349,477)(350,480)(351,479)(352,478)(353,473)(354,476)(355,475)(356,474)(357,469)(358,472)(359,471)(360,470);
s3 := Sym(480)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)(121,421)(122,422)(123,423)(124,424)(125,425)(126,426)(127,427)(128,428)(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,435)(136,436)(137,437)(138,438)(139,439)(140,440)(141,441)(142,442)(143,443)(144,444)(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,451)(152,452)(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)(160,460)(161,461)(162,462)(163,463)(164,464)(165,465)(166,466)(167,467)(168,468)(169,469)(170,470)(171,471)(172,472)(173,473)(174,474)(175,475)(176,476)(177,477)(178,478)(179,479)(180,480)(181,361)(182,362)(183,363)(184,364)(185,365)(186,366)(187,367)(188,368)(189,369)(190,370)(191,371)(192,372)(193,373)(194,374)(195,375)(196,376)(197,377)(198,378)(199,379)(200,380)(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)(208,388)(209,389)(210,390)(211,391)(212,392)(213,393)(214,394)(215,395)(216,396)(217,397)(218,398)(219,399)(220,400)(221,401)(222,402)(223,403)(224,404)(225,405)(226,406)(227,407)(228,408)(229,409)(230,410)(231,411)(232,412)(233,413)(234,414)(235,415)(236,416)(237,417)(238,418)(239,419)(240,420);
poly := sub<Sym(480)|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*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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