Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,12,20}

Atlas Canonical Name {3,12,20}*1920

Overview

Group
SmallGroup(1920,238596)
Rank
4
Schläfli Type
{3,12,20}
Vertices, edges, …
4, 24, 160, 20
Order of s0s1s2s3
40
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

10-fold

20-fold

40-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.