Polytope of Type {4,12,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,20}*1920b
if this polytope has a name.
Group : SmallGroup(1920,238871)
Rank : 4
Schlafli Type : {4,12,20}
Number of vertices, edges, etc : 4, 24, 120, 20
Order of s0s1s2s3 : 60
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 : {4,12,10}*960b, {4,6,20}*960b
4-fold quotients : {4,6,10}*480b
5-fold quotients : {4,12,4}*384d
10-fold quotients : {4,12,2}*192b, {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.
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)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)( 23, 44)
( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)( 31, 52)
( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)( 39, 60)
( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)( 90,110)
( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)( 98,118)
( 99,120)(100,119)(123,124)(127,128)(131,132)(135,136)(139,140)(141,161)
(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)(149,169)
(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)(157,177)
(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)(199,200)
(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)(208,227)
(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)(216,235)
(217,237)(218,238)(219,240)(220,239)(241,361)(242,362)(243,364)(244,363)
(245,365)(246,366)(247,368)(248,367)(249,369)(250,370)(251,372)(252,371)
(253,373)(254,374)(255,376)(256,375)(257,377)(258,378)(259,380)(260,379)
(261,401)(262,402)(263,404)(264,403)(265,405)(266,406)(267,408)(268,407)
(269,409)(270,410)(271,412)(272,411)(273,413)(274,414)(275,416)(276,415)
(277,417)(278,418)(279,420)(280,419)(281,381)(282,382)(283,384)(284,383)
(285,385)(286,386)(287,388)(288,387)(289,389)(290,390)(291,392)(292,391)
(293,393)(294,394)(295,396)(296,395)(297,397)(298,398)(299,400)(300,399)
(301,421)(302,422)(303,424)(304,423)(305,425)(306,426)(307,428)(308,427)
(309,429)(310,430)(311,432)(312,431)(313,433)(314,434)(315,436)(316,435)
(317,437)(318,438)(319,440)(320,439)(321,461)(322,462)(323,464)(324,463)
(325,465)(326,466)(327,468)(328,467)(329,469)(330,470)(331,472)(332,471)
(333,473)(334,474)(335,476)(336,475)(337,477)(338,478)(339,480)(340,479)
(341,441)(342,442)(343,444)(344,443)(345,445)(346,446)(347,448)(348,447)
(349,449)(350,450)(351,452)(352,451)(353,453)(354,454)(355,456)(356,455)
(357,457)(358,458)(359,460)(360,459);;
s2 := ( 1,261)( 2,264)( 3,263)( 4,262)( 5,277)( 6,280)( 7,279)( 8,278)
( 9,273)( 10,276)( 11,275)( 12,274)( 13,269)( 14,272)( 15,271)( 16,270)
( 17,265)( 18,268)( 19,267)( 20,266)( 21,241)( 22,244)( 23,243)( 24,242)
( 25,257)( 26,260)( 27,259)( 28,258)( 29,253)( 30,256)( 31,255)( 32,254)
( 33,249)( 34,252)( 35,251)( 36,250)( 37,245)( 38,248)( 39,247)( 40,246)
( 41,281)( 42,284)( 43,283)( 44,282)( 45,297)( 46,300)( 47,299)( 48,298)
( 49,293)( 50,296)( 51,295)( 52,294)( 53,289)( 54,292)( 55,291)( 56,290)
( 57,285)( 58,288)( 59,287)( 60,286)( 61,321)( 62,324)( 63,323)( 64,322)
( 65,337)( 66,340)( 67,339)( 68,338)( 69,333)( 70,336)( 71,335)( 72,334)
( 73,329)( 74,332)( 75,331)( 76,330)( 77,325)( 78,328)( 79,327)( 80,326)
( 81,301)( 82,304)( 83,303)( 84,302)( 85,317)( 86,320)( 87,319)( 88,318)
( 89,313)( 90,316)( 91,315)( 92,314)( 93,309)( 94,312)( 95,311)( 96,310)
( 97,305)( 98,308)( 99,307)(100,306)(101,341)(102,344)(103,343)(104,342)
(105,357)(106,360)(107,359)(108,358)(109,353)(110,356)(111,355)(112,354)
(113,349)(114,352)(115,351)(116,350)(117,345)(118,348)(119,347)(120,346)
(121,381)(122,384)(123,383)(124,382)(125,397)(126,400)(127,399)(128,398)
(129,393)(130,396)(131,395)(132,394)(133,389)(134,392)(135,391)(136,390)
(137,385)(138,388)(139,387)(140,386)(141,361)(142,364)(143,363)(144,362)
(145,377)(146,380)(147,379)(148,378)(149,373)(150,376)(151,375)(152,374)
(153,369)(154,372)(155,371)(156,370)(157,365)(158,368)(159,367)(160,366)
(161,401)(162,404)(163,403)(164,402)(165,417)(166,420)(167,419)(168,418)
(169,413)(170,416)(171,415)(172,414)(173,409)(174,412)(175,411)(176,410)
(177,405)(178,408)(179,407)(180,406)(181,441)(182,444)(183,443)(184,442)
(185,457)(186,460)(187,459)(188,458)(189,453)(190,456)(191,455)(192,454)
(193,449)(194,452)(195,451)(196,450)(197,445)(198,448)(199,447)(200,446)
(201,421)(202,424)(203,423)(204,422)(205,437)(206,440)(207,439)(208,438)
(209,433)(210,436)(211,435)(212,434)(213,429)(214,432)(215,431)(216,430)
(217,425)(218,428)(219,427)(220,426)(221,461)(222,464)(223,463)(224,462)
(225,477)(226,480)(227,479)(228,478)(229,473)(230,476)(231,475)(232,474)
(233,469)(234,472)(235,471)(236,470)(237,465)(238,468)(239,467)(240,466);;
s3 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 17)( 10, 18)( 11, 19)( 12, 20)
( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 37)( 30, 38)( 31, 39)( 32, 40)
( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)
( 61, 65)( 62, 66)( 63, 67)( 64, 68)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 97)( 90, 98)( 91, 99)( 92,100)
(101,105)(102,106)(103,107)(104,108)(109,117)(110,118)(111,119)(112,120)
(121,125)(122,126)(123,127)(124,128)(129,137)(130,138)(131,139)(132,140)
(141,145)(142,146)(143,147)(144,148)(149,157)(150,158)(151,159)(152,160)
(161,165)(162,166)(163,167)(164,168)(169,177)(170,178)(171,179)(172,180)
(181,185)(182,186)(183,187)(184,188)(189,197)(190,198)(191,199)(192,200)
(201,205)(202,206)(203,207)(204,208)(209,217)(210,218)(211,219)(212,220)
(221,225)(222,226)(223,227)(224,228)(229,237)(230,238)(231,239)(232,240)
(241,305)(242,306)(243,307)(244,308)(245,301)(246,302)(247,303)(248,304)
(249,317)(250,318)(251,319)(252,320)(253,313)(254,314)(255,315)(256,316)
(257,309)(258,310)(259,311)(260,312)(261,325)(262,326)(263,327)(264,328)
(265,321)(266,322)(267,323)(268,324)(269,337)(270,338)(271,339)(272,340)
(273,333)(274,334)(275,335)(276,336)(277,329)(278,330)(279,331)(280,332)
(281,345)(282,346)(283,347)(284,348)(285,341)(286,342)(287,343)(288,344)
(289,357)(290,358)(291,359)(292,360)(293,353)(294,354)(295,355)(296,356)
(297,349)(298,350)(299,351)(300,352)(361,425)(362,426)(363,427)(364,428)
(365,421)(366,422)(367,423)(368,424)(369,437)(370,438)(371,439)(372,440)
(373,433)(374,434)(375,435)(376,436)(377,429)(378,430)(379,431)(380,432)
(381,445)(382,446)(383,447)(384,448)(385,441)(386,442)(387,443)(388,444)
(389,457)(390,458)(391,459)(392,460)(393,453)(394,454)(395,455)(396,456)
(397,449)(398,450)(399,451)(400,452)(401,465)(402,466)(403,467)(404,468)
(405,461)(406,462)(407,463)(408,464)(409,477)(410,478)(411,479)(412,480)
(413,473)(414,474)(415,475)(416,476)(417,469)(418,470)(419,471)(420,472);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!( 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)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)
( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)
( 31, 52)( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)
( 39, 60)( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)
( 90,110)( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)
( 98,118)( 99,120)(100,119)(123,124)(127,128)(131,132)(135,136)(139,140)
(141,161)(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)
(149,169)(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)
(157,177)(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)
(199,200)(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)
(208,227)(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)
(216,235)(217,237)(218,238)(219,240)(220,239)(241,361)(242,362)(243,364)
(244,363)(245,365)(246,366)(247,368)(248,367)(249,369)(250,370)(251,372)
(252,371)(253,373)(254,374)(255,376)(256,375)(257,377)(258,378)(259,380)
(260,379)(261,401)(262,402)(263,404)(264,403)(265,405)(266,406)(267,408)
(268,407)(269,409)(270,410)(271,412)(272,411)(273,413)(274,414)(275,416)
(276,415)(277,417)(278,418)(279,420)(280,419)(281,381)(282,382)(283,384)
(284,383)(285,385)(286,386)(287,388)(288,387)(289,389)(290,390)(291,392)
(292,391)(293,393)(294,394)(295,396)(296,395)(297,397)(298,398)(299,400)
(300,399)(301,421)(302,422)(303,424)(304,423)(305,425)(306,426)(307,428)
(308,427)(309,429)(310,430)(311,432)(312,431)(313,433)(314,434)(315,436)
(316,435)(317,437)(318,438)(319,440)(320,439)(321,461)(322,462)(323,464)
(324,463)(325,465)(326,466)(327,468)(328,467)(329,469)(330,470)(331,472)
(332,471)(333,473)(334,474)(335,476)(336,475)(337,477)(338,478)(339,480)
(340,479)(341,441)(342,442)(343,444)(344,443)(345,445)(346,446)(347,448)
(348,447)(349,449)(350,450)(351,452)(352,451)(353,453)(354,454)(355,456)
(356,455)(357,457)(358,458)(359,460)(360,459);
s2 := Sym(480)!( 1,261)( 2,264)( 3,263)( 4,262)( 5,277)( 6,280)( 7,279)
( 8,278)( 9,273)( 10,276)( 11,275)( 12,274)( 13,269)( 14,272)( 15,271)
( 16,270)( 17,265)( 18,268)( 19,267)( 20,266)( 21,241)( 22,244)( 23,243)
( 24,242)( 25,257)( 26,260)( 27,259)( 28,258)( 29,253)( 30,256)( 31,255)
( 32,254)( 33,249)( 34,252)( 35,251)( 36,250)( 37,245)( 38,248)( 39,247)
( 40,246)( 41,281)( 42,284)( 43,283)( 44,282)( 45,297)( 46,300)( 47,299)
( 48,298)( 49,293)( 50,296)( 51,295)( 52,294)( 53,289)( 54,292)( 55,291)
( 56,290)( 57,285)( 58,288)( 59,287)( 60,286)( 61,321)( 62,324)( 63,323)
( 64,322)( 65,337)( 66,340)( 67,339)( 68,338)( 69,333)( 70,336)( 71,335)
( 72,334)( 73,329)( 74,332)( 75,331)( 76,330)( 77,325)( 78,328)( 79,327)
( 80,326)( 81,301)( 82,304)( 83,303)( 84,302)( 85,317)( 86,320)( 87,319)
( 88,318)( 89,313)( 90,316)( 91,315)( 92,314)( 93,309)( 94,312)( 95,311)
( 96,310)( 97,305)( 98,308)( 99,307)(100,306)(101,341)(102,344)(103,343)
(104,342)(105,357)(106,360)(107,359)(108,358)(109,353)(110,356)(111,355)
(112,354)(113,349)(114,352)(115,351)(116,350)(117,345)(118,348)(119,347)
(120,346)(121,381)(122,384)(123,383)(124,382)(125,397)(126,400)(127,399)
(128,398)(129,393)(130,396)(131,395)(132,394)(133,389)(134,392)(135,391)
(136,390)(137,385)(138,388)(139,387)(140,386)(141,361)(142,364)(143,363)
(144,362)(145,377)(146,380)(147,379)(148,378)(149,373)(150,376)(151,375)
(152,374)(153,369)(154,372)(155,371)(156,370)(157,365)(158,368)(159,367)
(160,366)(161,401)(162,404)(163,403)(164,402)(165,417)(166,420)(167,419)
(168,418)(169,413)(170,416)(171,415)(172,414)(173,409)(174,412)(175,411)
(176,410)(177,405)(178,408)(179,407)(180,406)(181,441)(182,444)(183,443)
(184,442)(185,457)(186,460)(187,459)(188,458)(189,453)(190,456)(191,455)
(192,454)(193,449)(194,452)(195,451)(196,450)(197,445)(198,448)(199,447)
(200,446)(201,421)(202,424)(203,423)(204,422)(205,437)(206,440)(207,439)
(208,438)(209,433)(210,436)(211,435)(212,434)(213,429)(214,432)(215,431)
(216,430)(217,425)(218,428)(219,427)(220,426)(221,461)(222,464)(223,463)
(224,462)(225,477)(226,480)(227,479)(228,478)(229,473)(230,476)(231,475)
(232,474)(233,469)(234,472)(235,471)(236,470)(237,465)(238,468)(239,467)
(240,466);
s3 := Sym(480)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 17)( 10, 18)( 11, 19)
( 12, 20)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 37)( 30, 38)( 31, 39)
( 32, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 57)( 50, 58)( 51, 59)
( 52, 60)( 61, 65)( 62, 66)( 63, 67)( 64, 68)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 97)( 90, 98)( 91, 99)
( 92,100)(101,105)(102,106)(103,107)(104,108)(109,117)(110,118)(111,119)
(112,120)(121,125)(122,126)(123,127)(124,128)(129,137)(130,138)(131,139)
(132,140)(141,145)(142,146)(143,147)(144,148)(149,157)(150,158)(151,159)
(152,160)(161,165)(162,166)(163,167)(164,168)(169,177)(170,178)(171,179)
(172,180)(181,185)(182,186)(183,187)(184,188)(189,197)(190,198)(191,199)
(192,200)(201,205)(202,206)(203,207)(204,208)(209,217)(210,218)(211,219)
(212,220)(221,225)(222,226)(223,227)(224,228)(229,237)(230,238)(231,239)
(232,240)(241,305)(242,306)(243,307)(244,308)(245,301)(246,302)(247,303)
(248,304)(249,317)(250,318)(251,319)(252,320)(253,313)(254,314)(255,315)
(256,316)(257,309)(258,310)(259,311)(260,312)(261,325)(262,326)(263,327)
(264,328)(265,321)(266,322)(267,323)(268,324)(269,337)(270,338)(271,339)
(272,340)(273,333)(274,334)(275,335)(276,336)(277,329)(278,330)(279,331)
(280,332)(281,345)(282,346)(283,347)(284,348)(285,341)(286,342)(287,343)
(288,344)(289,357)(290,358)(291,359)(292,360)(293,353)(294,354)(295,355)
(296,356)(297,349)(298,350)(299,351)(300,352)(361,425)(362,426)(363,427)
(364,428)(365,421)(366,422)(367,423)(368,424)(369,437)(370,438)(371,439)
(372,440)(373,433)(374,434)(375,435)(376,436)(377,429)(378,430)(379,431)
(380,432)(381,445)(382,446)(383,447)(384,448)(385,441)(386,442)(387,443)
(388,444)(389,457)(390,458)(391,459)(392,460)(393,453)(394,454)(395,455)
(396,456)(397,449)(398,450)(399,451)(400,452)(401,465)(402,466)(403,467)
(404,468)(405,461)(406,462)(407,463)(408,464)(409,477)(410,478)(411,479)
(412,480)(413,473)(414,474)(415,475)(416,476)(417,469)(418,470)(419,471)
(420,472);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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