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Polytope of Type {20,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240142)
Rank : 4
Schlafli Type : {20,6,4}
Number of vertices, edges, etc : 20, 120, 24, 8
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 : {20,6,4}*960b, {10,6,4}*960e
   4-fold quotients : {20,6,2}*480a, {10,6,4}*480b
   5-fold quotients : {4,6,4}*384a
   8-fold quotients : {10,6,2}*240
   10-fold quotients : {4,6,4}*192b, {2,6,4}*192
   12-fold quotients : {20,2,2}*160
   20-fold quotients : {4,6,2}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   24-fold quotients : {10,2,2}*80
   40-fold quotients : {2,3,4}*48, {2,6,2}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {4,2,2}*32
   80-fold quotients : {2,3,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)
( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)
( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116)
(121,181)(122,182)(123,183)(124,184)(125,197)(126,198)(127,199)(128,200)
(129,193)(130,194)(131,195)(132,196)(133,189)(134,190)(135,191)(136,192)
(137,185)(138,186)(139,187)(140,188)(141,201)(142,202)(143,203)(144,204)
(145,217)(146,218)(147,219)(148,220)(149,213)(150,214)(151,215)(152,216)
(153,209)(154,210)(155,211)(156,212)(157,205)(158,206)(159,207)(160,208)
(161,221)(162,222)(163,223)(164,224)(165,237)(166,238)(167,239)(168,240)
(169,233)(170,234)(171,235)(172,236)(173,229)(174,230)(175,231)(176,232)
(177,225)(178,226)(179,227)(180,228)(245,257)(246,258)(247,259)(248,260)
(249,253)(250,254)(251,255)(252,256)(265,277)(266,278)(267,279)(268,280)
(269,273)(270,274)(271,275)(272,276)(285,297)(286,298)(287,299)(288,300)
(289,293)(290,294)(291,295)(292,296)(305,317)(306,318)(307,319)(308,320)
(309,313)(310,314)(311,315)(312,316)(325,337)(326,338)(327,339)(328,340)
(329,333)(330,334)(331,335)(332,336)(345,357)(346,358)(347,359)(348,360)
(349,353)(350,354)(351,355)(352,356)(361,421)(362,422)(363,423)(364,424)
(365,437)(366,438)(367,439)(368,440)(369,433)(370,434)(371,435)(372,436)
(373,429)(374,430)(375,431)(376,432)(377,425)(378,426)(379,427)(380,428)
(381,441)(382,442)(383,443)(384,444)(385,457)(386,458)(387,459)(388,460)
(389,453)(390,454)(391,455)(392,456)(393,449)(394,450)(395,451)(396,452)
(397,445)(398,446)(399,447)(400,448)(401,461)(402,462)(403,463)(404,464)
(405,477)(406,478)(407,479)(408,480)(409,473)(410,474)(411,475)(412,476)
(413,469)(414,470)(415,471)(416,472)(417,465)(418,466)(419,467)(420,468);;
s1 := (  1,125)(  2,126)(  3,128)(  4,127)(  5,121)(  6,122)(  7,124)(  8,123)
(  9,137)( 10,138)( 11,140)( 12,139)( 13,133)( 14,134)( 15,136)( 16,135)
( 17,129)( 18,130)( 19,132)( 20,131)( 21,165)( 22,166)( 23,168)( 24,167)
( 25,161)( 26,162)( 27,164)( 28,163)( 29,177)( 30,178)( 31,180)( 32,179)
( 33,173)( 34,174)( 35,176)( 36,175)( 37,169)( 38,170)( 39,172)( 40,171)
( 41,145)( 42,146)( 43,148)( 44,147)( 45,141)( 46,142)( 47,144)( 48,143)
( 49,157)( 50,158)( 51,160)( 52,159)( 53,153)( 54,154)( 55,156)( 56,155)
( 57,149)( 58,150)( 59,152)( 60,151)( 61,185)( 62,186)( 63,188)( 64,187)
( 65,181)( 66,182)( 67,184)( 68,183)( 69,197)( 70,198)( 71,200)( 72,199)
( 73,193)( 74,194)( 75,196)( 76,195)( 77,189)( 78,190)( 79,192)( 80,191)
( 81,225)( 82,226)( 83,228)( 84,227)( 85,221)( 86,222)( 87,224)( 88,223)
( 89,237)( 90,238)( 91,240)( 92,239)( 93,233)( 94,234)( 95,236)( 96,235)
( 97,229)( 98,230)( 99,232)(100,231)(101,205)(102,206)(103,208)(104,207)
(105,201)(106,202)(107,204)(108,203)(109,217)(110,218)(111,220)(112,219)
(113,213)(114,214)(115,216)(116,215)(117,209)(118,210)(119,212)(120,211)
(241,365)(242,366)(243,368)(244,367)(245,361)(246,362)(247,364)(248,363)
(249,377)(250,378)(251,380)(252,379)(253,373)(254,374)(255,376)(256,375)
(257,369)(258,370)(259,372)(260,371)(261,405)(262,406)(263,408)(264,407)
(265,401)(266,402)(267,404)(268,403)(269,417)(270,418)(271,420)(272,419)
(273,413)(274,414)(275,416)(276,415)(277,409)(278,410)(279,412)(280,411)
(281,385)(282,386)(283,388)(284,387)(285,381)(286,382)(287,384)(288,383)
(289,397)(290,398)(291,400)(292,399)(293,393)(294,394)(295,396)(296,395)
(297,389)(298,390)(299,392)(300,391)(301,425)(302,426)(303,428)(304,427)
(305,421)(306,422)(307,424)(308,423)(309,437)(310,438)(311,440)(312,439)
(313,433)(314,434)(315,436)(316,435)(317,429)(318,430)(319,432)(320,431)
(321,465)(322,466)(323,468)(324,467)(325,461)(326,462)(327,464)(328,463)
(329,477)(330,478)(331,480)(332,479)(333,473)(334,474)(335,476)(336,475)
(337,469)(338,470)(339,472)(340,471)(341,445)(342,446)(343,448)(344,447)
(345,441)(346,442)(347,444)(348,443)(349,457)(350,458)(351,460)(352,459)
(353,453)(354,454)(355,456)(356,455)(357,449)(358,450)(359,452)(360,451);;
s2 := (  1, 21)(  2, 24)(  3, 23)(  4, 22)(  5, 25)(  6, 28)(  7, 27)(  8, 26)
(  9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)
( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)
( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)
( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)
(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)
(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)
(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)
(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)
(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)
(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)
(226,228)(230,232)(234,236)(238,240)(241,261)(242,264)(243,263)(244,262)
(245,265)(246,268)(247,267)(248,266)(249,269)(250,272)(251,271)(252,270)
(253,273)(254,276)(255,275)(256,274)(257,277)(258,280)(259,279)(260,278)
(282,284)(286,288)(290,292)(294,296)(298,300)(301,321)(302,324)(303,323)
(304,322)(305,325)(306,328)(307,327)(308,326)(309,329)(310,332)(311,331)
(312,330)(313,333)(314,336)(315,335)(316,334)(317,337)(318,340)(319,339)
(320,338)(342,344)(346,348)(350,352)(354,356)(358,360)(361,381)(362,384)
(363,383)(364,382)(365,385)(366,388)(367,387)(368,386)(369,389)(370,392)
(371,391)(372,390)(373,393)(374,396)(375,395)(376,394)(377,397)(378,400)
(379,399)(380,398)(402,404)(406,408)(410,412)(414,416)(418,420)(421,441)
(422,444)(423,443)(424,442)(425,445)(426,448)(427,447)(428,446)(429,449)
(430,452)(431,451)(432,450)(433,453)(434,456)(435,455)(436,454)(437,457)
(438,460)(439,459)(440,458)(462,464)(466,468)(470,472)(474,476)(478,480);;
s3 := (  1,242)(  2,241)(  3,244)(  4,243)(  5,246)(  6,245)(  7,248)(  8,247)
(  9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)( 16,255)
( 17,258)( 18,257)( 19,260)( 20,259)( 21,262)( 22,261)( 23,264)( 24,263)
( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)( 32,271)
( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)( 40,279)
( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)( 48,287)
( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)( 56,295)
( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)( 64,303)
( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)( 72,311)
( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)( 80,319)
( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)( 88,327)
( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)( 96,335)
( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)(104,343)
(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)(112,351)
(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)(120,359)
(121,362)(122,361)(123,364)(124,363)(125,366)(126,365)(127,368)(128,367)
(129,370)(130,369)(131,372)(132,371)(133,374)(134,373)(135,376)(136,375)
(137,378)(138,377)(139,380)(140,379)(141,382)(142,381)(143,384)(144,383)
(145,386)(146,385)(147,388)(148,387)(149,390)(150,389)(151,392)(152,391)
(153,394)(154,393)(155,396)(156,395)(157,398)(158,397)(159,400)(160,399)
(161,402)(162,401)(163,404)(164,403)(165,406)(166,405)(167,408)(168,407)
(169,410)(170,409)(171,412)(172,411)(173,414)(174,413)(175,416)(176,415)
(177,418)(178,417)(179,420)(180,419)(181,422)(182,421)(183,424)(184,423)
(185,426)(186,425)(187,428)(188,427)(189,430)(190,429)(191,432)(192,431)
(193,434)(194,433)(195,436)(196,435)(197,438)(198,437)(199,440)(200,439)
(201,442)(202,441)(203,444)(204,443)(205,446)(206,445)(207,448)(208,447)
(209,450)(210,449)(211,452)(212,451)(213,454)(214,453)(215,456)(216,455)
(217,458)(218,457)(219,460)(220,459)(221,462)(222,461)(223,464)(224,463)
(225,466)(226,465)(227,468)(228,467)(229,470)(230,469)(231,472)(232,471)
(233,474)(234,473)(235,476)(236,475)(237,478)(238,477)(239,480)(240,479);;
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*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(480)!(  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)
( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)
( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)
( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)
(112,116)(121,181)(122,182)(123,183)(124,184)(125,197)(126,198)(127,199)
(128,200)(129,193)(130,194)(131,195)(132,196)(133,189)(134,190)(135,191)
(136,192)(137,185)(138,186)(139,187)(140,188)(141,201)(142,202)(143,203)
(144,204)(145,217)(146,218)(147,219)(148,220)(149,213)(150,214)(151,215)
(152,216)(153,209)(154,210)(155,211)(156,212)(157,205)(158,206)(159,207)
(160,208)(161,221)(162,222)(163,223)(164,224)(165,237)(166,238)(167,239)
(168,240)(169,233)(170,234)(171,235)(172,236)(173,229)(174,230)(175,231)
(176,232)(177,225)(178,226)(179,227)(180,228)(245,257)(246,258)(247,259)
(248,260)(249,253)(250,254)(251,255)(252,256)(265,277)(266,278)(267,279)
(268,280)(269,273)(270,274)(271,275)(272,276)(285,297)(286,298)(287,299)
(288,300)(289,293)(290,294)(291,295)(292,296)(305,317)(306,318)(307,319)
(308,320)(309,313)(310,314)(311,315)(312,316)(325,337)(326,338)(327,339)
(328,340)(329,333)(330,334)(331,335)(332,336)(345,357)(346,358)(347,359)
(348,360)(349,353)(350,354)(351,355)(352,356)(361,421)(362,422)(363,423)
(364,424)(365,437)(366,438)(367,439)(368,440)(369,433)(370,434)(371,435)
(372,436)(373,429)(374,430)(375,431)(376,432)(377,425)(378,426)(379,427)
(380,428)(381,441)(382,442)(383,443)(384,444)(385,457)(386,458)(387,459)
(388,460)(389,453)(390,454)(391,455)(392,456)(393,449)(394,450)(395,451)
(396,452)(397,445)(398,446)(399,447)(400,448)(401,461)(402,462)(403,463)
(404,464)(405,477)(406,478)(407,479)(408,480)(409,473)(410,474)(411,475)
(412,476)(413,469)(414,470)(415,471)(416,472)(417,465)(418,466)(419,467)
(420,468);
s1 := Sym(480)!(  1,125)(  2,126)(  3,128)(  4,127)(  5,121)(  6,122)(  7,124)
(  8,123)(  9,137)( 10,138)( 11,140)( 12,139)( 13,133)( 14,134)( 15,136)
( 16,135)( 17,129)( 18,130)( 19,132)( 20,131)( 21,165)( 22,166)( 23,168)
( 24,167)( 25,161)( 26,162)( 27,164)( 28,163)( 29,177)( 30,178)( 31,180)
( 32,179)( 33,173)( 34,174)( 35,176)( 36,175)( 37,169)( 38,170)( 39,172)
( 40,171)( 41,145)( 42,146)( 43,148)( 44,147)( 45,141)( 46,142)( 47,144)
( 48,143)( 49,157)( 50,158)( 51,160)( 52,159)( 53,153)( 54,154)( 55,156)
( 56,155)( 57,149)( 58,150)( 59,152)( 60,151)( 61,185)( 62,186)( 63,188)
( 64,187)( 65,181)( 66,182)( 67,184)( 68,183)( 69,197)( 70,198)( 71,200)
( 72,199)( 73,193)( 74,194)( 75,196)( 76,195)( 77,189)( 78,190)( 79,192)
( 80,191)( 81,225)( 82,226)( 83,228)( 84,227)( 85,221)( 86,222)( 87,224)
( 88,223)( 89,237)( 90,238)( 91,240)( 92,239)( 93,233)( 94,234)( 95,236)
( 96,235)( 97,229)( 98,230)( 99,232)(100,231)(101,205)(102,206)(103,208)
(104,207)(105,201)(106,202)(107,204)(108,203)(109,217)(110,218)(111,220)
(112,219)(113,213)(114,214)(115,216)(116,215)(117,209)(118,210)(119,212)
(120,211)(241,365)(242,366)(243,368)(244,367)(245,361)(246,362)(247,364)
(248,363)(249,377)(250,378)(251,380)(252,379)(253,373)(254,374)(255,376)
(256,375)(257,369)(258,370)(259,372)(260,371)(261,405)(262,406)(263,408)
(264,407)(265,401)(266,402)(267,404)(268,403)(269,417)(270,418)(271,420)
(272,419)(273,413)(274,414)(275,416)(276,415)(277,409)(278,410)(279,412)
(280,411)(281,385)(282,386)(283,388)(284,387)(285,381)(286,382)(287,384)
(288,383)(289,397)(290,398)(291,400)(292,399)(293,393)(294,394)(295,396)
(296,395)(297,389)(298,390)(299,392)(300,391)(301,425)(302,426)(303,428)
(304,427)(305,421)(306,422)(307,424)(308,423)(309,437)(310,438)(311,440)
(312,439)(313,433)(314,434)(315,436)(316,435)(317,429)(318,430)(319,432)
(320,431)(321,465)(322,466)(323,468)(324,467)(325,461)(326,462)(327,464)
(328,463)(329,477)(330,478)(331,480)(332,479)(333,473)(334,474)(335,476)
(336,475)(337,469)(338,470)(339,472)(340,471)(341,445)(342,446)(343,448)
(344,447)(345,441)(346,442)(347,444)(348,443)(349,457)(350,458)(351,460)
(352,459)(353,453)(354,454)(355,456)(356,455)(357,449)(358,450)(359,452)
(360,451);
s2 := Sym(480)!(  1, 21)(  2, 24)(  3, 23)(  4, 22)(  5, 25)(  6, 28)(  7, 27)
(  8, 26)(  9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)
( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)
( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)
( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)
(110,112)(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)
(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)
(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)
(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)
(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)
(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)
(222,224)(226,228)(230,232)(234,236)(238,240)(241,261)(242,264)(243,263)
(244,262)(245,265)(246,268)(247,267)(248,266)(249,269)(250,272)(251,271)
(252,270)(253,273)(254,276)(255,275)(256,274)(257,277)(258,280)(259,279)
(260,278)(282,284)(286,288)(290,292)(294,296)(298,300)(301,321)(302,324)
(303,323)(304,322)(305,325)(306,328)(307,327)(308,326)(309,329)(310,332)
(311,331)(312,330)(313,333)(314,336)(315,335)(316,334)(317,337)(318,340)
(319,339)(320,338)(342,344)(346,348)(350,352)(354,356)(358,360)(361,381)
(362,384)(363,383)(364,382)(365,385)(366,388)(367,387)(368,386)(369,389)
(370,392)(371,391)(372,390)(373,393)(374,396)(375,395)(376,394)(377,397)
(378,400)(379,399)(380,398)(402,404)(406,408)(410,412)(414,416)(418,420)
(421,441)(422,444)(423,443)(424,442)(425,445)(426,448)(427,447)(428,446)
(429,449)(430,452)(431,451)(432,450)(433,453)(434,456)(435,455)(436,454)
(437,457)(438,460)(439,459)(440,458)(462,464)(466,468)(470,472)(474,476)
(478,480);
s3 := Sym(480)!(  1,242)(  2,241)(  3,244)(  4,243)(  5,246)(  6,245)(  7,248)
(  8,247)(  9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)
( 16,255)( 17,258)( 18,257)( 19,260)( 20,259)( 21,262)( 22,261)( 23,264)
( 24,263)( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)
( 32,271)( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)
( 40,279)( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)
( 48,287)( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)
( 56,295)( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)
( 64,303)( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)
( 72,311)( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)
( 80,319)( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)
( 88,327)( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)
( 96,335)( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)
(104,343)(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)
(112,351)(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)
(120,359)(121,362)(122,361)(123,364)(124,363)(125,366)(126,365)(127,368)
(128,367)(129,370)(130,369)(131,372)(132,371)(133,374)(134,373)(135,376)
(136,375)(137,378)(138,377)(139,380)(140,379)(141,382)(142,381)(143,384)
(144,383)(145,386)(146,385)(147,388)(148,387)(149,390)(150,389)(151,392)
(152,391)(153,394)(154,393)(155,396)(156,395)(157,398)(158,397)(159,400)
(160,399)(161,402)(162,401)(163,404)(164,403)(165,406)(166,405)(167,408)
(168,407)(169,410)(170,409)(171,412)(172,411)(173,414)(174,413)(175,416)
(176,415)(177,418)(178,417)(179,420)(180,419)(181,422)(182,421)(183,424)
(184,423)(185,426)(186,425)(187,428)(188,427)(189,430)(190,429)(191,432)
(192,431)(193,434)(194,433)(195,436)(196,435)(197,438)(198,437)(199,440)
(200,439)(201,442)(202,441)(203,444)(204,443)(205,446)(206,445)(207,448)
(208,447)(209,450)(210,449)(211,452)(212,451)(213,454)(214,453)(215,456)
(216,455)(217,458)(218,457)(219,460)(220,459)(221,462)(222,461)(223,464)
(224,463)(225,466)(226,465)(227,468)(228,467)(229,470)(230,469)(231,472)
(232,471)(233,474)(234,473)(235,476)(236,475)(237,478)(238,477)(239,480)
(240,479);
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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*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 >; 
 
References : None.
to this polytope