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Polytope of Type {20,4,6}

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