Polytope of Type {6,10,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,10,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240399)
Rank : 4
Schlafli Type : {6,10,4}
Number of vertices, edges, etc : 6, 120, 80, 16
Order of s0s1s2s3 : 30
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) :
   3-fold quotients : {2,10,4}*640a
   6-fold quotients : {2,5,4}*320
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := ( 81,161)( 82,162)( 83,163)( 84,164)( 85,165)( 86,166)( 87,167)( 88,168)
( 89,169)( 90,170)( 91,171)( 92,172)( 93,173)( 94,174)( 95,175)( 96,176)
( 97,177)( 98,178)( 99,179)(100,180)(101,181)(102,182)(103,183)(104,184)
(105,185)(106,186)(107,187)(108,188)(109,189)(110,190)(111,191)(112,192)
(113,193)(114,194)(115,195)(116,196)(117,197)(118,198)(119,199)(120,200)
(121,201)(122,202)(123,203)(124,204)(125,205)(126,206)(127,207)(128,208)
(129,209)(130,210)(131,211)(132,212)(133,213)(134,214)(135,215)(136,216)
(137,217)(138,218)(139,219)(140,220)(141,221)(142,222)(143,223)(144,224)
(145,225)(146,226)(147,227)(148,228)(149,229)(150,230)(151,231)(152,232)
(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)(160,240)
(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)(328,408)
(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)(336,416)
(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)(344,424)
(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)(352,432)
(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)(360,440)
(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)(368,448)
(369,449)(370,450)(371,451)(372,452)(373,453)(374,454)(375,455)(376,456)
(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)(384,464)
(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,471)(392,472)
(393,473)(394,474)(395,475)(396,476)(397,477)(398,478)(399,479)(400,480);;
s1 := (  1, 81)(  2, 82)(  3, 84)(  4, 83)(  5, 85)(  6, 86)(  7, 88)(  8, 87)
(  9, 94)( 10, 93)( 11, 95)( 12, 96)( 13, 90)( 14, 89)( 15, 91)( 16, 92)
( 17,145)( 18,146)( 19,148)( 20,147)( 21,149)( 22,150)( 23,152)( 24,151)
( 25,158)( 26,157)( 27,159)( 28,160)( 29,154)( 30,153)( 31,155)( 32,156)
( 33,129)( 34,130)( 35,132)( 36,131)( 37,133)( 38,134)( 39,136)( 40,135)
( 41,142)( 42,141)( 43,143)( 44,144)( 45,138)( 46,137)( 47,139)( 48,140)
( 49,113)( 50,114)( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)( 56,119)
( 57,126)( 58,125)( 59,127)( 60,128)( 61,122)( 62,121)( 63,123)( 64,124)
( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,101)( 70,102)( 71,104)( 72,103)
( 73,110)( 74,109)( 75,111)( 76,112)( 77,106)( 78,105)( 79,107)( 80,108)
(163,164)(167,168)(169,174)(170,173)(171,175)(172,176)(177,225)(178,226)
(179,228)(180,227)(181,229)(182,230)(183,232)(184,231)(185,238)(186,237)
(187,239)(188,240)(189,234)(190,233)(191,235)(192,236)(193,209)(194,210)
(195,212)(196,211)(197,213)(198,214)(199,216)(200,215)(201,222)(202,221)
(203,223)(204,224)(205,218)(206,217)(207,219)(208,220)(241,321)(242,322)
(243,324)(244,323)(245,325)(246,326)(247,328)(248,327)(249,334)(250,333)
(251,335)(252,336)(253,330)(254,329)(255,331)(256,332)(257,385)(258,386)
(259,388)(260,387)(261,389)(262,390)(263,392)(264,391)(265,398)(266,397)
(267,399)(268,400)(269,394)(270,393)(271,395)(272,396)(273,369)(274,370)
(275,372)(276,371)(277,373)(278,374)(279,376)(280,375)(281,382)(282,381)
(283,383)(284,384)(285,378)(286,377)(287,379)(288,380)(289,353)(290,354)
(291,356)(292,355)(293,357)(294,358)(295,360)(296,359)(297,366)(298,365)
(299,367)(300,368)(301,362)(302,361)(303,363)(304,364)(305,337)(306,338)
(307,340)(308,339)(309,341)(310,342)(311,344)(312,343)(313,350)(314,349)
(315,351)(316,352)(317,346)(318,345)(319,347)(320,348)(403,404)(407,408)
(409,414)(410,413)(411,415)(412,416)(417,465)(418,466)(419,468)(420,467)
(421,469)(422,470)(423,472)(424,471)(425,478)(426,477)(427,479)(428,480)
(429,474)(430,473)(431,475)(432,476)(433,449)(434,450)(435,452)(436,451)
(437,453)(438,454)(439,456)(440,455)(441,462)(442,461)(443,463)(444,464)
(445,458)(446,457)(447,459)(448,460);;
s2 := (  1,257)(  2,272)(  3,262)(  4,267)(  5,270)(  6,259)(  7,265)(  8,264)
(  9,263)( 10,266)( 11,260)( 12,269)( 13,268)( 14,261)( 15,271)( 16,258)
( 17,241)( 18,256)( 19,246)( 20,251)( 21,254)( 22,243)( 23,249)( 24,248)
( 25,247)( 26,250)( 27,244)( 28,253)( 29,252)( 30,245)( 31,255)( 32,242)
( 33,305)( 34,320)( 35,310)( 36,315)( 37,318)( 38,307)( 39,313)( 40,312)
( 41,311)( 42,314)( 43,308)( 44,317)( 45,316)( 46,309)( 47,319)( 48,306)
( 49,289)( 50,304)( 51,294)( 52,299)( 53,302)( 54,291)( 55,297)( 56,296)
( 57,295)( 58,298)( 59,292)( 60,301)( 61,300)( 62,293)( 63,303)( 64,290)
( 65,273)( 66,288)( 67,278)( 68,283)( 69,286)( 70,275)( 71,281)( 72,280)
( 73,279)( 74,282)( 75,276)( 76,285)( 77,284)( 78,277)( 79,287)( 80,274)
( 81,337)( 82,352)( 83,342)( 84,347)( 85,350)( 86,339)( 87,345)( 88,344)
( 89,343)( 90,346)( 91,340)( 92,349)( 93,348)( 94,341)( 95,351)( 96,338)
( 97,321)( 98,336)( 99,326)(100,331)(101,334)(102,323)(103,329)(104,328)
(105,327)(106,330)(107,324)(108,333)(109,332)(110,325)(111,335)(112,322)
(113,385)(114,400)(115,390)(116,395)(117,398)(118,387)(119,393)(120,392)
(121,391)(122,394)(123,388)(124,397)(125,396)(126,389)(127,399)(128,386)
(129,369)(130,384)(131,374)(132,379)(133,382)(134,371)(135,377)(136,376)
(137,375)(138,378)(139,372)(140,381)(141,380)(142,373)(143,383)(144,370)
(145,353)(146,368)(147,358)(148,363)(149,366)(150,355)(151,361)(152,360)
(153,359)(154,362)(155,356)(156,365)(157,364)(158,357)(159,367)(160,354)
(161,417)(162,432)(163,422)(164,427)(165,430)(166,419)(167,425)(168,424)
(169,423)(170,426)(171,420)(172,429)(173,428)(174,421)(175,431)(176,418)
(177,401)(178,416)(179,406)(180,411)(181,414)(182,403)(183,409)(184,408)
(185,407)(186,410)(187,404)(188,413)(189,412)(190,405)(191,415)(192,402)
(193,465)(194,480)(195,470)(196,475)(197,478)(198,467)(199,473)(200,472)
(201,471)(202,474)(203,468)(204,477)(205,476)(206,469)(207,479)(208,466)
(209,449)(210,464)(211,454)(212,459)(213,462)(214,451)(215,457)(216,456)
(217,455)(218,458)(219,452)(220,461)(221,460)(222,453)(223,463)(224,450)
(225,433)(226,448)(227,438)(228,443)(229,446)(230,435)(231,441)(232,440)
(233,439)(234,442)(235,436)(236,445)(237,444)(238,437)(239,447)(240,434);;
s3 := (  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 13)( 10, 14)( 11, 15)( 12, 16)
( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)( 28, 32)
( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)( 60, 64)
( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)( 76, 80)
( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
( 97,101)( 98,102)( 99,103)(100,104)(105,109)(106,110)(107,111)(108,112)
(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)
(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)
(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160)
(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)(172,176)
(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)(188,192)
(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)(204,208)
(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)(220,224)
(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)(236,240)
(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)(252,256)
(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)(268,272)
(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)(284,288)
(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)(300,304)
(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)(316,320)
(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)(332,336)
(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)(348,352)
(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)(364,368)
(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)(380,384)
(385,389)(386,390)(387,391)(388,392)(393,397)(394,398)(395,399)(396,400)
(401,405)(402,406)(403,407)(404,408)(409,413)(410,414)(411,415)(412,416)
(417,421)(418,422)(419,423)(420,424)(425,429)(426,430)(427,431)(428,432)
(433,437)(434,438)(435,439)(436,440)(441,445)(442,446)(443,447)(444,448)
(449,453)(450,454)(451,455)(452,456)(457,461)(458,462)(459,463)(460,464)
(465,469)(466,470)(467,471)(468,472)(473,477)(474,478)(475,479)(476,480);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*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)!( 81,161)( 82,162)( 83,163)( 84,164)( 85,165)( 86,166)( 87,167)
( 88,168)( 89,169)( 90,170)( 91,171)( 92,172)( 93,173)( 94,174)( 95,175)
( 96,176)( 97,177)( 98,178)( 99,179)(100,180)(101,181)(102,182)(103,183)
(104,184)(105,185)(106,186)(107,187)(108,188)(109,189)(110,190)(111,191)
(112,192)(113,193)(114,194)(115,195)(116,196)(117,197)(118,198)(119,199)
(120,200)(121,201)(122,202)(123,203)(124,204)(125,205)(126,206)(127,207)
(128,208)(129,209)(130,210)(131,211)(132,212)(133,213)(134,214)(135,215)
(136,216)(137,217)(138,218)(139,219)(140,220)(141,221)(142,222)(143,223)
(144,224)(145,225)(146,226)(147,227)(148,228)(149,229)(150,230)(151,231)
(152,232)(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)
(160,240)(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)
(328,408)(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)
(336,416)(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)
(344,424)(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)
(352,432)(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)
(360,440)(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)
(368,448)(369,449)(370,450)(371,451)(372,452)(373,453)(374,454)(375,455)
(376,456)(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)
(384,464)(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,471)
(392,472)(393,473)(394,474)(395,475)(396,476)(397,477)(398,478)(399,479)
(400,480);
s1 := Sym(480)!(  1, 81)(  2, 82)(  3, 84)(  4, 83)(  5, 85)(  6, 86)(  7, 88)
(  8, 87)(  9, 94)( 10, 93)( 11, 95)( 12, 96)( 13, 90)( 14, 89)( 15, 91)
( 16, 92)( 17,145)( 18,146)( 19,148)( 20,147)( 21,149)( 22,150)( 23,152)
( 24,151)( 25,158)( 26,157)( 27,159)( 28,160)( 29,154)( 30,153)( 31,155)
( 32,156)( 33,129)( 34,130)( 35,132)( 36,131)( 37,133)( 38,134)( 39,136)
( 40,135)( 41,142)( 42,141)( 43,143)( 44,144)( 45,138)( 46,137)( 47,139)
( 48,140)( 49,113)( 50,114)( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)
( 56,119)( 57,126)( 58,125)( 59,127)( 60,128)( 61,122)( 62,121)( 63,123)
( 64,124)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,101)( 70,102)( 71,104)
( 72,103)( 73,110)( 74,109)( 75,111)( 76,112)( 77,106)( 78,105)( 79,107)
( 80,108)(163,164)(167,168)(169,174)(170,173)(171,175)(172,176)(177,225)
(178,226)(179,228)(180,227)(181,229)(182,230)(183,232)(184,231)(185,238)
(186,237)(187,239)(188,240)(189,234)(190,233)(191,235)(192,236)(193,209)
(194,210)(195,212)(196,211)(197,213)(198,214)(199,216)(200,215)(201,222)
(202,221)(203,223)(204,224)(205,218)(206,217)(207,219)(208,220)(241,321)
(242,322)(243,324)(244,323)(245,325)(246,326)(247,328)(248,327)(249,334)
(250,333)(251,335)(252,336)(253,330)(254,329)(255,331)(256,332)(257,385)
(258,386)(259,388)(260,387)(261,389)(262,390)(263,392)(264,391)(265,398)
(266,397)(267,399)(268,400)(269,394)(270,393)(271,395)(272,396)(273,369)
(274,370)(275,372)(276,371)(277,373)(278,374)(279,376)(280,375)(281,382)
(282,381)(283,383)(284,384)(285,378)(286,377)(287,379)(288,380)(289,353)
(290,354)(291,356)(292,355)(293,357)(294,358)(295,360)(296,359)(297,366)
(298,365)(299,367)(300,368)(301,362)(302,361)(303,363)(304,364)(305,337)
(306,338)(307,340)(308,339)(309,341)(310,342)(311,344)(312,343)(313,350)
(314,349)(315,351)(316,352)(317,346)(318,345)(319,347)(320,348)(403,404)
(407,408)(409,414)(410,413)(411,415)(412,416)(417,465)(418,466)(419,468)
(420,467)(421,469)(422,470)(423,472)(424,471)(425,478)(426,477)(427,479)
(428,480)(429,474)(430,473)(431,475)(432,476)(433,449)(434,450)(435,452)
(436,451)(437,453)(438,454)(439,456)(440,455)(441,462)(442,461)(443,463)
(444,464)(445,458)(446,457)(447,459)(448,460);
s2 := Sym(480)!(  1,257)(  2,272)(  3,262)(  4,267)(  5,270)(  6,259)(  7,265)
(  8,264)(  9,263)( 10,266)( 11,260)( 12,269)( 13,268)( 14,261)( 15,271)
( 16,258)( 17,241)( 18,256)( 19,246)( 20,251)( 21,254)( 22,243)( 23,249)
( 24,248)( 25,247)( 26,250)( 27,244)( 28,253)( 29,252)( 30,245)( 31,255)
( 32,242)( 33,305)( 34,320)( 35,310)( 36,315)( 37,318)( 38,307)( 39,313)
( 40,312)( 41,311)( 42,314)( 43,308)( 44,317)( 45,316)( 46,309)( 47,319)
( 48,306)( 49,289)( 50,304)( 51,294)( 52,299)( 53,302)( 54,291)( 55,297)
( 56,296)( 57,295)( 58,298)( 59,292)( 60,301)( 61,300)( 62,293)( 63,303)
( 64,290)( 65,273)( 66,288)( 67,278)( 68,283)( 69,286)( 70,275)( 71,281)
( 72,280)( 73,279)( 74,282)( 75,276)( 76,285)( 77,284)( 78,277)( 79,287)
( 80,274)( 81,337)( 82,352)( 83,342)( 84,347)( 85,350)( 86,339)( 87,345)
( 88,344)( 89,343)( 90,346)( 91,340)( 92,349)( 93,348)( 94,341)( 95,351)
( 96,338)( 97,321)( 98,336)( 99,326)(100,331)(101,334)(102,323)(103,329)
(104,328)(105,327)(106,330)(107,324)(108,333)(109,332)(110,325)(111,335)
(112,322)(113,385)(114,400)(115,390)(116,395)(117,398)(118,387)(119,393)
(120,392)(121,391)(122,394)(123,388)(124,397)(125,396)(126,389)(127,399)
(128,386)(129,369)(130,384)(131,374)(132,379)(133,382)(134,371)(135,377)
(136,376)(137,375)(138,378)(139,372)(140,381)(141,380)(142,373)(143,383)
(144,370)(145,353)(146,368)(147,358)(148,363)(149,366)(150,355)(151,361)
(152,360)(153,359)(154,362)(155,356)(156,365)(157,364)(158,357)(159,367)
(160,354)(161,417)(162,432)(163,422)(164,427)(165,430)(166,419)(167,425)
(168,424)(169,423)(170,426)(171,420)(172,429)(173,428)(174,421)(175,431)
(176,418)(177,401)(178,416)(179,406)(180,411)(181,414)(182,403)(183,409)
(184,408)(185,407)(186,410)(187,404)(188,413)(189,412)(190,405)(191,415)
(192,402)(193,465)(194,480)(195,470)(196,475)(197,478)(198,467)(199,473)
(200,472)(201,471)(202,474)(203,468)(204,477)(205,476)(206,469)(207,479)
(208,466)(209,449)(210,464)(211,454)(212,459)(213,462)(214,451)(215,457)
(216,456)(217,455)(218,458)(219,452)(220,461)(221,460)(222,453)(223,463)
(224,450)(225,433)(226,448)(227,438)(228,443)(229,446)(230,435)(231,441)
(232,440)(233,439)(234,442)(235,436)(236,445)(237,444)(238,437)(239,447)
(240,434);
s3 := Sym(480)!(  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 13)( 10, 14)( 11, 15)
( 12, 16)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)
( 28, 32)( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)
( 60, 64)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)
( 76, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)( 97,101)( 98,102)( 99,103)(100,104)(105,109)(106,110)(107,111)
(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)
(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)
(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)
(156,160)(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)
(172,176)(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)
(188,192)(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)
(204,208)(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)
(220,224)(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)
(236,240)(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)
(252,256)(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)
(268,272)(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)
(284,288)(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)
(300,304)(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)
(316,320)(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)
(332,336)(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)
(348,352)(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)
(364,368)(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)
(380,384)(385,389)(386,390)(387,391)(388,392)(393,397)(394,398)(395,399)
(396,400)(401,405)(402,406)(403,407)(404,408)(409,413)(410,414)(411,415)
(412,416)(417,421)(418,422)(419,423)(420,424)(425,429)(426,430)(427,431)
(428,432)(433,437)(434,438)(435,439)(436,440)(441,445)(442,446)(443,447)
(444,448)(449,453)(450,454)(451,455)(452,456)(457,461)(458,462)(459,463)
(460,464)(465,469)(466,470)(467,471)(468,472)(473,477)(474,478)(475,479)
(476,480);
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*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