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Polytope of Type {4,6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,30}*1920
if this polytope has a name.
Group : SmallGroup(1920,240232)
Rank : 4
Schlafli Type : {4,6,30}
Number of vertices, edges, etc : 4, 16, 120, 40
Order of s0s1s2s3 : 20
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 : {4,6,15}*960, {2,6,30}*960
   4-fold quotients : {2,6,15}*480
   5-fold quotients : {4,6,6}*384
   10-fold quotients : {4,6,3}*192, {2,6,6}*192
   12-fold quotients : {4,2,10}*160
   20-fold quotients : {2,3,6}*96, {2,6,3}*96
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   40-fold quotients : {2,3,3}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {4,2,2}*32
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)
(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)
( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)
( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)
( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)
( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)
( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)
( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)
( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)
(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)
(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240)
(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)
(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)
(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)
(273,393)(274,394)(275,395)(276,396)(277,397)(278,398)(279,399)(280,400)
(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)(288,408)
(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)(296,416)
(297,417)(298,418)(299,419)(300,420)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)
(313,433)(314,434)(315,435)(316,436)(317,437)(318,438)(319,439)(320,440)
(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)(328,448)
(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)(336,456)
(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)(344,464)
(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)(352,472)
(353,473)(354,474)(355,475)(356,476)(357,477)(358,478)(359,479)(360,480);;
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)(121,181)(122,182)(123,184)(124,183)(125,185)(126,186)
(127,188)(128,187)(129,189)(130,190)(131,192)(132,191)(133,193)(134,194)
(135,196)(136,195)(137,197)(138,198)(139,200)(140,199)(141,221)(142,222)
(143,224)(144,223)(145,225)(146,226)(147,228)(148,227)(149,229)(150,230)
(151,232)(152,231)(153,233)(154,234)(155,236)(156,235)(157,237)(158,238)
(159,240)(160,239)(161,201)(162,202)(163,204)(164,203)(165,205)(166,206)
(167,208)(168,207)(169,209)(170,210)(171,212)(172,211)(173,213)(174,214)
(175,216)(176,215)(177,217)(178,218)(179,220)(180,219)(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)
(361,421)(362,422)(363,424)(364,423)(365,425)(366,426)(367,428)(368,427)
(369,429)(370,430)(371,432)(372,431)(373,433)(374,434)(375,436)(376,435)
(377,437)(378,438)(379,440)(380,439)(381,461)(382,462)(383,464)(384,463)
(385,465)(386,466)(387,468)(388,467)(389,469)(390,470)(391,472)(392,471)
(393,473)(394,474)(395,476)(396,475)(397,477)(398,478)(399,480)(400,479)
(401,441)(402,442)(403,444)(404,443)(405,445)(406,446)(407,448)(408,447)
(409,449)(410,450)(411,452)(412,451)(413,453)(414,454)(415,456)(416,455)
(417,457)(418,458)(419,460)(420,459);;
s2 := (  1, 21)(  2, 24)(  3, 23)(  4, 22)(  5, 37)(  6, 40)(  7, 39)(  8, 38)
(  9, 33)( 10, 36)( 11, 35)( 12, 34)( 13, 29)( 14, 32)( 15, 31)( 16, 30)
( 17, 25)( 18, 28)( 19, 27)( 20, 26)( 42, 44)( 45, 57)( 46, 60)( 47, 59)
( 48, 58)( 49, 53)( 50, 56)( 51, 55)( 52, 54)( 61, 81)( 62, 84)( 63, 83)
( 64, 82)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69, 93)( 70, 96)( 71, 95)
( 72, 94)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)( 78, 88)( 79, 87)
( 80, 86)(102,104)(105,117)(106,120)(107,119)(108,118)(109,113)(110,116)
(111,115)(112,114)(121,141)(122,144)(123,143)(124,142)(125,157)(126,160)
(127,159)(128,158)(129,153)(130,156)(131,155)(132,154)(133,149)(134,152)
(135,151)(136,150)(137,145)(138,148)(139,147)(140,146)(162,164)(165,177)
(166,180)(167,179)(168,178)(169,173)(170,176)(171,175)(172,174)(181,201)
(182,204)(183,203)(184,202)(185,217)(186,220)(187,219)(188,218)(189,213)
(190,216)(191,215)(192,214)(193,209)(194,212)(195,211)(196,210)(197,205)
(198,208)(199,207)(200,206)(222,224)(225,237)(226,240)(227,239)(228,238)
(229,233)(230,236)(231,235)(232,234)(241,261)(242,264)(243,263)(244,262)
(245,277)(246,280)(247,279)(248,278)(249,273)(250,276)(251,275)(252,274)
(253,269)(254,272)(255,271)(256,270)(257,265)(258,268)(259,267)(260,266)
(282,284)(285,297)(286,300)(287,299)(288,298)(289,293)(290,296)(291,295)
(292,294)(301,321)(302,324)(303,323)(304,322)(305,337)(306,340)(307,339)
(308,338)(309,333)(310,336)(311,335)(312,334)(313,329)(314,332)(315,331)
(316,330)(317,325)(318,328)(319,327)(320,326)(342,344)(345,357)(346,360)
(347,359)(348,358)(349,353)(350,356)(351,355)(352,354)(361,381)(362,384)
(363,383)(364,382)(365,397)(366,400)(367,399)(368,398)(369,393)(370,396)
(371,395)(372,394)(373,389)(374,392)(375,391)(376,390)(377,385)(378,388)
(379,387)(380,386)(402,404)(405,417)(406,420)(407,419)(408,418)(409,413)
(410,416)(411,415)(412,414)(421,441)(422,444)(423,443)(424,442)(425,457)
(426,460)(427,459)(428,458)(429,453)(430,456)(431,455)(432,454)(433,449)
(434,452)(435,451)(436,450)(437,445)(438,448)(439,447)(440,446)(462,464)
(465,477)(466,480)(467,479)(468,478)(469,473)(470,476)(471,475)(472,474);;
s3 := (  1,246)(  2,245)(  3,247)(  4,248)(  5,242)(  6,241)(  7,243)(  8,244)
(  9,258)( 10,257)( 11,259)( 12,260)( 13,254)( 14,253)( 15,255)( 16,256)
( 17,250)( 18,249)( 19,251)( 20,252)( 21,286)( 22,285)( 23,287)( 24,288)
( 25,282)( 26,281)( 27,283)( 28,284)( 29,298)( 30,297)( 31,299)( 32,300)
( 33,294)( 34,293)( 35,295)( 36,296)( 37,290)( 38,289)( 39,291)( 40,292)
( 41,266)( 42,265)( 43,267)( 44,268)( 45,262)( 46,261)( 47,263)( 48,264)
( 49,278)( 50,277)( 51,279)( 52,280)( 53,274)( 54,273)( 55,275)( 56,276)
( 57,270)( 58,269)( 59,271)( 60,272)( 61,306)( 62,305)( 63,307)( 64,308)
( 65,302)( 66,301)( 67,303)( 68,304)( 69,318)( 70,317)( 71,319)( 72,320)
( 73,314)( 74,313)( 75,315)( 76,316)( 77,310)( 78,309)( 79,311)( 80,312)
( 81,346)( 82,345)( 83,347)( 84,348)( 85,342)( 86,341)( 87,343)( 88,344)
( 89,358)( 90,357)( 91,359)( 92,360)( 93,354)( 94,353)( 95,355)( 96,356)
( 97,350)( 98,349)( 99,351)(100,352)(101,326)(102,325)(103,327)(104,328)
(105,322)(106,321)(107,323)(108,324)(109,338)(110,337)(111,339)(112,340)
(113,334)(114,333)(115,335)(116,336)(117,330)(118,329)(119,331)(120,332)
(121,366)(122,365)(123,367)(124,368)(125,362)(126,361)(127,363)(128,364)
(129,378)(130,377)(131,379)(132,380)(133,374)(134,373)(135,375)(136,376)
(137,370)(138,369)(139,371)(140,372)(141,406)(142,405)(143,407)(144,408)
(145,402)(146,401)(147,403)(148,404)(149,418)(150,417)(151,419)(152,420)
(153,414)(154,413)(155,415)(156,416)(157,410)(158,409)(159,411)(160,412)
(161,386)(162,385)(163,387)(164,388)(165,382)(166,381)(167,383)(168,384)
(169,398)(170,397)(171,399)(172,400)(173,394)(174,393)(175,395)(176,396)
(177,390)(178,389)(179,391)(180,392)(181,426)(182,425)(183,427)(184,428)
(185,422)(186,421)(187,423)(188,424)(189,438)(190,437)(191,439)(192,440)
(193,434)(194,433)(195,435)(196,436)(197,430)(198,429)(199,431)(200,432)
(201,466)(202,465)(203,467)(204,468)(205,462)(206,461)(207,463)(208,464)
(209,478)(210,477)(211,479)(212,480)(213,474)(214,473)(215,475)(216,476)
(217,470)(218,469)(219,471)(220,472)(221,446)(222,445)(223,447)(224,448)
(225,442)(226,441)(227,443)(228,444)(229,458)(230,457)(231,459)(232,460)
(233,454)(234,453)(235,455)(236,456)(237,450)(238,449)(239,451)(240,452);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(480)!(  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)
(  8,128)(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)
( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)
( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)
( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)
( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)
( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)
( 72,192)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)
( 88,208)( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)
( 96,216)( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)
(104,224)(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)
(112,232)(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)
(120,240)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)
(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)
(264,384)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)
(272,392)(273,393)(274,394)(275,395)(276,396)(277,397)(278,398)(279,399)
(280,400)(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)
(288,408)(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)
(296,416)(297,417)(298,418)(299,419)(300,420)(301,421)(302,422)(303,423)
(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)
(312,432)(313,433)(314,434)(315,435)(316,436)(317,437)(318,438)(319,439)
(320,440)(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)
(328,448)(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)
(336,456)(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)
(344,464)(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)
(352,472)(353,473)(354,474)(355,475)(356,476)(357,477)(358,478)(359,479)
(360,480);
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)(121,181)(122,182)(123,184)(124,183)(125,185)
(126,186)(127,188)(128,187)(129,189)(130,190)(131,192)(132,191)(133,193)
(134,194)(135,196)(136,195)(137,197)(138,198)(139,200)(140,199)(141,221)
(142,222)(143,224)(144,223)(145,225)(146,226)(147,228)(148,227)(149,229)
(150,230)(151,232)(152,231)(153,233)(154,234)(155,236)(156,235)(157,237)
(158,238)(159,240)(160,239)(161,201)(162,202)(163,204)(164,203)(165,205)
(166,206)(167,208)(168,207)(169,209)(170,210)(171,212)(172,211)(173,213)
(174,214)(175,216)(176,215)(177,217)(178,218)(179,220)(180,219)(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)(361,421)(362,422)(363,424)(364,423)(365,425)(366,426)(367,428)
(368,427)(369,429)(370,430)(371,432)(372,431)(373,433)(374,434)(375,436)
(376,435)(377,437)(378,438)(379,440)(380,439)(381,461)(382,462)(383,464)
(384,463)(385,465)(386,466)(387,468)(388,467)(389,469)(390,470)(391,472)
(392,471)(393,473)(394,474)(395,476)(396,475)(397,477)(398,478)(399,480)
(400,479)(401,441)(402,442)(403,444)(404,443)(405,445)(406,446)(407,448)
(408,447)(409,449)(410,450)(411,452)(412,451)(413,453)(414,454)(415,456)
(416,455)(417,457)(418,458)(419,460)(420,459);
s2 := Sym(480)!(  1, 21)(  2, 24)(  3, 23)(  4, 22)(  5, 37)(  6, 40)(  7, 39)
(  8, 38)(  9, 33)( 10, 36)( 11, 35)( 12, 34)( 13, 29)( 14, 32)( 15, 31)
( 16, 30)( 17, 25)( 18, 28)( 19, 27)( 20, 26)( 42, 44)( 45, 57)( 46, 60)
( 47, 59)( 48, 58)( 49, 53)( 50, 56)( 51, 55)( 52, 54)( 61, 81)( 62, 84)
( 63, 83)( 64, 82)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69, 93)( 70, 96)
( 71, 95)( 72, 94)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)( 78, 88)
( 79, 87)( 80, 86)(102,104)(105,117)(106,120)(107,119)(108,118)(109,113)
(110,116)(111,115)(112,114)(121,141)(122,144)(123,143)(124,142)(125,157)
(126,160)(127,159)(128,158)(129,153)(130,156)(131,155)(132,154)(133,149)
(134,152)(135,151)(136,150)(137,145)(138,148)(139,147)(140,146)(162,164)
(165,177)(166,180)(167,179)(168,178)(169,173)(170,176)(171,175)(172,174)
(181,201)(182,204)(183,203)(184,202)(185,217)(186,220)(187,219)(188,218)
(189,213)(190,216)(191,215)(192,214)(193,209)(194,212)(195,211)(196,210)
(197,205)(198,208)(199,207)(200,206)(222,224)(225,237)(226,240)(227,239)
(228,238)(229,233)(230,236)(231,235)(232,234)(241,261)(242,264)(243,263)
(244,262)(245,277)(246,280)(247,279)(248,278)(249,273)(250,276)(251,275)
(252,274)(253,269)(254,272)(255,271)(256,270)(257,265)(258,268)(259,267)
(260,266)(282,284)(285,297)(286,300)(287,299)(288,298)(289,293)(290,296)
(291,295)(292,294)(301,321)(302,324)(303,323)(304,322)(305,337)(306,340)
(307,339)(308,338)(309,333)(310,336)(311,335)(312,334)(313,329)(314,332)
(315,331)(316,330)(317,325)(318,328)(319,327)(320,326)(342,344)(345,357)
(346,360)(347,359)(348,358)(349,353)(350,356)(351,355)(352,354)(361,381)
(362,384)(363,383)(364,382)(365,397)(366,400)(367,399)(368,398)(369,393)
(370,396)(371,395)(372,394)(373,389)(374,392)(375,391)(376,390)(377,385)
(378,388)(379,387)(380,386)(402,404)(405,417)(406,420)(407,419)(408,418)
(409,413)(410,416)(411,415)(412,414)(421,441)(422,444)(423,443)(424,442)
(425,457)(426,460)(427,459)(428,458)(429,453)(430,456)(431,455)(432,454)
(433,449)(434,452)(435,451)(436,450)(437,445)(438,448)(439,447)(440,446)
(462,464)(465,477)(466,480)(467,479)(468,478)(469,473)(470,476)(471,475)
(472,474);
s3 := Sym(480)!(  1,246)(  2,245)(  3,247)(  4,248)(  5,242)(  6,241)(  7,243)
(  8,244)(  9,258)( 10,257)( 11,259)( 12,260)( 13,254)( 14,253)( 15,255)
( 16,256)( 17,250)( 18,249)( 19,251)( 20,252)( 21,286)( 22,285)( 23,287)
( 24,288)( 25,282)( 26,281)( 27,283)( 28,284)( 29,298)( 30,297)( 31,299)
( 32,300)( 33,294)( 34,293)( 35,295)( 36,296)( 37,290)( 38,289)( 39,291)
( 40,292)( 41,266)( 42,265)( 43,267)( 44,268)( 45,262)( 46,261)( 47,263)
( 48,264)( 49,278)( 50,277)( 51,279)( 52,280)( 53,274)( 54,273)( 55,275)
( 56,276)( 57,270)( 58,269)( 59,271)( 60,272)( 61,306)( 62,305)( 63,307)
( 64,308)( 65,302)( 66,301)( 67,303)( 68,304)( 69,318)( 70,317)( 71,319)
( 72,320)( 73,314)( 74,313)( 75,315)( 76,316)( 77,310)( 78,309)( 79,311)
( 80,312)( 81,346)( 82,345)( 83,347)( 84,348)( 85,342)( 86,341)( 87,343)
( 88,344)( 89,358)( 90,357)( 91,359)( 92,360)( 93,354)( 94,353)( 95,355)
( 96,356)( 97,350)( 98,349)( 99,351)(100,352)(101,326)(102,325)(103,327)
(104,328)(105,322)(106,321)(107,323)(108,324)(109,338)(110,337)(111,339)
(112,340)(113,334)(114,333)(115,335)(116,336)(117,330)(118,329)(119,331)
(120,332)(121,366)(122,365)(123,367)(124,368)(125,362)(126,361)(127,363)
(128,364)(129,378)(130,377)(131,379)(132,380)(133,374)(134,373)(135,375)
(136,376)(137,370)(138,369)(139,371)(140,372)(141,406)(142,405)(143,407)
(144,408)(145,402)(146,401)(147,403)(148,404)(149,418)(150,417)(151,419)
(152,420)(153,414)(154,413)(155,415)(156,416)(157,410)(158,409)(159,411)
(160,412)(161,386)(162,385)(163,387)(164,388)(165,382)(166,381)(167,383)
(168,384)(169,398)(170,397)(171,399)(172,400)(173,394)(174,393)(175,395)
(176,396)(177,390)(178,389)(179,391)(180,392)(181,426)(182,425)(183,427)
(184,428)(185,422)(186,421)(187,423)(188,424)(189,438)(190,437)(191,439)
(192,440)(193,434)(194,433)(195,435)(196,436)(197,430)(198,429)(199,431)
(200,432)(201,466)(202,465)(203,467)(204,468)(205,462)(206,461)(207,463)
(208,464)(209,478)(210,477)(211,479)(212,480)(213,474)(214,473)(215,475)
(216,476)(217,470)(218,469)(219,471)(220,472)(221,446)(222,445)(223,447)
(224,448)(225,442)(226,441)(227,443)(228,444)(229,458)(230,457)(231,459)
(232,460)(233,454)(234,453)(235,455)(236,456)(237,450)(238,449)(239,451)
(240,452);
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 >; 
 
References : None.
to this polytope