Polytope of Type {10,24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,24,4}*1920c
if this polytope has a name.
Group : SmallGroup(1920,238608)
Rank : 4
Schlafli Type : {10,24,4}
Number of vertices, edges, etc : 10, 120, 48, 4
Order of s0s1s2s3 : 120
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 : {10,12,4}*960b
4-fold quotients : {10,6,4}*480b
5-fold quotients : {2,24,4}*384c
10-fold quotients : {2,12,4}*192b
20-fold quotients : {2,6,4}*96c
40-fold quotients : {2,3,4}*48
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)
(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)
(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156)
(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)(172,176)
(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)(192,196)
(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)(212,216)
(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)(232,236)
(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)
(365,377)(366,378)(367,379)(368,380)(369,373)(370,374)(371,375)(372,376)
(385,397)(386,398)(387,399)(388,400)(389,393)(390,394)(391,395)(392,396)
(405,417)(406,418)(407,419)(408,420)(409,413)(410,414)(411,415)(412,416)
(425,437)(426,438)(427,439)(428,440)(429,433)(430,434)(431,435)(432,436)
(445,457)(446,458)(447,459)(448,460)(449,453)(450,454)(451,455)(452,456)
(465,477)(466,478)(467,479)(468,480)(469,473)(470,474)(471,475)(472,476);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 15, 16)( 21, 45)( 22, 46)( 23, 48)( 24, 47)( 25, 41)( 26, 42)( 27, 44)
( 28, 43)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 53)( 34, 54)( 35, 56)
( 36, 55)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 61, 65)( 62, 66)( 63, 68)
( 64, 67)( 69, 77)( 70, 78)( 71, 80)( 72, 79)( 75, 76)( 81,105)( 82,106)
( 83,108)( 84,107)( 85,101)( 86,102)( 87,104)( 88,103)( 89,117)( 90,118)
( 91,120)( 92,119)( 93,113)( 94,114)( 95,116)( 96,115)( 97,109)( 98,110)
( 99,112)(100,111)(121,185)(122,186)(123,188)(124,187)(125,181)(126,182)
(127,184)(128,183)(129,197)(130,198)(131,200)(132,199)(133,193)(134,194)
(135,196)(136,195)(137,189)(138,190)(139,192)(140,191)(141,225)(142,226)
(143,228)(144,227)(145,221)(146,222)(147,224)(148,223)(149,237)(150,238)
(151,240)(152,239)(153,233)(154,234)(155,236)(156,235)(157,229)(158,230)
(159,232)(160,231)(161,205)(162,206)(163,208)(164,207)(165,201)(166,202)
(167,204)(168,203)(169,217)(170,218)(171,220)(172,219)(173,213)(174,214)
(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(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 := ( 1,261)( 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)
(121,441)(122,444)(123,443)(124,442)(125,445)(126,448)(127,447)(128,446)
(129,449)(130,452)(131,451)(132,450)(133,453)(134,456)(135,455)(136,454)
(137,457)(138,460)(139,459)(140,458)(141,421)(142,424)(143,423)(144,422)
(145,425)(146,428)(147,427)(148,426)(149,429)(150,432)(151,431)(152,430)
(153,433)(154,436)(155,435)(156,434)(157,437)(158,440)(159,439)(160,438)
(161,461)(162,464)(163,463)(164,462)(165,465)(166,468)(167,467)(168,466)
(169,469)(170,472)(171,471)(172,470)(173,473)(174,476)(175,475)(176,474)
(177,477)(178,480)(179,479)(180,478)(181,381)(182,384)(183,383)(184,382)
(185,385)(186,388)(187,387)(188,386)(189,389)(190,392)(191,391)(192,390)
(193,393)(194,396)(195,395)(196,394)(197,397)(198,400)(199,399)(200,398)
(201,361)(202,364)(203,363)(204,362)(205,365)(206,368)(207,367)(208,366)
(209,369)(210,372)(211,371)(212,370)(213,373)(214,376)(215,375)(216,374)
(217,377)(218,380)(219,379)(220,378)(221,401)(222,404)(223,403)(224,402)
(225,405)(226,408)(227,407)(228,406)(229,409)(230,412)(231,411)(232,410)
(233,413)(234,416)(235,415)(236,414)(237,417)(238,420)(239,419)(240,418);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)
(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480);;
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, s3*s2*s1*s3*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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)!( 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)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)
(132,136)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)
(152,156)(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)
(172,176)(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)
(192,196)(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)
(212,216)(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)
(232,236)(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)(365,377)(366,378)(367,379)(368,380)(369,373)(370,374)(371,375)
(372,376)(385,397)(386,398)(387,399)(388,400)(389,393)(390,394)(391,395)
(392,396)(405,417)(406,418)(407,419)(408,420)(409,413)(410,414)(411,415)
(412,416)(425,437)(426,438)(427,439)(428,440)(429,433)(430,434)(431,435)
(432,436)(445,457)(446,458)(447,459)(448,460)(449,453)(450,454)(451,455)
(452,456)(465,477)(466,478)(467,479)(468,480)(469,473)(470,474)(471,475)
(472,476);
s1 := Sym(480)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 17)( 10, 18)( 11, 20)
( 12, 19)( 15, 16)( 21, 45)( 22, 46)( 23, 48)( 24, 47)( 25, 41)( 26, 42)
( 27, 44)( 28, 43)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 53)( 34, 54)
( 35, 56)( 36, 55)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 61, 65)( 62, 66)
( 63, 68)( 64, 67)( 69, 77)( 70, 78)( 71, 80)( 72, 79)( 75, 76)( 81,105)
( 82,106)( 83,108)( 84,107)( 85,101)( 86,102)( 87,104)( 88,103)( 89,117)
( 90,118)( 91,120)( 92,119)( 93,113)( 94,114)( 95,116)( 96,115)( 97,109)
( 98,110)( 99,112)(100,111)(121,185)(122,186)(123,188)(124,187)(125,181)
(126,182)(127,184)(128,183)(129,197)(130,198)(131,200)(132,199)(133,193)
(134,194)(135,196)(136,195)(137,189)(138,190)(139,192)(140,191)(141,225)
(142,226)(143,228)(144,227)(145,221)(146,222)(147,224)(148,223)(149,237)
(150,238)(151,240)(152,239)(153,233)(154,234)(155,236)(156,235)(157,229)
(158,230)(159,232)(160,231)(161,205)(162,206)(163,208)(164,207)(165,201)
(166,202)(167,204)(168,203)(169,217)(170,218)(171,220)(172,219)(173,213)
(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(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)!( 1,261)( 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)(121,441)(122,444)(123,443)(124,442)(125,445)(126,448)(127,447)
(128,446)(129,449)(130,452)(131,451)(132,450)(133,453)(134,456)(135,455)
(136,454)(137,457)(138,460)(139,459)(140,458)(141,421)(142,424)(143,423)
(144,422)(145,425)(146,428)(147,427)(148,426)(149,429)(150,432)(151,431)
(152,430)(153,433)(154,436)(155,435)(156,434)(157,437)(158,440)(159,439)
(160,438)(161,461)(162,464)(163,463)(164,462)(165,465)(166,468)(167,467)
(168,466)(169,469)(170,472)(171,471)(172,470)(173,473)(174,476)(175,475)
(176,474)(177,477)(178,480)(179,479)(180,478)(181,381)(182,384)(183,383)
(184,382)(185,385)(186,388)(187,387)(188,386)(189,389)(190,392)(191,391)
(192,390)(193,393)(194,396)(195,395)(196,394)(197,397)(198,400)(199,399)
(200,398)(201,361)(202,364)(203,363)(204,362)(205,365)(206,368)(207,367)
(208,366)(209,369)(210,372)(211,371)(212,370)(213,373)(214,376)(215,375)
(216,374)(217,377)(218,380)(219,379)(220,378)(221,401)(222,404)(223,403)
(224,402)(225,405)(226,408)(227,407)(228,406)(229,409)(230,412)(231,411)
(232,410)(233,413)(234,416)(235,415)(236,414)(237,417)(238,420)(239,419)
(240,418);
s3 := Sym(480)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)
(479,480);
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,
s3*s2*s1*s3*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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