Polytope of Type {15,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,4,8}*1920
if this polytope has a name.
Group : SmallGroup(1920,239556)
Rank : 4
Schlafli Type : {15,4,8}
Number of vertices, edges, etc : 30, 60, 32, 8
Order of s0s1s2s3 : 120
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 : {15,4,4}*960b
4-fold quotients : {15,2,8}*480, {15,4,2}*480
5-fold quotients : {3,4,8}*384
8-fold quotients : {15,2,4}*240, {15,4,2}*240
10-fold quotients : {3,4,4}*192b
12-fold quotients : {5,2,8}*160
16-fold quotients : {15,2,2}*120
20-fold quotients : {3,2,8}*96, {3,4,2}*96
24-fold quotients : {5,2,4}*80
40-fold quotients : {3,2,4}*48, {3,4,2}*48
48-fold quotients : {5,2,2}*40
80-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 16)
( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)
( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)
( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)
( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)
( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)
(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)
(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)
(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)
(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)
(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)
(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)
(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)(247,260)
(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)(263,284)
(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)(271,296)
(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)(279,288)
(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)
(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)(326,358)
(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)
(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)(365,377)
(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)(381,401)
(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)(389,413)
(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)(397,405)
(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)(428,439)
(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)(444,463)
(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)(452,475)
(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)(460,467);;
s1 := ( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)( 8, 22)
( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)
( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)
( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)
( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)
( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)
(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)(126,144)
(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)(134,156)
(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)(162,168)
(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)(181,205)
(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)(189,217)
(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)(197,209)
(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)(229,237)
(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)(244,266)
(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)(252,278)
(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)(260,270)
(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)(292,298)
(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)(307,323)
(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)(315,335)
(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)(343,347)
(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)(362,388)
(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)(370,400)
(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)(378,392)
(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)(410,420)
(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)(425,441)
(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)(433,453)
(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)(461,465)
(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)(474,476);;
s2 := ( 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)(121,182)(122,181)(123,184)(124,183)
(125,186)(126,185)(127,188)(128,187)(129,190)(130,189)(131,192)(132,191)
(133,194)(134,193)(135,196)(136,195)(137,198)(138,197)(139,200)(140,199)
(141,202)(142,201)(143,204)(144,203)(145,206)(146,205)(147,208)(148,207)
(149,210)(150,209)(151,212)(152,211)(153,214)(154,213)(155,216)(156,215)
(157,218)(158,217)(159,220)(160,219)(161,222)(162,221)(163,224)(164,223)
(165,226)(166,225)(167,228)(168,227)(169,230)(170,229)(171,232)(172,231)
(173,234)(174,233)(175,236)(176,235)(177,238)(178,237)(179,240)(180,239)
(241,362)(242,361)(243,364)(244,363)(245,366)(246,365)(247,368)(248,367)
(249,370)(250,369)(251,372)(252,371)(253,374)(254,373)(255,376)(256,375)
(257,378)(258,377)(259,380)(260,379)(261,382)(262,381)(263,384)(264,383)
(265,386)(266,385)(267,388)(268,387)(269,390)(270,389)(271,392)(272,391)
(273,394)(274,393)(275,396)(276,395)(277,398)(278,397)(279,400)(280,399)
(281,402)(282,401)(283,404)(284,403)(285,406)(286,405)(287,408)(288,407)
(289,410)(290,409)(291,412)(292,411)(293,414)(294,413)(295,416)(296,415)
(297,418)(298,417)(299,420)(300,419)(301,422)(302,421)(303,424)(304,423)
(305,426)(306,425)(307,428)(308,427)(309,430)(310,429)(311,432)(312,431)
(313,434)(314,433)(315,436)(316,435)(317,438)(318,437)(319,440)(320,439)
(321,442)(322,441)(323,444)(324,443)(325,446)(326,445)(327,448)(328,447)
(329,450)(330,449)(331,452)(332,451)(333,454)(334,453)(335,456)(336,455)
(337,458)(338,457)(339,460)(340,459)(341,462)(342,461)(343,464)(344,463)
(345,466)(346,465)(347,468)(348,467)(349,470)(350,469)(351,472)(352,471)
(353,474)(354,473)(355,476)(356,475)(357,478)(358,477)(359,480)(360,479);;
s3 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)
( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,421)(122,422)(123,423)(124,424)(125,425)(126,426)(127,427)(128,428)
(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,435)(136,436)
(137,437)(138,438)(139,439)(140,440)(141,441)(142,442)(143,443)(144,444)
(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,451)(152,452)
(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)(160,460)
(161,461)(162,462)(163,463)(164,464)(165,465)(166,466)(167,467)(168,468)
(169,469)(170,470)(171,471)(172,472)(173,473)(174,474)(175,475)(176,476)
(177,477)(178,478)(179,479)(180,480)(181,361)(182,362)(183,363)(184,364)
(185,365)(186,366)(187,367)(188,368)(189,369)(190,370)(191,371)(192,372)
(193,373)(194,374)(195,375)(196,376)(197,377)(198,378)(199,379)(200,380)
(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)(208,388)
(209,389)(210,390)(211,391)(212,392)(213,393)(214,394)(215,395)(216,396)
(217,397)(218,398)(219,399)(220,400)(221,401)(222,402)(223,403)(224,404)
(225,405)(226,406)(227,407)(228,408)(229,409)(230,410)(231,411)(232,412)
(233,413)(234,414)(235,415)(236,416)(237,417)(238,418)(239,419)(240,420);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s3*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)
( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)
( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)
( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)
( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)
( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)
(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)
(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)
(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)
(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)
(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)
(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)
(216,231)(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)
(247,260)(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)
(263,284)(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)
(271,296)(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)
(279,288)(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)
(310,314)(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)
(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)
(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)
(365,377)(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)
(381,401)(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)
(389,413)(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)
(397,405)(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)
(428,439)(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)
(444,463)(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)
(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)
(460,467);
s1 := Sym(480)!( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)
( 8, 22)( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)
( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)
( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)
( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)
( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)
(111,119)(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)
(126,144)(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)
(134,156)(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)
(162,168)(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)
(181,205)(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)
(189,217)(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)
(197,209)(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)
(229,237)(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)
(244,266)(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)
(252,278)(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)
(260,270)(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)
(292,298)(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)
(307,323)(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)
(315,335)(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)
(343,347)(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)
(362,388)(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)
(370,400)(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)
(378,392)(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)
(410,420)(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)
(425,441)(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)
(433,453)(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)
(461,465)(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)
(474,476);
s2 := 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)(121,182)(122,181)(123,184)
(124,183)(125,186)(126,185)(127,188)(128,187)(129,190)(130,189)(131,192)
(132,191)(133,194)(134,193)(135,196)(136,195)(137,198)(138,197)(139,200)
(140,199)(141,202)(142,201)(143,204)(144,203)(145,206)(146,205)(147,208)
(148,207)(149,210)(150,209)(151,212)(152,211)(153,214)(154,213)(155,216)
(156,215)(157,218)(158,217)(159,220)(160,219)(161,222)(162,221)(163,224)
(164,223)(165,226)(166,225)(167,228)(168,227)(169,230)(170,229)(171,232)
(172,231)(173,234)(174,233)(175,236)(176,235)(177,238)(178,237)(179,240)
(180,239)(241,362)(242,361)(243,364)(244,363)(245,366)(246,365)(247,368)
(248,367)(249,370)(250,369)(251,372)(252,371)(253,374)(254,373)(255,376)
(256,375)(257,378)(258,377)(259,380)(260,379)(261,382)(262,381)(263,384)
(264,383)(265,386)(266,385)(267,388)(268,387)(269,390)(270,389)(271,392)
(272,391)(273,394)(274,393)(275,396)(276,395)(277,398)(278,397)(279,400)
(280,399)(281,402)(282,401)(283,404)(284,403)(285,406)(286,405)(287,408)
(288,407)(289,410)(290,409)(291,412)(292,411)(293,414)(294,413)(295,416)
(296,415)(297,418)(298,417)(299,420)(300,419)(301,422)(302,421)(303,424)
(304,423)(305,426)(306,425)(307,428)(308,427)(309,430)(310,429)(311,432)
(312,431)(313,434)(314,433)(315,436)(316,435)(317,438)(318,437)(319,440)
(320,439)(321,442)(322,441)(323,444)(324,443)(325,446)(326,445)(327,448)
(328,447)(329,450)(330,449)(331,452)(332,451)(333,454)(334,453)(335,456)
(336,455)(337,458)(338,457)(339,460)(340,459)(341,462)(342,461)(343,464)
(344,463)(345,466)(346,465)(347,468)(348,467)(349,470)(350,469)(351,472)
(352,471)(353,474)(354,473)(355,476)(356,475)(357,478)(358,477)(359,480)
(360,479);
s3 := Sym(480)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)
( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,421)(122,422)(123,423)(124,424)(125,425)(126,426)(127,427)
(128,428)(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,435)
(136,436)(137,437)(138,438)(139,439)(140,440)(141,441)(142,442)(143,443)
(144,444)(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,451)
(152,452)(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)
(160,460)(161,461)(162,462)(163,463)(164,464)(165,465)(166,466)(167,467)
(168,468)(169,469)(170,470)(171,471)(172,472)(173,473)(174,474)(175,475)
(176,476)(177,477)(178,478)(179,479)(180,480)(181,361)(182,362)(183,363)
(184,364)(185,365)(186,366)(187,367)(188,368)(189,369)(190,370)(191,371)
(192,372)(193,373)(194,374)(195,375)(196,376)(197,377)(198,378)(199,379)
(200,380)(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)
(208,388)(209,389)(210,390)(211,391)(212,392)(213,393)(214,394)(215,395)
(216,396)(217,397)(218,398)(219,399)(220,400)(221,401)(222,402)(223,403)
(224,404)(225,405)(226,406)(227,407)(228,408)(229,409)(230,410)(231,411)
(232,412)(233,413)(234,414)(235,415)(236,416)(237,417)(238,418)(239,419)
(240,420);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s3*s2*s3*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 >;
References : None.
to this polytope