Polytope of Type {4,15,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,15,4,2}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240412)
Rank : 5
Schlafli Type : {4,15,4,2}
Number of vertices, edges, etc : 8, 60, 60, 4, 2
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {4,15,4,2}*960
4-fold quotients : {2,15,4,2}*480
5-fold quotients : {4,3,4,2}*384b
10-fold quotients : {4,3,4,2}*192
20-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,249)( 2,250)( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)( 8,256)
( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)
( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)
( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)
( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)
( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)
( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)
( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)
( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)
( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)
( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)
( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)
( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)
(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)
(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)
(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)
(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)
(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)
(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)
(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)
(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)
(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)
(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)
(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)
(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)
(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)
(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)
(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)
(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)
(233,465)(234,466)(235,467)(236,468)(237,469)(238,470)(239,471)(240,472);;
s1 := ( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 89)( 6, 92)( 7, 91)( 8, 90)
( 9, 85)( 10, 88)( 11, 87)( 12, 86)( 13, 93)( 14, 96)( 15, 95)( 16, 94)
( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)( 24,154)
( 25,149)( 26,152)( 27,151)( 28,150)( 29,157)( 30,160)( 31,159)( 32,158)
( 33,129)( 34,132)( 35,131)( 36,130)( 37,137)( 38,140)( 39,139)( 40,138)
( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)( 48,142)
( 49,113)( 50,116)( 51,115)( 52,114)( 53,121)( 54,124)( 55,123)( 56,122)
( 57,117)( 58,120)( 59,119)( 60,118)( 61,125)( 62,128)( 63,127)( 64,126)
( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,105)( 70,108)( 71,107)( 72,106)
( 73,101)( 74,104)( 75,103)( 76,102)( 77,109)( 78,112)( 79,111)( 80,110)
(162,164)(165,169)(166,172)(167,171)(168,170)(174,176)(177,225)(178,228)
(179,227)(180,226)(181,233)(182,236)(183,235)(184,234)(185,229)(186,232)
(187,231)(188,230)(189,237)(190,240)(191,239)(192,238)(193,209)(194,212)
(195,211)(196,210)(197,217)(198,220)(199,219)(200,218)(201,213)(202,216)
(203,215)(204,214)(205,221)(206,224)(207,223)(208,222)(241,321)(242,324)
(243,323)(244,322)(245,329)(246,332)(247,331)(248,330)(249,325)(250,328)
(251,327)(252,326)(253,333)(254,336)(255,335)(256,334)(257,385)(258,388)
(259,387)(260,386)(261,393)(262,396)(263,395)(264,394)(265,389)(266,392)
(267,391)(268,390)(269,397)(270,400)(271,399)(272,398)(273,369)(274,372)
(275,371)(276,370)(277,377)(278,380)(279,379)(280,378)(281,373)(282,376)
(283,375)(284,374)(285,381)(286,384)(287,383)(288,382)(289,353)(290,356)
(291,355)(292,354)(293,361)(294,364)(295,363)(296,362)(297,357)(298,360)
(299,359)(300,358)(301,365)(302,368)(303,367)(304,366)(305,337)(306,340)
(307,339)(308,338)(309,345)(310,348)(311,347)(312,346)(313,341)(314,344)
(315,343)(316,342)(317,349)(318,352)(319,351)(320,350)(402,404)(405,409)
(406,412)(407,411)(408,410)(414,416)(417,465)(418,468)(419,467)(420,466)
(421,473)(422,476)(423,475)(424,474)(425,469)(426,472)(427,471)(428,470)
(429,477)(430,480)(431,479)(432,478)(433,449)(434,452)(435,451)(436,450)
(437,457)(438,460)(439,459)(440,458)(441,453)(442,456)(443,455)(444,454)
(445,461)(446,464)(447,463)(448,462);;
s2 := ( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 29)( 6, 30)( 7, 32)( 8, 31)
( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 21)( 14, 22)( 15, 24)( 16, 23)
( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)( 40, 79)
( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)( 48, 71)
( 51, 52)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 59, 60)( 81,177)( 82,178)
( 83,180)( 84,179)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)
( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,161)( 98,162)
( 99,164)(100,163)(101,173)(102,174)(103,176)(104,175)(105,169)(106,170)
(107,172)(108,171)(109,165)(110,166)(111,168)(112,167)(113,225)(114,226)
(115,228)(116,227)(117,237)(118,238)(119,240)(120,239)(121,233)(122,234)
(123,236)(124,235)(125,229)(126,230)(127,232)(128,231)(129,209)(130,210)
(131,212)(132,211)(133,221)(134,222)(135,224)(136,223)(137,217)(138,218)
(139,220)(140,219)(141,213)(142,214)(143,216)(144,215)(145,193)(146,194)
(147,196)(148,195)(149,205)(150,206)(151,208)(152,207)(153,201)(154,202)
(155,204)(156,203)(157,197)(158,198)(159,200)(160,199)(241,257)(242,258)
(243,260)(244,259)(245,269)(246,270)(247,272)(248,271)(249,265)(250,266)
(251,268)(252,267)(253,261)(254,262)(255,264)(256,263)(273,305)(274,306)
(275,308)(276,307)(277,317)(278,318)(279,320)(280,319)(281,313)(282,314)
(283,316)(284,315)(285,309)(286,310)(287,312)(288,311)(291,292)(293,301)
(294,302)(295,304)(296,303)(299,300)(321,417)(322,418)(323,420)(324,419)
(325,429)(326,430)(327,432)(328,431)(329,425)(330,426)(331,428)(332,427)
(333,421)(334,422)(335,424)(336,423)(337,401)(338,402)(339,404)(340,403)
(341,413)(342,414)(343,416)(344,415)(345,409)(346,410)(347,412)(348,411)
(349,405)(350,406)(351,408)(352,407)(353,465)(354,466)(355,468)(356,467)
(357,477)(358,478)(359,480)(360,479)(361,473)(362,474)(363,476)(364,475)
(365,469)(366,470)(367,472)(368,471)(369,449)(370,450)(371,452)(372,451)
(373,461)(374,462)(375,464)(376,463)(377,457)(378,458)(379,460)(380,459)
(381,453)(382,454)(383,456)(384,455)(385,433)(386,434)(387,436)(388,435)
(389,445)(390,446)(391,448)(392,447)(393,441)(394,442)(395,444)(396,443)
(397,437)(398,438)(399,440)(400,439);;
s3 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)
(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)
(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)
(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480);;
s4 := (481,482);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(482)!( 1,249)( 2,250)( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)
( 8,256)( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)
( 16,248)( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)
( 24,272)( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)
( 32,264)( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)
( 40,288)( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)
( 48,280)( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)
( 56,304)( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)
( 64,296)( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)
( 72,320)( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)
( 80,312)( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)
( 88,336)( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)
( 96,328)( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)
(104,352)(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)
(112,344)(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)
(120,368)(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)
(128,360)(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)
(136,384)(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)
(144,376)(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)
(152,400)(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)
(160,392)(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)
(168,416)(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)
(176,408)(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)
(184,432)(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)
(192,424)(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)
(200,448)(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)
(208,440)(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)
(216,464)(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)
(224,456)(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)
(232,480)(233,465)(234,466)(235,467)(236,468)(237,469)(238,470)(239,471)
(240,472);
s1 := Sym(482)!( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 89)( 6, 92)( 7, 91)
( 8, 90)( 9, 85)( 10, 88)( 11, 87)( 12, 86)( 13, 93)( 14, 96)( 15, 95)
( 16, 94)( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)
( 24,154)( 25,149)( 26,152)( 27,151)( 28,150)( 29,157)( 30,160)( 31,159)
( 32,158)( 33,129)( 34,132)( 35,131)( 36,130)( 37,137)( 38,140)( 39,139)
( 40,138)( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)
( 48,142)( 49,113)( 50,116)( 51,115)( 52,114)( 53,121)( 54,124)( 55,123)
( 56,122)( 57,117)( 58,120)( 59,119)( 60,118)( 61,125)( 62,128)( 63,127)
( 64,126)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,105)( 70,108)( 71,107)
( 72,106)( 73,101)( 74,104)( 75,103)( 76,102)( 77,109)( 78,112)( 79,111)
( 80,110)(162,164)(165,169)(166,172)(167,171)(168,170)(174,176)(177,225)
(178,228)(179,227)(180,226)(181,233)(182,236)(183,235)(184,234)(185,229)
(186,232)(187,231)(188,230)(189,237)(190,240)(191,239)(192,238)(193,209)
(194,212)(195,211)(196,210)(197,217)(198,220)(199,219)(200,218)(201,213)
(202,216)(203,215)(204,214)(205,221)(206,224)(207,223)(208,222)(241,321)
(242,324)(243,323)(244,322)(245,329)(246,332)(247,331)(248,330)(249,325)
(250,328)(251,327)(252,326)(253,333)(254,336)(255,335)(256,334)(257,385)
(258,388)(259,387)(260,386)(261,393)(262,396)(263,395)(264,394)(265,389)
(266,392)(267,391)(268,390)(269,397)(270,400)(271,399)(272,398)(273,369)
(274,372)(275,371)(276,370)(277,377)(278,380)(279,379)(280,378)(281,373)
(282,376)(283,375)(284,374)(285,381)(286,384)(287,383)(288,382)(289,353)
(290,356)(291,355)(292,354)(293,361)(294,364)(295,363)(296,362)(297,357)
(298,360)(299,359)(300,358)(301,365)(302,368)(303,367)(304,366)(305,337)
(306,340)(307,339)(308,338)(309,345)(310,348)(311,347)(312,346)(313,341)
(314,344)(315,343)(316,342)(317,349)(318,352)(319,351)(320,350)(402,404)
(405,409)(406,412)(407,411)(408,410)(414,416)(417,465)(418,468)(419,467)
(420,466)(421,473)(422,476)(423,475)(424,474)(425,469)(426,472)(427,471)
(428,470)(429,477)(430,480)(431,479)(432,478)(433,449)(434,452)(435,451)
(436,450)(437,457)(438,460)(439,459)(440,458)(441,453)(442,456)(443,455)
(444,454)(445,461)(446,464)(447,463)(448,462);
s2 := Sym(482)!( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 29)( 6, 30)( 7, 32)
( 8, 31)( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 21)( 14, 22)( 15, 24)
( 16, 23)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)
( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)
( 48, 71)( 51, 52)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 59, 60)( 81,177)
( 82,178)( 83,180)( 84,179)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)
( 90,186)( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,161)
( 98,162)( 99,164)(100,163)(101,173)(102,174)(103,176)(104,175)(105,169)
(106,170)(107,172)(108,171)(109,165)(110,166)(111,168)(112,167)(113,225)
(114,226)(115,228)(116,227)(117,237)(118,238)(119,240)(120,239)(121,233)
(122,234)(123,236)(124,235)(125,229)(126,230)(127,232)(128,231)(129,209)
(130,210)(131,212)(132,211)(133,221)(134,222)(135,224)(136,223)(137,217)
(138,218)(139,220)(140,219)(141,213)(142,214)(143,216)(144,215)(145,193)
(146,194)(147,196)(148,195)(149,205)(150,206)(151,208)(152,207)(153,201)
(154,202)(155,204)(156,203)(157,197)(158,198)(159,200)(160,199)(241,257)
(242,258)(243,260)(244,259)(245,269)(246,270)(247,272)(248,271)(249,265)
(250,266)(251,268)(252,267)(253,261)(254,262)(255,264)(256,263)(273,305)
(274,306)(275,308)(276,307)(277,317)(278,318)(279,320)(280,319)(281,313)
(282,314)(283,316)(284,315)(285,309)(286,310)(287,312)(288,311)(291,292)
(293,301)(294,302)(295,304)(296,303)(299,300)(321,417)(322,418)(323,420)
(324,419)(325,429)(326,430)(327,432)(328,431)(329,425)(330,426)(331,428)
(332,427)(333,421)(334,422)(335,424)(336,423)(337,401)(338,402)(339,404)
(340,403)(341,413)(342,414)(343,416)(344,415)(345,409)(346,410)(347,412)
(348,411)(349,405)(350,406)(351,408)(352,407)(353,465)(354,466)(355,468)
(356,467)(357,477)(358,478)(359,480)(360,479)(361,473)(362,474)(363,476)
(364,475)(365,469)(366,470)(367,472)(368,471)(369,449)(370,450)(371,452)
(372,451)(373,461)(374,462)(375,464)(376,463)(377,457)(378,458)(379,460)
(380,459)(381,453)(382,454)(383,456)(384,455)(385,433)(386,434)(387,436)
(388,435)(389,445)(390,446)(391,448)(392,447)(393,441)(394,442)(395,444)
(396,443)(397,437)(398,438)(399,440)(400,439);
s3 := Sym(482)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)
(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)
(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)
(478,480);
s4 := Sym(482)!(481,482);
poly := sub<Sym(482)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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 >;
to this polytope