Polytope of Type {10,4,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,3,4}*1920
Also Known As : {{10,4|2},{4,3},{3,4}3}. if this polytope has another name.
Group : SmallGroup(1920,240408)
Rank : 5
Schlafli Type : {10,4,3,4}
Number of vertices, edges, etc : 10, 40, 12, 12, 4
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 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) :
4-fold quotients : {10,2,3,4}*480
5-fold quotients : {2,4,3,4}*384b
8-fold quotients : {5,2,3,4}*240
10-fold quotients : {2,4,3,4}*192
20-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)( 24, 72)
( 25, 73)( 26, 74)( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)( 32, 80)
( 33, 49)( 34, 50)( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)( 40, 56)
( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)
( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)
(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)(112,160)
(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)(120,136)
(121,137)(122,138)(123,139)(124,140)(125,141)(126,142)(127,143)(128,144)
(177,225)(178,226)(179,227)(180,228)(181,229)(182,230)(183,231)(184,232)
(185,233)(186,234)(187,235)(188,236)(189,237)(190,238)(191,239)(192,240)
(193,209)(194,210)(195,211)(196,212)(197,213)(198,214)(199,215)(200,216)
(201,217)(202,218)(203,219)(204,220)(205,221)(206,222)(207,223)(208,224)
(257,305)(258,306)(259,307)(260,308)(261,309)(262,310)(263,311)(264,312)
(265,313)(266,314)(267,315)(268,316)(269,317)(270,318)(271,319)(272,320)
(273,289)(274,290)(275,291)(276,292)(277,293)(278,294)(279,295)(280,296)
(281,297)(282,298)(283,299)(284,300)(285,301)(286,302)(287,303)(288,304)
(337,385)(338,386)(339,387)(340,388)(341,389)(342,390)(343,391)(344,392)
(345,393)(346,394)(347,395)(348,396)(349,397)(350,398)(351,399)(352,400)
(353,369)(354,370)(355,371)(356,372)(357,373)(358,374)(359,375)(360,376)
(361,377)(362,378)(363,379)(364,380)(365,381)(366,382)(367,383)(368,384)
(417,465)(418,466)(419,467)(420,468)(421,469)(422,470)(423,471)(424,472)
(425,473)(426,474)(427,475)(428,476)(429,477)(430,478)(431,479)(432,480)
(433,449)(434,450)(435,451)(436,452)(437,453)(438,454)(439,455)(440,456)
(441,457)(442,458)(443,459)(444,460)(445,461)(446,462)(447,463)(448,464);;
s1 := ( 1,265)( 2,266)( 3,267)( 4,268)( 5,269)( 6,270)( 7,271)( 8,272)
( 9,257)( 10,258)( 11,259)( 12,260)( 13,261)( 14,262)( 15,263)( 16,264)
( 17,249)( 18,250)( 19,251)( 20,252)( 21,253)( 22,254)( 23,255)( 24,256)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,313)( 34,314)( 35,315)( 36,316)( 37,317)( 38,318)( 39,319)( 40,320)
( 41,305)( 42,306)( 43,307)( 44,308)( 45,309)( 46,310)( 47,311)( 48,312)
( 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)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,273)( 74,274)( 75,275)( 76,276)( 77,277)( 78,278)( 79,279)( 80,280)
( 81,345)( 82,346)( 83,347)( 84,348)( 85,349)( 86,350)( 87,351)( 88,352)
( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)( 96,344)
( 97,329)( 98,330)( 99,331)(100,332)(101,333)(102,334)(103,335)(104,336)
(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)
(113,393)(114,394)(115,395)(116,396)(117,397)(118,398)(119,399)(120,400)
(121,385)(122,386)(123,387)(124,388)(125,389)(126,390)(127,391)(128,392)
(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)
(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)(152,368)
(153,353)(154,354)(155,355)(156,356)(157,357)(158,358)(159,359)(160,360)
(161,425)(162,426)(163,427)(164,428)(165,429)(166,430)(167,431)(168,432)
(169,417)(170,418)(171,419)(172,420)(173,421)(174,422)(175,423)(176,424)
(177,409)(178,410)(179,411)(180,412)(181,413)(182,414)(183,415)(184,416)
(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)(192,408)
(193,473)(194,474)(195,475)(196,476)(197,477)(198,478)(199,479)(200,480)
(201,465)(202,466)(203,467)(204,468)(205,469)(206,470)(207,471)(208,472)
(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)
(225,441)(226,442)(227,443)(228,444)(229,445)(230,446)(231,447)(232,448)
(233,433)(234,434)(235,435)(236,436)(237,437)(238,438)(239,439)(240,440);;
s2 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)( 23, 24)
( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)( 42, 46)
( 43, 48)( 44, 47)( 51, 52)( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)
( 67, 68)( 71, 72)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 81,161)( 82,162)
( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,177)( 98,178)
( 99,180)(100,179)(101,181)(102,182)(103,184)(104,183)(105,189)(106,190)
(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,193)(114,194)
(115,196)(116,195)(117,197)(118,198)(119,200)(120,199)(121,205)(122,206)
(123,208)(124,207)(125,201)(126,202)(127,204)(128,203)(129,209)(130,210)
(131,212)(132,211)(133,213)(134,214)(135,216)(136,215)(137,221)(138,222)
(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,225)(146,226)
(147,228)(148,227)(149,229)(150,230)(151,232)(152,231)(153,237)(154,238)
(155,240)(156,239)(157,233)(158,234)(159,236)(160,235)(243,244)(247,248)
(249,253)(250,254)(251,256)(252,255)(259,260)(263,264)(265,269)(266,270)
(267,272)(268,271)(275,276)(279,280)(281,285)(282,286)(283,288)(284,287)
(291,292)(295,296)(297,301)(298,302)(299,304)(300,303)(307,308)(311,312)
(313,317)(314,318)(315,320)(316,319)(321,401)(322,402)(323,404)(324,403)
(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)(332,415)
(333,409)(334,410)(335,412)(336,411)(337,417)(338,418)(339,420)(340,419)
(341,421)(342,422)(343,424)(344,423)(345,429)(346,430)(347,432)(348,431)
(349,425)(350,426)(351,428)(352,427)(353,433)(354,434)(355,436)(356,435)
(357,437)(358,438)(359,440)(360,439)(361,445)(362,446)(363,448)(364,447)
(365,441)(366,442)(367,444)(368,443)(369,449)(370,450)(371,452)(372,451)
(373,453)(374,454)(375,456)(376,455)(377,461)(378,462)(379,464)(380,463)
(381,457)(382,458)(383,460)(384,459)(385,465)(386,466)(387,468)(388,467)
(389,469)(390,470)(391,472)(392,471)(393,477)(394,478)(395,480)(396,479)
(397,473)(398,474)(399,476)(400,475);;
s3 := ( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 93)( 6, 96)( 7, 95)( 8, 94)
( 9, 89)( 10, 92)( 11, 91)( 12, 90)( 13, 85)( 14, 88)( 15, 87)( 16, 86)
( 17, 97)( 18,100)( 19, 99)( 20, 98)( 21,109)( 22,112)( 23,111)( 24,110)
( 25,105)( 26,108)( 27,107)( 28,106)( 29,101)( 30,104)( 31,103)( 32,102)
( 33,113)( 34,116)( 35,115)( 36,114)( 37,125)( 38,128)( 39,127)( 40,126)
( 41,121)( 42,124)( 43,123)( 44,122)( 45,117)( 46,120)( 47,119)( 48,118)
( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)( 56,142)
( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)
( 65,145)( 66,148)( 67,147)( 68,146)( 69,157)( 70,160)( 71,159)( 72,158)
( 73,153)( 74,156)( 75,155)( 76,154)( 77,149)( 78,152)( 79,151)( 80,150)
(162,164)(165,173)(166,176)(167,175)(168,174)(170,172)(178,180)(181,189)
(182,192)(183,191)(184,190)(186,188)(194,196)(197,205)(198,208)(199,207)
(200,206)(202,204)(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)
(226,228)(229,237)(230,240)(231,239)(232,238)(234,236)(241,321)(242,324)
(243,323)(244,322)(245,333)(246,336)(247,335)(248,334)(249,329)(250,332)
(251,331)(252,330)(253,325)(254,328)(255,327)(256,326)(257,337)(258,340)
(259,339)(260,338)(261,349)(262,352)(263,351)(264,350)(265,345)(266,348)
(267,347)(268,346)(269,341)(270,344)(271,343)(272,342)(273,353)(274,356)
(275,355)(276,354)(277,365)(278,368)(279,367)(280,366)(281,361)(282,364)
(283,363)(284,362)(285,357)(286,360)(287,359)(288,358)(289,369)(290,372)
(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)(298,380)
(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,385)(306,388)
(307,387)(308,386)(309,397)(310,400)(311,399)(312,398)(313,393)(314,396)
(315,395)(316,394)(317,389)(318,392)(319,391)(320,390)(402,404)(405,413)
(406,416)(407,415)(408,414)(410,412)(418,420)(421,429)(422,432)(423,431)
(424,430)(426,428)(434,436)(437,445)(438,448)(439,447)(440,446)(442,444)
(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(466,468)(469,477)
(470,480)(471,479)(472,478)(474,476);;
s4 := ( 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,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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3,
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)!( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)
( 24, 72)( 25, 73)( 26, 74)( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)
( 32, 80)( 33, 49)( 34, 50)( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)
( 40, 56)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)
( 48, 64)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)
(104,152)(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)
(112,160)(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)
(120,136)(121,137)(122,138)(123,139)(124,140)(125,141)(126,142)(127,143)
(128,144)(177,225)(178,226)(179,227)(180,228)(181,229)(182,230)(183,231)
(184,232)(185,233)(186,234)(187,235)(188,236)(189,237)(190,238)(191,239)
(192,240)(193,209)(194,210)(195,211)(196,212)(197,213)(198,214)(199,215)
(200,216)(201,217)(202,218)(203,219)(204,220)(205,221)(206,222)(207,223)
(208,224)(257,305)(258,306)(259,307)(260,308)(261,309)(262,310)(263,311)
(264,312)(265,313)(266,314)(267,315)(268,316)(269,317)(270,318)(271,319)
(272,320)(273,289)(274,290)(275,291)(276,292)(277,293)(278,294)(279,295)
(280,296)(281,297)(282,298)(283,299)(284,300)(285,301)(286,302)(287,303)
(288,304)(337,385)(338,386)(339,387)(340,388)(341,389)(342,390)(343,391)
(344,392)(345,393)(346,394)(347,395)(348,396)(349,397)(350,398)(351,399)
(352,400)(353,369)(354,370)(355,371)(356,372)(357,373)(358,374)(359,375)
(360,376)(361,377)(362,378)(363,379)(364,380)(365,381)(366,382)(367,383)
(368,384)(417,465)(418,466)(419,467)(420,468)(421,469)(422,470)(423,471)
(424,472)(425,473)(426,474)(427,475)(428,476)(429,477)(430,478)(431,479)
(432,480)(433,449)(434,450)(435,451)(436,452)(437,453)(438,454)(439,455)
(440,456)(441,457)(442,458)(443,459)(444,460)(445,461)(446,462)(447,463)
(448,464);
s1 := Sym(480)!( 1,265)( 2,266)( 3,267)( 4,268)( 5,269)( 6,270)( 7,271)
( 8,272)( 9,257)( 10,258)( 11,259)( 12,260)( 13,261)( 14,262)( 15,263)
( 16,264)( 17,249)( 18,250)( 19,251)( 20,252)( 21,253)( 22,254)( 23,255)
( 24,256)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,313)( 34,314)( 35,315)( 36,316)( 37,317)( 38,318)( 39,319)
( 40,320)( 41,305)( 42,306)( 43,307)( 44,308)( 45,309)( 46,310)( 47,311)
( 48,312)( 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)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,273)( 74,274)( 75,275)( 76,276)( 77,277)( 78,278)( 79,279)
( 80,280)( 81,345)( 82,346)( 83,347)( 84,348)( 85,349)( 86,350)( 87,351)
( 88,352)( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)
( 96,344)( 97,329)( 98,330)( 99,331)(100,332)(101,333)(102,334)(103,335)
(104,336)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)
(112,328)(113,393)(114,394)(115,395)(116,396)(117,397)(118,398)(119,399)
(120,400)(121,385)(122,386)(123,387)(124,388)(125,389)(126,390)(127,391)
(128,392)(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)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)
(152,368)(153,353)(154,354)(155,355)(156,356)(157,357)(158,358)(159,359)
(160,360)(161,425)(162,426)(163,427)(164,428)(165,429)(166,430)(167,431)
(168,432)(169,417)(170,418)(171,419)(172,420)(173,421)(174,422)(175,423)
(176,424)(177,409)(178,410)(179,411)(180,412)(181,413)(182,414)(183,415)
(184,416)(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)
(192,408)(193,473)(194,474)(195,475)(196,476)(197,477)(198,478)(199,479)
(200,480)(201,465)(202,466)(203,467)(204,468)(205,469)(206,470)(207,471)
(208,472)(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)(225,441)(226,442)(227,443)(228,444)(229,445)(230,446)(231,447)
(232,448)(233,433)(234,434)(235,435)(236,436)(237,437)(238,438)(239,439)
(240,440);
s2 := Sym(480)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)
( 23, 24)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)
( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 55, 56)( 57, 61)( 58, 62)( 59, 64)
( 60, 63)( 67, 68)( 71, 72)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 81,161)
( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)
( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,177)
( 98,178)( 99,180)(100,179)(101,181)(102,182)(103,184)(104,183)(105,189)
(106,190)(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,193)
(114,194)(115,196)(116,195)(117,197)(118,198)(119,200)(120,199)(121,205)
(122,206)(123,208)(124,207)(125,201)(126,202)(127,204)(128,203)(129,209)
(130,210)(131,212)(132,211)(133,213)(134,214)(135,216)(136,215)(137,221)
(138,222)(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,225)
(146,226)(147,228)(148,227)(149,229)(150,230)(151,232)(152,231)(153,237)
(154,238)(155,240)(156,239)(157,233)(158,234)(159,236)(160,235)(243,244)
(247,248)(249,253)(250,254)(251,256)(252,255)(259,260)(263,264)(265,269)
(266,270)(267,272)(268,271)(275,276)(279,280)(281,285)(282,286)(283,288)
(284,287)(291,292)(295,296)(297,301)(298,302)(299,304)(300,303)(307,308)
(311,312)(313,317)(314,318)(315,320)(316,319)(321,401)(322,402)(323,404)
(324,403)(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)
(332,415)(333,409)(334,410)(335,412)(336,411)(337,417)(338,418)(339,420)
(340,419)(341,421)(342,422)(343,424)(344,423)(345,429)(346,430)(347,432)
(348,431)(349,425)(350,426)(351,428)(352,427)(353,433)(354,434)(355,436)
(356,435)(357,437)(358,438)(359,440)(360,439)(361,445)(362,446)(363,448)
(364,447)(365,441)(366,442)(367,444)(368,443)(369,449)(370,450)(371,452)
(372,451)(373,453)(374,454)(375,456)(376,455)(377,461)(378,462)(379,464)
(380,463)(381,457)(382,458)(383,460)(384,459)(385,465)(386,466)(387,468)
(388,467)(389,469)(390,470)(391,472)(392,471)(393,477)(394,478)(395,480)
(396,479)(397,473)(398,474)(399,476)(400,475);
s3 := Sym(480)!( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 93)( 6, 96)( 7, 95)
( 8, 94)( 9, 89)( 10, 92)( 11, 91)( 12, 90)( 13, 85)( 14, 88)( 15, 87)
( 16, 86)( 17, 97)( 18,100)( 19, 99)( 20, 98)( 21,109)( 22,112)( 23,111)
( 24,110)( 25,105)( 26,108)( 27,107)( 28,106)( 29,101)( 30,104)( 31,103)
( 32,102)( 33,113)( 34,116)( 35,115)( 36,114)( 37,125)( 38,128)( 39,127)
( 40,126)( 41,121)( 42,124)( 43,123)( 44,122)( 45,117)( 46,120)( 47,119)
( 48,118)( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)
( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)
( 64,134)( 65,145)( 66,148)( 67,147)( 68,146)( 69,157)( 70,160)( 71,159)
( 72,158)( 73,153)( 74,156)( 75,155)( 76,154)( 77,149)( 78,152)( 79,151)
( 80,150)(162,164)(165,173)(166,176)(167,175)(168,174)(170,172)(178,180)
(181,189)(182,192)(183,191)(184,190)(186,188)(194,196)(197,205)(198,208)
(199,207)(200,206)(202,204)(210,212)(213,221)(214,224)(215,223)(216,222)
(218,220)(226,228)(229,237)(230,240)(231,239)(232,238)(234,236)(241,321)
(242,324)(243,323)(244,322)(245,333)(246,336)(247,335)(248,334)(249,329)
(250,332)(251,331)(252,330)(253,325)(254,328)(255,327)(256,326)(257,337)
(258,340)(259,339)(260,338)(261,349)(262,352)(263,351)(264,350)(265,345)
(266,348)(267,347)(268,346)(269,341)(270,344)(271,343)(272,342)(273,353)
(274,356)(275,355)(276,354)(277,365)(278,368)(279,367)(280,366)(281,361)
(282,364)(283,363)(284,362)(285,357)(286,360)(287,359)(288,358)(289,369)
(290,372)(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)
(298,380)(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,385)
(306,388)(307,387)(308,386)(309,397)(310,400)(311,399)(312,398)(313,393)
(314,396)(315,395)(316,394)(317,389)(318,392)(319,391)(320,390)(402,404)
(405,413)(406,416)(407,415)(408,414)(410,412)(418,420)(421,429)(422,432)
(423,431)(424,430)(426,428)(434,436)(437,445)(438,448)(439,447)(440,446)
(442,444)(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(466,468)
(469,477)(470,480)(471,479)(472,478)(474,476);
s4 := 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,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, s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s4*s3, 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