Polytope of Type {6,12,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 4
Schlafli Type : {6,12,10}
Number of vertices, edges, etc : 8, 48, 80, 10
Order of s0s1s2s3 : 40
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 : {3,12,10}*960, {6,6,10}*960
4-fold quotients : {3,6,10}*480
5-fold quotients : {6,12,2}*384b
10-fold quotients : {3,12,2}*192, {6,6,2}*192
20-fold quotients : {3,6,2}*96, {6,3,2}*96
24-fold quotients : {2,2,10}*80
40-fold quotients : {3,3,2}*48
48-fold quotients : {2,2,5}*40
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 41, 81)
( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)( 49, 89)
( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 97)
( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)( 65,105)
( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)( 73,113)
( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)(121,122)
(125,128)(126,127)(129,130)(133,136)(134,135)(137,138)(141,144)(142,143)
(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,202)(162,201)
(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,210)(170,209)
(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)(178,217)
(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,226)(186,225)
(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,234)(194,233)
(195,235)(196,236)(197,240)(198,239)(199,238)(200,237)(243,244)(245,247)
(246,248)(251,252)(253,255)(254,256)(259,260)(261,263)(262,264)(267,268)
(269,271)(270,272)(275,276)(277,279)(278,280)(281,321)(282,322)(283,324)
(284,323)(285,327)(286,328)(287,325)(288,326)(289,329)(290,330)(291,332)
(292,331)(293,335)(294,336)(295,333)(296,334)(297,337)(298,338)(299,340)
(300,339)(301,343)(302,344)(303,341)(304,342)(305,345)(306,346)(307,348)
(308,347)(309,351)(310,352)(311,349)(312,350)(313,353)(314,354)(315,356)
(316,355)(317,359)(318,360)(319,357)(320,358)(361,362)(365,368)(366,367)
(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,386)(389,392)
(390,391)(393,394)(397,400)(398,399)(401,442)(402,441)(403,443)(404,444)
(405,448)(406,447)(407,446)(408,445)(409,450)(410,449)(411,451)(412,452)
(413,456)(414,455)(415,454)(416,453)(417,458)(418,457)(419,459)(420,460)
(421,464)(422,463)(423,462)(424,461)(425,466)(426,465)(427,467)(428,468)
(429,472)(430,471)(431,470)(432,469)(433,474)(434,473)(435,475)(436,476)
(437,480)(438,479)(439,478)(440,477);;
s1 := ( 1,281)( 2,282)( 3,287)( 4,288)( 5,286)( 6,285)( 7,283)( 8,284)
( 9,289)( 10,290)( 11,295)( 12,296)( 13,294)( 14,293)( 15,291)( 16,292)
( 17,297)( 18,298)( 19,303)( 20,304)( 21,302)( 22,301)( 23,299)( 24,300)
( 25,305)( 26,306)( 27,311)( 28,312)( 29,310)( 30,309)( 31,307)( 32,308)
( 33,313)( 34,314)( 35,319)( 36,320)( 37,318)( 38,317)( 39,315)( 40,316)
( 41,241)( 42,242)( 43,247)( 44,248)( 45,246)( 46,245)( 47,243)( 48,244)
( 49,249)( 50,250)( 51,255)( 52,256)( 53,254)( 54,253)( 55,251)( 56,252)
( 57,257)( 58,258)( 59,263)( 60,264)( 61,262)( 62,261)( 63,259)( 64,260)
( 65,265)( 66,266)( 67,271)( 68,272)( 69,270)( 70,269)( 71,267)( 72,268)
( 73,273)( 74,274)( 75,279)( 76,280)( 77,278)( 78,277)( 79,275)( 80,276)
( 81,321)( 82,322)( 83,327)( 84,328)( 85,326)( 86,325)( 87,323)( 88,324)
( 89,329)( 90,330)( 91,335)( 92,336)( 93,334)( 94,333)( 95,331)( 96,332)
( 97,337)( 98,338)( 99,343)(100,344)(101,342)(102,341)(103,339)(104,340)
(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)(112,348)
(113,353)(114,354)(115,359)(116,360)(117,358)(118,357)(119,355)(120,356)
(121,402)(122,401)(123,408)(124,407)(125,405)(126,406)(127,404)(128,403)
(129,410)(130,409)(131,416)(132,415)(133,413)(134,414)(135,412)(136,411)
(137,418)(138,417)(139,424)(140,423)(141,421)(142,422)(143,420)(144,419)
(145,426)(146,425)(147,432)(148,431)(149,429)(150,430)(151,428)(152,427)
(153,434)(154,433)(155,440)(156,439)(157,437)(158,438)(159,436)(160,435)
(161,362)(162,361)(163,368)(164,367)(165,365)(166,366)(167,364)(168,363)
(169,370)(170,369)(171,376)(172,375)(173,373)(174,374)(175,372)(176,371)
(177,378)(178,377)(179,384)(180,383)(181,381)(182,382)(183,380)(184,379)
(185,386)(186,385)(187,392)(188,391)(189,389)(190,390)(191,388)(192,387)
(193,394)(194,393)(195,400)(196,399)(197,397)(198,398)(199,396)(200,395)
(201,442)(202,441)(203,448)(204,447)(205,445)(206,446)(207,444)(208,443)
(209,450)(210,449)(211,456)(212,455)(213,453)(214,454)(215,452)(216,451)
(217,458)(218,457)(219,464)(220,463)(221,461)(222,462)(223,460)(224,459)
(225,466)(226,465)(227,472)(228,471)(229,469)(230,470)(231,468)(232,467)
(233,474)(234,473)(235,480)(236,479)(237,477)(238,478)(239,476)(240,475);;
s2 := ( 1,123)( 2,124)( 3,121)( 4,122)( 5,126)( 6,125)( 7,127)( 8,128)
( 9,155)( 10,156)( 11,153)( 12,154)( 13,158)( 14,157)( 15,159)( 16,160)
( 17,147)( 18,148)( 19,145)( 20,146)( 21,150)( 22,149)( 23,151)( 24,152)
( 25,139)( 26,140)( 27,137)( 28,138)( 29,142)( 30,141)( 31,143)( 32,144)
( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,135)( 40,136)
( 41,203)( 42,204)( 43,201)( 44,202)( 45,206)( 46,205)( 47,207)( 48,208)
( 49,235)( 50,236)( 51,233)( 52,234)( 53,238)( 54,237)( 55,239)( 56,240)
( 57,227)( 58,228)( 59,225)( 60,226)( 61,230)( 62,229)( 63,231)( 64,232)
( 65,219)( 66,220)( 67,217)( 68,218)( 69,222)( 70,221)( 71,223)( 72,224)
( 73,211)( 74,212)( 75,209)( 76,210)( 77,214)( 78,213)( 79,215)( 80,216)
( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)( 88,168)
( 89,195)( 90,196)( 91,193)( 92,194)( 93,198)( 94,197)( 95,199)( 96,200)
( 97,187)( 98,188)( 99,185)(100,186)(101,190)(102,189)(103,191)(104,192)
(105,179)(106,180)(107,177)(108,178)(109,182)(110,181)(111,183)(112,184)
(113,171)(114,172)(115,169)(116,170)(117,174)(118,173)(119,175)(120,176)
(241,363)(242,364)(243,361)(244,362)(245,366)(246,365)(247,367)(248,368)
(249,395)(250,396)(251,393)(252,394)(253,398)(254,397)(255,399)(256,400)
(257,387)(258,388)(259,385)(260,386)(261,390)(262,389)(263,391)(264,392)
(265,379)(266,380)(267,377)(268,378)(269,382)(270,381)(271,383)(272,384)
(273,371)(274,372)(275,369)(276,370)(277,374)(278,373)(279,375)(280,376)
(281,443)(282,444)(283,441)(284,442)(285,446)(286,445)(287,447)(288,448)
(289,475)(290,476)(291,473)(292,474)(293,478)(294,477)(295,479)(296,480)
(297,467)(298,468)(299,465)(300,466)(301,470)(302,469)(303,471)(304,472)
(305,459)(306,460)(307,457)(308,458)(309,462)(310,461)(311,463)(312,464)
(313,451)(314,452)(315,449)(316,450)(317,454)(318,453)(319,455)(320,456)
(321,403)(322,404)(323,401)(324,402)(325,406)(326,405)(327,407)(328,408)
(329,435)(330,436)(331,433)(332,434)(333,438)(334,437)(335,439)(336,440)
(337,427)(338,428)(339,425)(340,426)(341,430)(342,429)(343,431)(344,432)
(345,419)(346,420)(347,417)(348,418)(349,422)(350,421)(351,423)(352,424)
(353,411)(354,412)(355,409)(356,410)(357,414)(358,413)(359,415)(360,416);;
s3 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)
( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)( 48, 56)
( 57, 73)( 58, 74)( 59, 75)( 60, 76)( 61, 77)( 62, 78)( 63, 79)( 64, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)
(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)
(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,193)(178,194)(179,195)(180,196)(181,197)(182,198)(183,199)(184,200)
(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)
(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,239)(224,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)(264,280)
(281,289)(282,290)(283,291)(284,292)(285,293)(286,294)(287,295)(288,296)
(297,313)(298,314)(299,315)(300,316)(301,317)(302,318)(303,319)(304,320)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,353)(338,354)(339,355)(340,356)(341,357)(342,358)(343,359)(344,360)
(361,369)(362,370)(363,371)(364,372)(365,373)(366,374)(367,375)(368,376)
(377,393)(378,394)(379,395)(380,396)(381,397)(382,398)(383,399)(384,400)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)
(417,433)(418,434)(419,435)(420,436)(421,437)(422,438)(423,439)(424,440)
(441,449)(442,450)(443,451)(444,452)(445,453)(446,454)(447,455)(448,456)
(457,473)(458,474)(459,475)(460,476)(461,477)(462,478)(463,479)(464,480);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)
( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)
( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)
( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)
( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)
( 73,113)( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)
(121,122)(125,128)(126,127)(129,130)(133,136)(134,135)(137,138)(141,144)
(142,143)(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,202)
(162,201)(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,210)
(170,209)(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)
(178,217)(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,226)
(186,225)(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,234)
(194,233)(195,235)(196,236)(197,240)(198,239)(199,238)(200,237)(243,244)
(245,247)(246,248)(251,252)(253,255)(254,256)(259,260)(261,263)(262,264)
(267,268)(269,271)(270,272)(275,276)(277,279)(278,280)(281,321)(282,322)
(283,324)(284,323)(285,327)(286,328)(287,325)(288,326)(289,329)(290,330)
(291,332)(292,331)(293,335)(294,336)(295,333)(296,334)(297,337)(298,338)
(299,340)(300,339)(301,343)(302,344)(303,341)(304,342)(305,345)(306,346)
(307,348)(308,347)(309,351)(310,352)(311,349)(312,350)(313,353)(314,354)
(315,356)(316,355)(317,359)(318,360)(319,357)(320,358)(361,362)(365,368)
(366,367)(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,386)
(389,392)(390,391)(393,394)(397,400)(398,399)(401,442)(402,441)(403,443)
(404,444)(405,448)(406,447)(407,446)(408,445)(409,450)(410,449)(411,451)
(412,452)(413,456)(414,455)(415,454)(416,453)(417,458)(418,457)(419,459)
(420,460)(421,464)(422,463)(423,462)(424,461)(425,466)(426,465)(427,467)
(428,468)(429,472)(430,471)(431,470)(432,469)(433,474)(434,473)(435,475)
(436,476)(437,480)(438,479)(439,478)(440,477);
s1 := Sym(480)!( 1,281)( 2,282)( 3,287)( 4,288)( 5,286)( 6,285)( 7,283)
( 8,284)( 9,289)( 10,290)( 11,295)( 12,296)( 13,294)( 14,293)( 15,291)
( 16,292)( 17,297)( 18,298)( 19,303)( 20,304)( 21,302)( 22,301)( 23,299)
( 24,300)( 25,305)( 26,306)( 27,311)( 28,312)( 29,310)( 30,309)( 31,307)
( 32,308)( 33,313)( 34,314)( 35,319)( 36,320)( 37,318)( 38,317)( 39,315)
( 40,316)( 41,241)( 42,242)( 43,247)( 44,248)( 45,246)( 46,245)( 47,243)
( 48,244)( 49,249)( 50,250)( 51,255)( 52,256)( 53,254)( 54,253)( 55,251)
( 56,252)( 57,257)( 58,258)( 59,263)( 60,264)( 61,262)( 62,261)( 63,259)
( 64,260)( 65,265)( 66,266)( 67,271)( 68,272)( 69,270)( 70,269)( 71,267)
( 72,268)( 73,273)( 74,274)( 75,279)( 76,280)( 77,278)( 78,277)( 79,275)
( 80,276)( 81,321)( 82,322)( 83,327)( 84,328)( 85,326)( 86,325)( 87,323)
( 88,324)( 89,329)( 90,330)( 91,335)( 92,336)( 93,334)( 94,333)( 95,331)
( 96,332)( 97,337)( 98,338)( 99,343)(100,344)(101,342)(102,341)(103,339)
(104,340)(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)
(112,348)(113,353)(114,354)(115,359)(116,360)(117,358)(118,357)(119,355)
(120,356)(121,402)(122,401)(123,408)(124,407)(125,405)(126,406)(127,404)
(128,403)(129,410)(130,409)(131,416)(132,415)(133,413)(134,414)(135,412)
(136,411)(137,418)(138,417)(139,424)(140,423)(141,421)(142,422)(143,420)
(144,419)(145,426)(146,425)(147,432)(148,431)(149,429)(150,430)(151,428)
(152,427)(153,434)(154,433)(155,440)(156,439)(157,437)(158,438)(159,436)
(160,435)(161,362)(162,361)(163,368)(164,367)(165,365)(166,366)(167,364)
(168,363)(169,370)(170,369)(171,376)(172,375)(173,373)(174,374)(175,372)
(176,371)(177,378)(178,377)(179,384)(180,383)(181,381)(182,382)(183,380)
(184,379)(185,386)(186,385)(187,392)(188,391)(189,389)(190,390)(191,388)
(192,387)(193,394)(194,393)(195,400)(196,399)(197,397)(198,398)(199,396)
(200,395)(201,442)(202,441)(203,448)(204,447)(205,445)(206,446)(207,444)
(208,443)(209,450)(210,449)(211,456)(212,455)(213,453)(214,454)(215,452)
(216,451)(217,458)(218,457)(219,464)(220,463)(221,461)(222,462)(223,460)
(224,459)(225,466)(226,465)(227,472)(228,471)(229,469)(230,470)(231,468)
(232,467)(233,474)(234,473)(235,480)(236,479)(237,477)(238,478)(239,476)
(240,475);
s2 := Sym(480)!( 1,123)( 2,124)( 3,121)( 4,122)( 5,126)( 6,125)( 7,127)
( 8,128)( 9,155)( 10,156)( 11,153)( 12,154)( 13,158)( 14,157)( 15,159)
( 16,160)( 17,147)( 18,148)( 19,145)( 20,146)( 21,150)( 22,149)( 23,151)
( 24,152)( 25,139)( 26,140)( 27,137)( 28,138)( 29,142)( 30,141)( 31,143)
( 32,144)( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,135)
( 40,136)( 41,203)( 42,204)( 43,201)( 44,202)( 45,206)( 46,205)( 47,207)
( 48,208)( 49,235)( 50,236)( 51,233)( 52,234)( 53,238)( 54,237)( 55,239)
( 56,240)( 57,227)( 58,228)( 59,225)( 60,226)( 61,230)( 62,229)( 63,231)
( 64,232)( 65,219)( 66,220)( 67,217)( 68,218)( 69,222)( 70,221)( 71,223)
( 72,224)( 73,211)( 74,212)( 75,209)( 76,210)( 77,214)( 78,213)( 79,215)
( 80,216)( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)
( 88,168)( 89,195)( 90,196)( 91,193)( 92,194)( 93,198)( 94,197)( 95,199)
( 96,200)( 97,187)( 98,188)( 99,185)(100,186)(101,190)(102,189)(103,191)
(104,192)(105,179)(106,180)(107,177)(108,178)(109,182)(110,181)(111,183)
(112,184)(113,171)(114,172)(115,169)(116,170)(117,174)(118,173)(119,175)
(120,176)(241,363)(242,364)(243,361)(244,362)(245,366)(246,365)(247,367)
(248,368)(249,395)(250,396)(251,393)(252,394)(253,398)(254,397)(255,399)
(256,400)(257,387)(258,388)(259,385)(260,386)(261,390)(262,389)(263,391)
(264,392)(265,379)(266,380)(267,377)(268,378)(269,382)(270,381)(271,383)
(272,384)(273,371)(274,372)(275,369)(276,370)(277,374)(278,373)(279,375)
(280,376)(281,443)(282,444)(283,441)(284,442)(285,446)(286,445)(287,447)
(288,448)(289,475)(290,476)(291,473)(292,474)(293,478)(294,477)(295,479)
(296,480)(297,467)(298,468)(299,465)(300,466)(301,470)(302,469)(303,471)
(304,472)(305,459)(306,460)(307,457)(308,458)(309,462)(310,461)(311,463)
(312,464)(313,451)(314,452)(315,449)(316,450)(317,454)(318,453)(319,455)
(320,456)(321,403)(322,404)(323,401)(324,402)(325,406)(326,405)(327,407)
(328,408)(329,435)(330,436)(331,433)(332,434)(333,438)(334,437)(335,439)
(336,440)(337,427)(338,428)(339,425)(340,426)(341,430)(342,429)(343,431)
(344,432)(345,419)(346,420)(347,417)(348,418)(349,422)(350,421)(351,423)
(352,424)(353,411)(354,412)(355,409)(356,410)(357,414)(358,413)(359,415)
(360,416);
s3 := Sym(480)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)
( 24, 40)( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)
( 48, 56)( 57, 73)( 58, 74)( 59, 75)( 60, 76)( 61, 77)( 62, 78)( 63, 79)
( 64, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)
(104,120)(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)
(128,136)(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)
(144,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,193)(178,194)(179,195)(180,196)(181,197)(182,198)(183,199)
(184,200)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)
(208,216)(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,239)
(224,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)
(264,280)(281,289)(282,290)(283,291)(284,292)(285,293)(286,294)(287,295)
(288,296)(297,313)(298,314)(299,315)(300,316)(301,317)(302,318)(303,319)
(304,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)
(328,336)(337,353)(338,354)(339,355)(340,356)(341,357)(342,358)(343,359)
(344,360)(361,369)(362,370)(363,371)(364,372)(365,373)(366,374)(367,375)
(368,376)(377,393)(378,394)(379,395)(380,396)(381,397)(382,398)(383,399)
(384,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416)(417,433)(418,434)(419,435)(420,436)(421,437)(422,438)(423,439)
(424,440)(441,449)(442,450)(443,451)(444,452)(445,453)(446,454)(447,455)
(448,456)(457,473)(458,474)(459,475)(460,476)(461,477)(462,478)(463,479)
(464,480);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope