Polytope of Type {28,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,6,3}*1008
if this polytope has a name.
Group : SmallGroup(1008,599)
Rank : 4
Schlafli Type : {28,6,3}
Number of vertices, edges, etc : 28, 84, 9, 3
Order of s0s1s2s3 : 84
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 : {14,6,3}*504
3-fold quotients : {28,2,3}*336
6-fold quotients : {14,2,3}*168
7-fold quotients : {4,6,3}*144
12-fold quotients : {7,2,3}*84
14-fold quotients : {2,6,3}*72
21-fold quotients : {4,2,3}*48
42-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)
( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)
( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)
( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)
( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)
(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(127,190)(128,196)
(129,195)(130,194)(131,193)(132,192)(133,191)(134,197)(135,203)(136,202)
(137,201)(138,200)(139,199)(140,198)(141,204)(142,210)(143,209)(144,208)
(145,207)(146,206)(147,205)(148,211)(149,217)(150,216)(151,215)(152,214)
(153,213)(154,212)(155,218)(156,224)(157,223)(158,222)(159,221)(160,220)
(161,219)(162,225)(163,231)(164,230)(165,229)(166,228)(167,227)(168,226)
(169,232)(170,238)(171,237)(172,236)(173,235)(174,234)(175,233)(176,239)
(177,245)(178,244)(179,243)(180,242)(181,241)(182,240)(183,246)(184,252)
(185,251)(186,250)(187,249)(188,248)(189,247)(253,316)(254,322)(255,321)
(256,320)(257,319)(258,318)(259,317)(260,323)(261,329)(262,328)(263,327)
(264,326)(265,325)(266,324)(267,330)(268,336)(269,335)(270,334)(271,333)
(272,332)(273,331)(274,337)(275,343)(276,342)(277,341)(278,340)(279,339)
(280,338)(281,344)(282,350)(283,349)(284,348)(285,347)(286,346)(287,345)
(288,351)(289,357)(290,356)(291,355)(292,354)(293,353)(294,352)(295,358)
(296,364)(297,363)(298,362)(299,361)(300,360)(301,359)(302,365)(303,371)
(304,370)(305,369)(306,368)(307,367)(308,366)(309,372)(310,378)(311,377)
(312,376)(313,375)(314,374)(315,373)(380,385)(381,384)(382,383)(387,392)
(388,391)(389,390)(394,399)(395,398)(396,397)(401,406)(402,405)(403,404)
(408,413)(409,412)(410,411)(415,420)(416,419)(417,418)(422,427)(423,426)
(424,425)(429,434)(430,433)(431,432)(436,441)(437,440)(438,439)(443,448)
(444,447)(445,446)(450,455)(451,454)(452,453)(457,462)(458,461)(459,460)
(464,469)(465,468)(466,467)(471,476)(472,475)(473,474)(478,483)(479,482)
(480,481)(485,490)(486,489)(487,488)(492,497)(493,496)(494,495)(499,504)
(500,503)(501,502);;
s1 := ( 1,254)( 2,253)( 3,259)( 4,258)( 5,257)( 6,256)( 7,255)( 8,261)
( 9,260)( 10,266)( 11,265)( 12,264)( 13,263)( 14,262)( 15,268)( 16,267)
( 17,273)( 18,272)( 19,271)( 20,270)( 21,269)( 22,296)( 23,295)( 24,301)
( 25,300)( 26,299)( 27,298)( 28,297)( 29,303)( 30,302)( 31,308)( 32,307)
( 33,306)( 34,305)( 35,304)( 36,310)( 37,309)( 38,315)( 39,314)( 40,313)
( 41,312)( 42,311)( 43,275)( 44,274)( 45,280)( 46,279)( 47,278)( 48,277)
( 49,276)( 50,282)( 51,281)( 52,287)( 53,286)( 54,285)( 55,284)( 56,283)
( 57,289)( 58,288)( 59,294)( 60,293)( 61,292)( 62,291)( 63,290)( 64,317)
( 65,316)( 66,322)( 67,321)( 68,320)( 69,319)( 70,318)( 71,324)( 72,323)
( 73,329)( 74,328)( 75,327)( 76,326)( 77,325)( 78,331)( 79,330)( 80,336)
( 81,335)( 82,334)( 83,333)( 84,332)( 85,359)( 86,358)( 87,364)( 88,363)
( 89,362)( 90,361)( 91,360)( 92,366)( 93,365)( 94,371)( 95,370)( 96,369)
( 97,368)( 98,367)( 99,373)(100,372)(101,378)(102,377)(103,376)(104,375)
(105,374)(106,338)(107,337)(108,343)(109,342)(110,341)(111,340)(112,339)
(113,345)(114,344)(115,350)(116,349)(117,348)(118,347)(119,346)(120,352)
(121,351)(122,357)(123,356)(124,355)(125,354)(126,353)(127,443)(128,442)
(129,448)(130,447)(131,446)(132,445)(133,444)(134,450)(135,449)(136,455)
(137,454)(138,453)(139,452)(140,451)(141,457)(142,456)(143,462)(144,461)
(145,460)(146,459)(147,458)(148,485)(149,484)(150,490)(151,489)(152,488)
(153,487)(154,486)(155,492)(156,491)(157,497)(158,496)(159,495)(160,494)
(161,493)(162,499)(163,498)(164,504)(165,503)(166,502)(167,501)(168,500)
(169,464)(170,463)(171,469)(172,468)(173,467)(174,466)(175,465)(176,471)
(177,470)(178,476)(179,475)(180,474)(181,473)(182,472)(183,478)(184,477)
(185,483)(186,482)(187,481)(188,480)(189,479)(190,380)(191,379)(192,385)
(193,384)(194,383)(195,382)(196,381)(197,387)(198,386)(199,392)(200,391)
(201,390)(202,389)(203,388)(204,394)(205,393)(206,399)(207,398)(208,397)
(209,396)(210,395)(211,422)(212,421)(213,427)(214,426)(215,425)(216,424)
(217,423)(218,429)(219,428)(220,434)(221,433)(222,432)(223,431)(224,430)
(225,436)(226,435)(227,441)(228,440)(229,439)(230,438)(231,437)(232,401)
(233,400)(234,406)(235,405)(236,404)(237,403)(238,402)(239,408)(240,407)
(241,413)(242,412)(243,411)(244,410)(245,409)(246,415)(247,414)(248,420)
(249,419)(250,418)(251,417)(252,416);;
s2 := ( 1,400)( 2,401)( 3,402)( 4,403)( 5,404)( 6,405)( 7,406)( 8,414)
( 9,415)( 10,416)( 11,417)( 12,418)( 13,419)( 14,420)( 15,407)( 16,408)
( 17,409)( 18,410)( 19,411)( 20,412)( 21,413)( 22,379)( 23,380)( 24,381)
( 25,382)( 26,383)( 27,384)( 28,385)( 29,393)( 30,394)( 31,395)( 32,396)
( 33,397)( 34,398)( 35,399)( 36,386)( 37,387)( 38,388)( 39,389)( 40,390)
( 41,391)( 42,392)( 43,421)( 44,422)( 45,423)( 46,424)( 47,425)( 48,426)
( 49,427)( 50,435)( 51,436)( 52,437)( 53,438)( 54,439)( 55,440)( 56,441)
( 57,428)( 58,429)( 59,430)( 60,431)( 61,432)( 62,433)( 63,434)( 64,463)
( 65,464)( 66,465)( 67,466)( 68,467)( 69,468)( 70,469)( 71,477)( 72,478)
( 73,479)( 74,480)( 75,481)( 76,482)( 77,483)( 78,470)( 79,471)( 80,472)
( 81,473)( 82,474)( 83,475)( 84,476)( 85,442)( 86,443)( 87,444)( 88,445)
( 89,446)( 90,447)( 91,448)( 92,456)( 93,457)( 94,458)( 95,459)( 96,460)
( 97,461)( 98,462)( 99,449)(100,450)(101,451)(102,452)(103,453)(104,454)
(105,455)(106,484)(107,485)(108,486)(109,487)(110,488)(111,489)(112,490)
(113,498)(114,499)(115,500)(116,501)(117,502)(118,503)(119,504)(120,491)
(121,492)(122,493)(123,494)(124,495)(125,496)(126,497)(127,337)(128,338)
(129,339)(130,340)(131,341)(132,342)(133,343)(134,351)(135,352)(136,353)
(137,354)(138,355)(139,356)(140,357)(141,344)(142,345)(143,346)(144,347)
(145,348)(146,349)(147,350)(148,316)(149,317)(150,318)(151,319)(152,320)
(153,321)(154,322)(155,330)(156,331)(157,332)(158,333)(159,334)(160,335)
(161,336)(162,323)(163,324)(164,325)(165,326)(166,327)(167,328)(168,329)
(169,358)(170,359)(171,360)(172,361)(173,362)(174,363)(175,364)(176,372)
(177,373)(178,374)(179,375)(180,376)(181,377)(182,378)(183,365)(184,366)
(185,367)(186,368)(187,369)(188,370)(189,371)(190,274)(191,275)(192,276)
(193,277)(194,278)(195,279)(196,280)(197,288)(198,289)(199,290)(200,291)
(201,292)(202,293)(203,294)(204,281)(205,282)(206,283)(207,284)(208,285)
(209,286)(210,287)(211,253)(212,254)(213,255)(214,256)(215,257)(216,258)
(217,259)(218,267)(219,268)(220,269)(221,270)(222,271)(223,272)(224,273)
(225,260)(226,261)(227,262)(228,263)(229,264)(230,265)(231,266)(232,295)
(233,296)(234,297)(235,298)(236,299)(237,300)(238,301)(239,309)(240,310)
(241,311)(242,312)(243,313)(244,314)(245,315)(246,302)(247,303)(248,304)
(249,305)(250,306)(251,307)(252,308);;
s3 := ( 1,386)( 2,387)( 3,388)( 4,389)( 5,390)( 6,391)( 7,392)( 8,379)
( 9,380)( 10,381)( 11,382)( 12,383)( 13,384)( 14,385)( 15,393)( 16,394)
( 17,395)( 18,396)( 19,397)( 20,398)( 21,399)( 22,428)( 23,429)( 24,430)
( 25,431)( 26,432)( 27,433)( 28,434)( 29,421)( 30,422)( 31,423)( 32,424)
( 33,425)( 34,426)( 35,427)( 36,435)( 37,436)( 38,437)( 39,438)( 40,439)
( 41,440)( 42,441)( 43,407)( 44,408)( 45,409)( 46,410)( 47,411)( 48,412)
( 49,413)( 50,400)( 51,401)( 52,402)( 53,403)( 54,404)( 55,405)( 56,406)
( 57,414)( 58,415)( 59,416)( 60,417)( 61,418)( 62,419)( 63,420)( 64,449)
( 65,450)( 66,451)( 67,452)( 68,453)( 69,454)( 70,455)( 71,442)( 72,443)
( 73,444)( 74,445)( 75,446)( 76,447)( 77,448)( 78,456)( 79,457)( 80,458)
( 81,459)( 82,460)( 83,461)( 84,462)( 85,491)( 86,492)( 87,493)( 88,494)
( 89,495)( 90,496)( 91,497)( 92,484)( 93,485)( 94,486)( 95,487)( 96,488)
( 97,489)( 98,490)( 99,498)(100,499)(101,500)(102,501)(103,502)(104,503)
(105,504)(106,470)(107,471)(108,472)(109,473)(110,474)(111,475)(112,476)
(113,463)(114,464)(115,465)(116,466)(117,467)(118,468)(119,469)(120,477)
(121,478)(122,479)(123,480)(124,481)(125,482)(126,483)(127,323)(128,324)
(129,325)(130,326)(131,327)(132,328)(133,329)(134,316)(135,317)(136,318)
(137,319)(138,320)(139,321)(140,322)(141,330)(142,331)(143,332)(144,333)
(145,334)(146,335)(147,336)(148,365)(149,366)(150,367)(151,368)(152,369)
(153,370)(154,371)(155,358)(156,359)(157,360)(158,361)(159,362)(160,363)
(161,364)(162,372)(163,373)(164,374)(165,375)(166,376)(167,377)(168,378)
(169,344)(170,345)(171,346)(172,347)(173,348)(174,349)(175,350)(176,337)
(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,351)(184,352)
(185,353)(186,354)(187,355)(188,356)(189,357)(190,260)(191,261)(192,262)
(193,263)(194,264)(195,265)(196,266)(197,253)(198,254)(199,255)(200,256)
(201,257)(202,258)(203,259)(204,267)(205,268)(206,269)(207,270)(208,271)
(209,272)(210,273)(211,302)(212,303)(213,304)(214,305)(215,306)(216,307)
(217,308)(218,295)(219,296)(220,297)(221,298)(222,299)(223,300)(224,301)
(225,309)(226,310)(227,311)(228,312)(229,313)(230,314)(231,315)(232,281)
(233,282)(234,283)(235,284)(236,285)(237,286)(238,287)(239,274)(240,275)
(241,276)(242,277)(243,278)(244,279)(245,280)(246,288)(247,289)(248,290)
(249,291)(250,292)(251,293)(252,294);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
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*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(504)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)
( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)
( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)
( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)
(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(127,190)
(128,196)(129,195)(130,194)(131,193)(132,192)(133,191)(134,197)(135,203)
(136,202)(137,201)(138,200)(139,199)(140,198)(141,204)(142,210)(143,209)
(144,208)(145,207)(146,206)(147,205)(148,211)(149,217)(150,216)(151,215)
(152,214)(153,213)(154,212)(155,218)(156,224)(157,223)(158,222)(159,221)
(160,220)(161,219)(162,225)(163,231)(164,230)(165,229)(166,228)(167,227)
(168,226)(169,232)(170,238)(171,237)(172,236)(173,235)(174,234)(175,233)
(176,239)(177,245)(178,244)(179,243)(180,242)(181,241)(182,240)(183,246)
(184,252)(185,251)(186,250)(187,249)(188,248)(189,247)(253,316)(254,322)
(255,321)(256,320)(257,319)(258,318)(259,317)(260,323)(261,329)(262,328)
(263,327)(264,326)(265,325)(266,324)(267,330)(268,336)(269,335)(270,334)
(271,333)(272,332)(273,331)(274,337)(275,343)(276,342)(277,341)(278,340)
(279,339)(280,338)(281,344)(282,350)(283,349)(284,348)(285,347)(286,346)
(287,345)(288,351)(289,357)(290,356)(291,355)(292,354)(293,353)(294,352)
(295,358)(296,364)(297,363)(298,362)(299,361)(300,360)(301,359)(302,365)
(303,371)(304,370)(305,369)(306,368)(307,367)(308,366)(309,372)(310,378)
(311,377)(312,376)(313,375)(314,374)(315,373)(380,385)(381,384)(382,383)
(387,392)(388,391)(389,390)(394,399)(395,398)(396,397)(401,406)(402,405)
(403,404)(408,413)(409,412)(410,411)(415,420)(416,419)(417,418)(422,427)
(423,426)(424,425)(429,434)(430,433)(431,432)(436,441)(437,440)(438,439)
(443,448)(444,447)(445,446)(450,455)(451,454)(452,453)(457,462)(458,461)
(459,460)(464,469)(465,468)(466,467)(471,476)(472,475)(473,474)(478,483)
(479,482)(480,481)(485,490)(486,489)(487,488)(492,497)(493,496)(494,495)
(499,504)(500,503)(501,502);
s1 := Sym(504)!( 1,254)( 2,253)( 3,259)( 4,258)( 5,257)( 6,256)( 7,255)
( 8,261)( 9,260)( 10,266)( 11,265)( 12,264)( 13,263)( 14,262)( 15,268)
( 16,267)( 17,273)( 18,272)( 19,271)( 20,270)( 21,269)( 22,296)( 23,295)
( 24,301)( 25,300)( 26,299)( 27,298)( 28,297)( 29,303)( 30,302)( 31,308)
( 32,307)( 33,306)( 34,305)( 35,304)( 36,310)( 37,309)( 38,315)( 39,314)
( 40,313)( 41,312)( 42,311)( 43,275)( 44,274)( 45,280)( 46,279)( 47,278)
( 48,277)( 49,276)( 50,282)( 51,281)( 52,287)( 53,286)( 54,285)( 55,284)
( 56,283)( 57,289)( 58,288)( 59,294)( 60,293)( 61,292)( 62,291)( 63,290)
( 64,317)( 65,316)( 66,322)( 67,321)( 68,320)( 69,319)( 70,318)( 71,324)
( 72,323)( 73,329)( 74,328)( 75,327)( 76,326)( 77,325)( 78,331)( 79,330)
( 80,336)( 81,335)( 82,334)( 83,333)( 84,332)( 85,359)( 86,358)( 87,364)
( 88,363)( 89,362)( 90,361)( 91,360)( 92,366)( 93,365)( 94,371)( 95,370)
( 96,369)( 97,368)( 98,367)( 99,373)(100,372)(101,378)(102,377)(103,376)
(104,375)(105,374)(106,338)(107,337)(108,343)(109,342)(110,341)(111,340)
(112,339)(113,345)(114,344)(115,350)(116,349)(117,348)(118,347)(119,346)
(120,352)(121,351)(122,357)(123,356)(124,355)(125,354)(126,353)(127,443)
(128,442)(129,448)(130,447)(131,446)(132,445)(133,444)(134,450)(135,449)
(136,455)(137,454)(138,453)(139,452)(140,451)(141,457)(142,456)(143,462)
(144,461)(145,460)(146,459)(147,458)(148,485)(149,484)(150,490)(151,489)
(152,488)(153,487)(154,486)(155,492)(156,491)(157,497)(158,496)(159,495)
(160,494)(161,493)(162,499)(163,498)(164,504)(165,503)(166,502)(167,501)
(168,500)(169,464)(170,463)(171,469)(172,468)(173,467)(174,466)(175,465)
(176,471)(177,470)(178,476)(179,475)(180,474)(181,473)(182,472)(183,478)
(184,477)(185,483)(186,482)(187,481)(188,480)(189,479)(190,380)(191,379)
(192,385)(193,384)(194,383)(195,382)(196,381)(197,387)(198,386)(199,392)
(200,391)(201,390)(202,389)(203,388)(204,394)(205,393)(206,399)(207,398)
(208,397)(209,396)(210,395)(211,422)(212,421)(213,427)(214,426)(215,425)
(216,424)(217,423)(218,429)(219,428)(220,434)(221,433)(222,432)(223,431)
(224,430)(225,436)(226,435)(227,441)(228,440)(229,439)(230,438)(231,437)
(232,401)(233,400)(234,406)(235,405)(236,404)(237,403)(238,402)(239,408)
(240,407)(241,413)(242,412)(243,411)(244,410)(245,409)(246,415)(247,414)
(248,420)(249,419)(250,418)(251,417)(252,416);
s2 := Sym(504)!( 1,400)( 2,401)( 3,402)( 4,403)( 5,404)( 6,405)( 7,406)
( 8,414)( 9,415)( 10,416)( 11,417)( 12,418)( 13,419)( 14,420)( 15,407)
( 16,408)( 17,409)( 18,410)( 19,411)( 20,412)( 21,413)( 22,379)( 23,380)
( 24,381)( 25,382)( 26,383)( 27,384)( 28,385)( 29,393)( 30,394)( 31,395)
( 32,396)( 33,397)( 34,398)( 35,399)( 36,386)( 37,387)( 38,388)( 39,389)
( 40,390)( 41,391)( 42,392)( 43,421)( 44,422)( 45,423)( 46,424)( 47,425)
( 48,426)( 49,427)( 50,435)( 51,436)( 52,437)( 53,438)( 54,439)( 55,440)
( 56,441)( 57,428)( 58,429)( 59,430)( 60,431)( 61,432)( 62,433)( 63,434)
( 64,463)( 65,464)( 66,465)( 67,466)( 68,467)( 69,468)( 70,469)( 71,477)
( 72,478)( 73,479)( 74,480)( 75,481)( 76,482)( 77,483)( 78,470)( 79,471)
( 80,472)( 81,473)( 82,474)( 83,475)( 84,476)( 85,442)( 86,443)( 87,444)
( 88,445)( 89,446)( 90,447)( 91,448)( 92,456)( 93,457)( 94,458)( 95,459)
( 96,460)( 97,461)( 98,462)( 99,449)(100,450)(101,451)(102,452)(103,453)
(104,454)(105,455)(106,484)(107,485)(108,486)(109,487)(110,488)(111,489)
(112,490)(113,498)(114,499)(115,500)(116,501)(117,502)(118,503)(119,504)
(120,491)(121,492)(122,493)(123,494)(124,495)(125,496)(126,497)(127,337)
(128,338)(129,339)(130,340)(131,341)(132,342)(133,343)(134,351)(135,352)
(136,353)(137,354)(138,355)(139,356)(140,357)(141,344)(142,345)(143,346)
(144,347)(145,348)(146,349)(147,350)(148,316)(149,317)(150,318)(151,319)
(152,320)(153,321)(154,322)(155,330)(156,331)(157,332)(158,333)(159,334)
(160,335)(161,336)(162,323)(163,324)(164,325)(165,326)(166,327)(167,328)
(168,329)(169,358)(170,359)(171,360)(172,361)(173,362)(174,363)(175,364)
(176,372)(177,373)(178,374)(179,375)(180,376)(181,377)(182,378)(183,365)
(184,366)(185,367)(186,368)(187,369)(188,370)(189,371)(190,274)(191,275)
(192,276)(193,277)(194,278)(195,279)(196,280)(197,288)(198,289)(199,290)
(200,291)(201,292)(202,293)(203,294)(204,281)(205,282)(206,283)(207,284)
(208,285)(209,286)(210,287)(211,253)(212,254)(213,255)(214,256)(215,257)
(216,258)(217,259)(218,267)(219,268)(220,269)(221,270)(222,271)(223,272)
(224,273)(225,260)(226,261)(227,262)(228,263)(229,264)(230,265)(231,266)
(232,295)(233,296)(234,297)(235,298)(236,299)(237,300)(238,301)(239,309)
(240,310)(241,311)(242,312)(243,313)(244,314)(245,315)(246,302)(247,303)
(248,304)(249,305)(250,306)(251,307)(252,308);
s3 := Sym(504)!( 1,386)( 2,387)( 3,388)( 4,389)( 5,390)( 6,391)( 7,392)
( 8,379)( 9,380)( 10,381)( 11,382)( 12,383)( 13,384)( 14,385)( 15,393)
( 16,394)( 17,395)( 18,396)( 19,397)( 20,398)( 21,399)( 22,428)( 23,429)
( 24,430)( 25,431)( 26,432)( 27,433)( 28,434)( 29,421)( 30,422)( 31,423)
( 32,424)( 33,425)( 34,426)( 35,427)( 36,435)( 37,436)( 38,437)( 39,438)
( 40,439)( 41,440)( 42,441)( 43,407)( 44,408)( 45,409)( 46,410)( 47,411)
( 48,412)( 49,413)( 50,400)( 51,401)( 52,402)( 53,403)( 54,404)( 55,405)
( 56,406)( 57,414)( 58,415)( 59,416)( 60,417)( 61,418)( 62,419)( 63,420)
( 64,449)( 65,450)( 66,451)( 67,452)( 68,453)( 69,454)( 70,455)( 71,442)
( 72,443)( 73,444)( 74,445)( 75,446)( 76,447)( 77,448)( 78,456)( 79,457)
( 80,458)( 81,459)( 82,460)( 83,461)( 84,462)( 85,491)( 86,492)( 87,493)
( 88,494)( 89,495)( 90,496)( 91,497)( 92,484)( 93,485)( 94,486)( 95,487)
( 96,488)( 97,489)( 98,490)( 99,498)(100,499)(101,500)(102,501)(103,502)
(104,503)(105,504)(106,470)(107,471)(108,472)(109,473)(110,474)(111,475)
(112,476)(113,463)(114,464)(115,465)(116,466)(117,467)(118,468)(119,469)
(120,477)(121,478)(122,479)(123,480)(124,481)(125,482)(126,483)(127,323)
(128,324)(129,325)(130,326)(131,327)(132,328)(133,329)(134,316)(135,317)
(136,318)(137,319)(138,320)(139,321)(140,322)(141,330)(142,331)(143,332)
(144,333)(145,334)(146,335)(147,336)(148,365)(149,366)(150,367)(151,368)
(152,369)(153,370)(154,371)(155,358)(156,359)(157,360)(158,361)(159,362)
(160,363)(161,364)(162,372)(163,373)(164,374)(165,375)(166,376)(167,377)
(168,378)(169,344)(170,345)(171,346)(172,347)(173,348)(174,349)(175,350)
(176,337)(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,351)
(184,352)(185,353)(186,354)(187,355)(188,356)(189,357)(190,260)(191,261)
(192,262)(193,263)(194,264)(195,265)(196,266)(197,253)(198,254)(199,255)
(200,256)(201,257)(202,258)(203,259)(204,267)(205,268)(206,269)(207,270)
(208,271)(209,272)(210,273)(211,302)(212,303)(213,304)(214,305)(215,306)
(216,307)(217,308)(218,295)(219,296)(220,297)(221,298)(222,299)(223,300)
(224,301)(225,309)(226,310)(227,311)(228,312)(229,313)(230,314)(231,315)
(232,281)(233,282)(234,283)(235,284)(236,285)(237,286)(238,287)(239,274)
(240,275)(241,276)(242,277)(243,278)(244,279)(245,280)(246,288)(247,289)
(248,290)(249,291)(250,292)(251,293)(252,294);
poly := sub<Sym(504)|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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 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*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