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Polytope of Type {3,6,28}

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