Polytope of Type {6,84}

Play with this polytope as a twisty puzzle

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)(  2,413)(  3,412)(  4,411)(  5,410)(  6,409)(  7,408)(  8,400)(  9,406)( 10,405)( 11,404)( 12,403)( 13,402)( 14,401)( 15,414)( 16,420)( 17,419)( 18,418)( 19,417)( 20,416)( 21,415)( 22,386)( 23,392)( 24,391)( 25,390)( 26,389)( 27,388)( 28,387)( 29,379)( 30,385)( 31,384)( 32,383)( 33,382)( 34,381)( 35,380)( 36,393)( 37,399)( 38,398)( 39,397)( 40,396)( 41,395)( 42,394)( 43,428)( 44,434)( 45,433)( 46,432)( 47,431)( 48,430)( 49,429)( 50,421)( 51,427)( 52,426)( 53,425)( 54,424)( 55,423)( 56,422)( 57,435)( 58,441)( 59,440)( 60,439)( 61,438)( 62,437)( 63,436)( 64,470)( 65,476)( 66,475)( 67,474)( 68,473)( 69,472)( 70,471)( 71,463)( 72,469)( 73,468)( 74,467)( 75,466)( 76,465)( 77,464)( 78,477)( 79,483)( 80,482)( 81,481)( 82,480)( 83,479)( 84,478)( 85,449)( 86,455)( 87,454)( 88,453)( 89,452)( 90,451)( 91,450)( 92,442)( 93,448)( 94,447)( 95,446)( 96,445)( 97,444)( 98,443)( 99,456)(100,462)(101,461)(102,460)(103,459)(104,458)(105,457)(106,491)(107,497)(108,496)(109,495)(110,494)(111,493)(112,492)(113,484)(114,490)(115,489)(116,488)(117,487)(118,486)(119,485)(120,498)(121,504)(122,503)(123,502)(124,501)(125,500)(126,499)(127,281)(128,287)(129,286)(130,285)(131,284)(132,283)(133,282)(134,274)(135,280)(136,279)(137,278)(138,277)(139,276)(140,275)(141,288)(142,294)(143,293)(144,292)(145,291)(146,290)(147,289)(148,260)(149,266)(150,265)(151,264)(152,263)(153,262)(154,261)(155,253)(156,259)(157,258)(158,257)(159,256)(160,255)(161,254)(162,267)(163,273)(164,272)(165,271)(166,270)(167,269)(168,268)(169,302)(170,308)(171,307)(172,306)(173,305)(174,304)(175,303)(176,295)(177,301)(178,300)(179,299)(180,298)(181,297)(182,296)(183,309)(184,315)(185,314)(186,313)(187,312)(188,311)(189,310)(190,344)(191,350)(192,349)(193,348)(194,347)(195,346)(196,345)(197,337)(198,343)(199,342)(200,341)(201,340)(202,339)(203,338)(204,351)(205,357)(206,356)(207,355)(208,354)(209,353)(210,352)(211,323)(212,329)(213,328)(214,327)(215,326)(216,325)(217,324)(218,316)(219,322)(220,321)(221,320)(222,319)(223,318)(224,317)(225,330)(226,336)(227,335)(228,334)(229,333)(230,332)(231,331)(232,365)(233,371)(234,370)(235,369)(236,368)(237,367)(238,366)(239,358)(240,364)(241,363)(242,362)(243,361)(244,360)(245,359)(246,372)(247,378)(248,377)(249,376)(250,375)(251,374)(252,373);;
s2 := (  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);;
poly := Group([s0,s1,s2]);;
 

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s2*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1 ];;
poly := F / rels;;
 

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)(  2,413)(  3,412)(  4,411)(  5,410)(  6,409)(  7,408)(  8,400)(  9,406)( 10,405)( 11,404)( 12,403)( 13,402)( 14,401)( 15,414)( 16,420)( 17,419)( 18,418)( 19,417)( 20,416)( 21,415)( 22,386)( 23,392)( 24,391)( 25,390)( 26,389)( 27,388)( 28,387)( 29,379)( 30,385)( 31,384)( 32,383)( 33,382)( 34,381)( 35,380)( 36,393)( 37,399)( 38,398)( 39,397)( 40,396)( 41,395)( 42,394)( 43,428)( 44,434)( 45,433)( 46,432)( 47,431)( 48,430)( 49,429)( 50,421)( 51,427)( 52,426)( 53,425)( 54,424)( 55,423)( 56,422)( 57,435)( 58,441)( 59,440)( 60,439)( 61,438)( 62,437)( 63,436)( 64,470)( 65,476)( 66,475)( 67,474)( 68,473)( 69,472)( 70,471)( 71,463)( 72,469)( 73,468)( 74,467)( 75,466)( 76,465)( 77,464)( 78,477)( 79,483)( 80,482)( 81,481)( 82,480)( 83,479)( 84,478)( 85,449)( 86,455)( 87,454)( 88,453)( 89,452)( 90,451)( 91,450)( 92,442)( 93,448)( 94,447)( 95,446)( 96,445)( 97,444)( 98,443)( 99,456)(100,462)(101,461)(102,460)(103,459)(104,458)(105,457)(106,491)(107,497)(108,496)(109,495)(110,494)(111,493)(112,492)(113,484)(114,490)(115,489)(116,488)(117,487)(118,486)(119,485)(120,498)(121,504)(122,503)(123,502)(124,501)(125,500)(126,499)(127,281)(128,287)(129,286)(130,285)(131,284)(132,283)(133,282)(134,274)(135,280)(136,279)(137,278)(138,277)(139,276)(140,275)(141,288)(142,294)(143,293)(144,292)(145,291)(146,290)(147,289)(148,260)(149,266)(150,265)(151,264)(152,263)(153,262)(154,261)(155,253)(156,259)(157,258)(158,257)(159,256)(160,255)(161,254)(162,267)(163,273)(164,272)(165,271)(166,270)(167,269)(168,268)(169,302)(170,308)(171,307)(172,306)(173,305)(174,304)(175,303)(176,295)(177,301)(178,300)(179,299)(180,298)(181,297)(182,296)(183,309)(184,315)(185,314)(186,313)(187,312)(188,311)(189,310)(190,344)(191,350)(192,349)(193,348)(194,347)(195,346)(196,345)(197,337)(198,343)(199,342)(200,341)(201,340)(202,339)(203,338)(204,351)(205,357)(206,356)(207,355)(208,354)(209,353)(210,352)(211,323)(212,329)(213,328)(214,327)(215,326)(216,325)(217,324)(218,316)(219,322)(220,321)(221,320)(222,319)(223,318)(224,317)(225,330)(226,336)(227,335)(228,334)(229,333)(230,332)(231,331)(232,365)(233,371)(234,370)(235,369)(236,368)(237,367)(238,366)(239,358)(240,364)(241,363)(242,362)(243,361)(244,360)(245,359)(246,372)(247,378)(248,377)(249,376)(250,375)(251,374)(252,373);
s2 := 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);
poly := sub<Sym(504)|s0,s1,s2>;
 

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s2*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1 >; 
 

Twisty Puzzle