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Polytope of Type {2,6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,24}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157570)
Rank : 4
Schlafli Type : {2,6,24}
Number of vertices, edges, etc : 2, 12, 144, 48
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   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 : {2,3,24}*576, {2,6,12}*576b
   3-fold quotients : {2,6,8}*384b
   4-fold quotients : {2,3,12}*288
   6-fold quotients : {2,3,8}*192, {2,6,4}*192
   8-fold quotients : {2,6,6}*144c
   12-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {2,3,4}*48, {2,6,2}*48
   48-fold quotients : {2,3,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,435)(  4,436)(  5,440)(  6,439)(  7,438)(  8,437)(  9,442)( 10,441)
( 11,451)( 12,452)( 13,456)( 14,455)( 15,454)( 16,453)( 17,458)( 18,457)
( 19,443)( 20,444)( 21,448)( 22,447)( 23,446)( 24,445)( 25,450)( 26,449)
( 27,483)( 28,484)( 29,488)( 30,487)( 31,486)( 32,485)( 33,490)( 34,489)
( 35,499)( 36,500)( 37,504)( 38,503)( 39,502)( 40,501)( 41,506)( 42,505)
( 43,491)( 44,492)( 45,496)( 46,495)( 47,494)( 48,493)( 49,498)( 50,497)
( 51,459)( 52,460)( 53,464)( 54,463)( 55,462)( 56,461)( 57,466)( 58,465)
( 59,475)( 60,476)( 61,480)( 62,479)( 63,478)( 64,477)( 65,482)( 66,481)
( 67,467)( 68,468)( 69,472)( 70,471)( 71,470)( 72,469)( 73,474)( 74,473)
( 75,507)( 76,508)( 77,512)( 78,511)( 79,510)( 80,509)( 81,514)( 82,513)
( 83,523)( 84,524)( 85,528)( 86,527)( 87,526)( 88,525)( 89,530)( 90,529)
( 91,515)( 92,516)( 93,520)( 94,519)( 95,518)( 96,517)( 97,522)( 98,521)
( 99,555)(100,556)(101,560)(102,559)(103,558)(104,557)(105,562)(106,561)
(107,571)(108,572)(109,576)(110,575)(111,574)(112,573)(113,578)(114,577)
(115,563)(116,564)(117,568)(118,567)(119,566)(120,565)(121,570)(122,569)
(123,531)(124,532)(125,536)(126,535)(127,534)(128,533)(129,538)(130,537)
(131,547)(132,548)(133,552)(134,551)(135,550)(136,549)(137,554)(138,553)
(139,539)(140,540)(141,544)(142,543)(143,542)(144,541)(145,546)(146,545)
(147,292)(148,291)(149,295)(150,296)(151,293)(152,294)(153,297)(154,298)
(155,308)(156,307)(157,311)(158,312)(159,309)(160,310)(161,313)(162,314)
(163,300)(164,299)(165,303)(166,304)(167,301)(168,302)(169,305)(170,306)
(171,340)(172,339)(173,343)(174,344)(175,341)(176,342)(177,345)(178,346)
(179,356)(180,355)(181,359)(182,360)(183,357)(184,358)(185,361)(186,362)
(187,348)(188,347)(189,351)(190,352)(191,349)(192,350)(193,353)(194,354)
(195,316)(196,315)(197,319)(198,320)(199,317)(200,318)(201,321)(202,322)
(203,332)(204,331)(205,335)(206,336)(207,333)(208,334)(209,337)(210,338)
(211,324)(212,323)(213,327)(214,328)(215,325)(216,326)(217,329)(218,330)
(219,364)(220,363)(221,367)(222,368)(223,365)(224,366)(225,369)(226,370)
(227,380)(228,379)(229,383)(230,384)(231,381)(232,382)(233,385)(234,386)
(235,372)(236,371)(237,375)(238,376)(239,373)(240,374)(241,377)(242,378)
(243,412)(244,411)(245,415)(246,416)(247,413)(248,414)(249,417)(250,418)
(251,428)(252,427)(253,431)(254,432)(255,429)(256,430)(257,433)(258,434)
(259,420)(260,419)(261,423)(262,424)(263,421)(264,422)(265,425)(266,426)
(267,388)(268,387)(269,391)(270,392)(271,389)(272,390)(273,393)(274,394)
(275,404)(276,403)(277,407)(278,408)(279,405)(280,406)(281,409)(282,410)
(283,396)(284,395)(285,399)(286,400)(287,397)(288,398)(289,401)(290,402);;
s2 := (  3,539)(  4,540)(  5,542)(  6,541)(  7,545)(  8,546)(  9,543)( 10,544)
( 11,531)( 12,532)( 13,534)( 14,533)( 15,537)( 16,538)( 17,535)( 18,536)
( 19,547)( 20,548)( 21,550)( 22,549)( 23,553)( 24,554)( 25,551)( 26,552)
( 27,515)( 28,516)( 29,518)( 30,517)( 31,521)( 32,522)( 33,519)( 34,520)
( 35,507)( 36,508)( 37,510)( 38,509)( 39,513)( 40,514)( 41,511)( 42,512)
( 43,523)( 44,524)( 45,526)( 46,525)( 47,529)( 48,530)( 49,527)( 50,528)
( 51,563)( 52,564)( 53,566)( 54,565)( 55,569)( 56,570)( 57,567)( 58,568)
( 59,555)( 60,556)( 61,558)( 62,557)( 63,561)( 64,562)( 65,559)( 66,560)
( 67,571)( 68,572)( 69,574)( 70,573)( 71,577)( 72,578)( 73,575)( 74,576)
( 75,467)( 76,468)( 77,470)( 78,469)( 79,473)( 80,474)( 81,471)( 82,472)
( 83,459)( 84,460)( 85,462)( 86,461)( 87,465)( 88,466)( 89,463)( 90,464)
( 91,475)( 92,476)( 93,478)( 94,477)( 95,481)( 96,482)( 97,479)( 98,480)
( 99,443)(100,444)(101,446)(102,445)(103,449)(104,450)(105,447)(106,448)
(107,435)(108,436)(109,438)(110,437)(111,441)(112,442)(113,439)(114,440)
(115,451)(116,452)(117,454)(118,453)(119,457)(120,458)(121,455)(122,456)
(123,491)(124,492)(125,494)(126,493)(127,497)(128,498)(129,495)(130,496)
(131,483)(132,484)(133,486)(134,485)(135,489)(136,490)(137,487)(138,488)
(139,499)(140,500)(141,502)(142,501)(143,505)(144,506)(145,503)(146,504)
(147,396)(148,395)(149,397)(150,398)(151,402)(152,401)(153,400)(154,399)
(155,388)(156,387)(157,389)(158,390)(159,394)(160,393)(161,392)(162,391)
(163,404)(164,403)(165,405)(166,406)(167,410)(168,409)(169,408)(170,407)
(171,372)(172,371)(173,373)(174,374)(175,378)(176,377)(177,376)(178,375)
(179,364)(180,363)(181,365)(182,366)(183,370)(184,369)(185,368)(186,367)
(187,380)(188,379)(189,381)(190,382)(191,386)(192,385)(193,384)(194,383)
(195,420)(196,419)(197,421)(198,422)(199,426)(200,425)(201,424)(202,423)
(203,412)(204,411)(205,413)(206,414)(207,418)(208,417)(209,416)(210,415)
(211,428)(212,427)(213,429)(214,430)(215,434)(216,433)(217,432)(218,431)
(219,324)(220,323)(221,325)(222,326)(223,330)(224,329)(225,328)(226,327)
(227,316)(228,315)(229,317)(230,318)(231,322)(232,321)(233,320)(234,319)
(235,332)(236,331)(237,333)(238,334)(239,338)(240,337)(241,336)(242,335)
(243,300)(244,299)(245,301)(246,302)(247,306)(248,305)(249,304)(250,303)
(251,292)(252,291)(253,293)(254,294)(255,298)(256,297)(257,296)(258,295)
(259,308)(260,307)(261,309)(262,310)(263,314)(264,313)(265,312)(266,311)
(267,348)(268,347)(269,349)(270,350)(271,354)(272,353)(273,352)(274,351)
(275,340)(276,339)(277,341)(278,342)(279,346)(280,345)(281,344)(282,343)
(283,356)(284,355)(285,357)(286,358)(287,362)(288,361)(289,360)(290,359);;
s3 := (  3,297)(  4,298)(  5,295)(  6,296)(  7,294)(  8,293)(  9,292)( 10,291)
( 11,313)( 12,314)( 13,311)( 14,312)( 15,310)( 16,309)( 17,308)( 18,307)
( 19,305)( 20,306)( 21,303)( 22,304)( 23,302)( 24,301)( 25,300)( 26,299)
( 27,321)( 28,322)( 29,319)( 30,320)( 31,318)( 32,317)( 33,316)( 34,315)
( 35,337)( 36,338)( 37,335)( 38,336)( 39,334)( 40,333)( 41,332)( 42,331)
( 43,329)( 44,330)( 45,327)( 46,328)( 47,326)( 48,325)( 49,324)( 50,323)
( 51,345)( 52,346)( 53,343)( 54,344)( 55,342)( 56,341)( 57,340)( 58,339)
( 59,361)( 60,362)( 61,359)( 62,360)( 63,358)( 64,357)( 65,356)( 66,355)
( 67,353)( 68,354)( 69,351)( 70,352)( 71,350)( 72,349)( 73,348)( 74,347)
( 75,369)( 76,370)( 77,367)( 78,368)( 79,366)( 80,365)( 81,364)( 82,363)
( 83,385)( 84,386)( 85,383)( 86,384)( 87,382)( 88,381)( 89,380)( 90,379)
( 91,377)( 92,378)( 93,375)( 94,376)( 95,374)( 96,373)( 97,372)( 98,371)
( 99,393)(100,394)(101,391)(102,392)(103,390)(104,389)(105,388)(106,387)
(107,409)(108,410)(109,407)(110,408)(111,406)(112,405)(113,404)(114,403)
(115,401)(116,402)(117,399)(118,400)(119,398)(120,397)(121,396)(122,395)
(123,417)(124,418)(125,415)(126,416)(127,414)(128,413)(129,412)(130,411)
(131,433)(132,434)(133,431)(134,432)(135,430)(136,429)(137,428)(138,427)
(139,425)(140,426)(141,423)(142,424)(143,422)(144,421)(145,420)(146,419)
(147,442)(148,441)(149,440)(150,439)(151,437)(152,438)(153,435)(154,436)
(155,458)(156,457)(157,456)(158,455)(159,453)(160,454)(161,451)(162,452)
(163,450)(164,449)(165,448)(166,447)(167,445)(168,446)(169,443)(170,444)
(171,466)(172,465)(173,464)(174,463)(175,461)(176,462)(177,459)(178,460)
(179,482)(180,481)(181,480)(182,479)(183,477)(184,478)(185,475)(186,476)
(187,474)(188,473)(189,472)(190,471)(191,469)(192,470)(193,467)(194,468)
(195,490)(196,489)(197,488)(198,487)(199,485)(200,486)(201,483)(202,484)
(203,506)(204,505)(205,504)(206,503)(207,501)(208,502)(209,499)(210,500)
(211,498)(212,497)(213,496)(214,495)(215,493)(216,494)(217,491)(218,492)
(219,514)(220,513)(221,512)(222,511)(223,509)(224,510)(225,507)(226,508)
(227,530)(228,529)(229,528)(230,527)(231,525)(232,526)(233,523)(234,524)
(235,522)(236,521)(237,520)(238,519)(239,517)(240,518)(241,515)(242,516)
(243,538)(244,537)(245,536)(246,535)(247,533)(248,534)(249,531)(250,532)
(251,554)(252,553)(253,552)(254,551)(255,549)(256,550)(257,547)(258,548)
(259,546)(260,545)(261,544)(262,543)(263,541)(264,542)(265,539)(266,540)
(267,562)(268,561)(269,560)(270,559)(271,557)(272,558)(273,555)(274,556)
(275,578)(276,577)(277,576)(278,575)(279,573)(280,574)(281,571)(282,572)
(283,570)(284,569)(285,568)(286,567)(287,565)(288,566)(289,563)(290,564);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(578)!(1,2);
s1 := Sym(578)!(  3,435)(  4,436)(  5,440)(  6,439)(  7,438)(  8,437)(  9,442)
( 10,441)( 11,451)( 12,452)( 13,456)( 14,455)( 15,454)( 16,453)( 17,458)
( 18,457)( 19,443)( 20,444)( 21,448)( 22,447)( 23,446)( 24,445)( 25,450)
( 26,449)( 27,483)( 28,484)( 29,488)( 30,487)( 31,486)( 32,485)( 33,490)
( 34,489)( 35,499)( 36,500)( 37,504)( 38,503)( 39,502)( 40,501)( 41,506)
( 42,505)( 43,491)( 44,492)( 45,496)( 46,495)( 47,494)( 48,493)( 49,498)
( 50,497)( 51,459)( 52,460)( 53,464)( 54,463)( 55,462)( 56,461)( 57,466)
( 58,465)( 59,475)( 60,476)( 61,480)( 62,479)( 63,478)( 64,477)( 65,482)
( 66,481)( 67,467)( 68,468)( 69,472)( 70,471)( 71,470)( 72,469)( 73,474)
( 74,473)( 75,507)( 76,508)( 77,512)( 78,511)( 79,510)( 80,509)( 81,514)
( 82,513)( 83,523)( 84,524)( 85,528)( 86,527)( 87,526)( 88,525)( 89,530)
( 90,529)( 91,515)( 92,516)( 93,520)( 94,519)( 95,518)( 96,517)( 97,522)
( 98,521)( 99,555)(100,556)(101,560)(102,559)(103,558)(104,557)(105,562)
(106,561)(107,571)(108,572)(109,576)(110,575)(111,574)(112,573)(113,578)
(114,577)(115,563)(116,564)(117,568)(118,567)(119,566)(120,565)(121,570)
(122,569)(123,531)(124,532)(125,536)(126,535)(127,534)(128,533)(129,538)
(130,537)(131,547)(132,548)(133,552)(134,551)(135,550)(136,549)(137,554)
(138,553)(139,539)(140,540)(141,544)(142,543)(143,542)(144,541)(145,546)
(146,545)(147,292)(148,291)(149,295)(150,296)(151,293)(152,294)(153,297)
(154,298)(155,308)(156,307)(157,311)(158,312)(159,309)(160,310)(161,313)
(162,314)(163,300)(164,299)(165,303)(166,304)(167,301)(168,302)(169,305)
(170,306)(171,340)(172,339)(173,343)(174,344)(175,341)(176,342)(177,345)
(178,346)(179,356)(180,355)(181,359)(182,360)(183,357)(184,358)(185,361)
(186,362)(187,348)(188,347)(189,351)(190,352)(191,349)(192,350)(193,353)
(194,354)(195,316)(196,315)(197,319)(198,320)(199,317)(200,318)(201,321)
(202,322)(203,332)(204,331)(205,335)(206,336)(207,333)(208,334)(209,337)
(210,338)(211,324)(212,323)(213,327)(214,328)(215,325)(216,326)(217,329)
(218,330)(219,364)(220,363)(221,367)(222,368)(223,365)(224,366)(225,369)
(226,370)(227,380)(228,379)(229,383)(230,384)(231,381)(232,382)(233,385)
(234,386)(235,372)(236,371)(237,375)(238,376)(239,373)(240,374)(241,377)
(242,378)(243,412)(244,411)(245,415)(246,416)(247,413)(248,414)(249,417)
(250,418)(251,428)(252,427)(253,431)(254,432)(255,429)(256,430)(257,433)
(258,434)(259,420)(260,419)(261,423)(262,424)(263,421)(264,422)(265,425)
(266,426)(267,388)(268,387)(269,391)(270,392)(271,389)(272,390)(273,393)
(274,394)(275,404)(276,403)(277,407)(278,408)(279,405)(280,406)(281,409)
(282,410)(283,396)(284,395)(285,399)(286,400)(287,397)(288,398)(289,401)
(290,402);
s2 := Sym(578)!(  3,539)(  4,540)(  5,542)(  6,541)(  7,545)(  8,546)(  9,543)
( 10,544)( 11,531)( 12,532)( 13,534)( 14,533)( 15,537)( 16,538)( 17,535)
( 18,536)( 19,547)( 20,548)( 21,550)( 22,549)( 23,553)( 24,554)( 25,551)
( 26,552)( 27,515)( 28,516)( 29,518)( 30,517)( 31,521)( 32,522)( 33,519)
( 34,520)( 35,507)( 36,508)( 37,510)( 38,509)( 39,513)( 40,514)( 41,511)
( 42,512)( 43,523)( 44,524)( 45,526)( 46,525)( 47,529)( 48,530)( 49,527)
( 50,528)( 51,563)( 52,564)( 53,566)( 54,565)( 55,569)( 56,570)( 57,567)
( 58,568)( 59,555)( 60,556)( 61,558)( 62,557)( 63,561)( 64,562)( 65,559)
( 66,560)( 67,571)( 68,572)( 69,574)( 70,573)( 71,577)( 72,578)( 73,575)
( 74,576)( 75,467)( 76,468)( 77,470)( 78,469)( 79,473)( 80,474)( 81,471)
( 82,472)( 83,459)( 84,460)( 85,462)( 86,461)( 87,465)( 88,466)( 89,463)
( 90,464)( 91,475)( 92,476)( 93,478)( 94,477)( 95,481)( 96,482)( 97,479)
( 98,480)( 99,443)(100,444)(101,446)(102,445)(103,449)(104,450)(105,447)
(106,448)(107,435)(108,436)(109,438)(110,437)(111,441)(112,442)(113,439)
(114,440)(115,451)(116,452)(117,454)(118,453)(119,457)(120,458)(121,455)
(122,456)(123,491)(124,492)(125,494)(126,493)(127,497)(128,498)(129,495)
(130,496)(131,483)(132,484)(133,486)(134,485)(135,489)(136,490)(137,487)
(138,488)(139,499)(140,500)(141,502)(142,501)(143,505)(144,506)(145,503)
(146,504)(147,396)(148,395)(149,397)(150,398)(151,402)(152,401)(153,400)
(154,399)(155,388)(156,387)(157,389)(158,390)(159,394)(160,393)(161,392)
(162,391)(163,404)(164,403)(165,405)(166,406)(167,410)(168,409)(169,408)
(170,407)(171,372)(172,371)(173,373)(174,374)(175,378)(176,377)(177,376)
(178,375)(179,364)(180,363)(181,365)(182,366)(183,370)(184,369)(185,368)
(186,367)(187,380)(188,379)(189,381)(190,382)(191,386)(192,385)(193,384)
(194,383)(195,420)(196,419)(197,421)(198,422)(199,426)(200,425)(201,424)
(202,423)(203,412)(204,411)(205,413)(206,414)(207,418)(208,417)(209,416)
(210,415)(211,428)(212,427)(213,429)(214,430)(215,434)(216,433)(217,432)
(218,431)(219,324)(220,323)(221,325)(222,326)(223,330)(224,329)(225,328)
(226,327)(227,316)(228,315)(229,317)(230,318)(231,322)(232,321)(233,320)
(234,319)(235,332)(236,331)(237,333)(238,334)(239,338)(240,337)(241,336)
(242,335)(243,300)(244,299)(245,301)(246,302)(247,306)(248,305)(249,304)
(250,303)(251,292)(252,291)(253,293)(254,294)(255,298)(256,297)(257,296)
(258,295)(259,308)(260,307)(261,309)(262,310)(263,314)(264,313)(265,312)
(266,311)(267,348)(268,347)(269,349)(270,350)(271,354)(272,353)(273,352)
(274,351)(275,340)(276,339)(277,341)(278,342)(279,346)(280,345)(281,344)
(282,343)(283,356)(284,355)(285,357)(286,358)(287,362)(288,361)(289,360)
(290,359);
s3 := Sym(578)!(  3,297)(  4,298)(  5,295)(  6,296)(  7,294)(  8,293)(  9,292)
( 10,291)( 11,313)( 12,314)( 13,311)( 14,312)( 15,310)( 16,309)( 17,308)
( 18,307)( 19,305)( 20,306)( 21,303)( 22,304)( 23,302)( 24,301)( 25,300)
( 26,299)( 27,321)( 28,322)( 29,319)( 30,320)( 31,318)( 32,317)( 33,316)
( 34,315)( 35,337)( 36,338)( 37,335)( 38,336)( 39,334)( 40,333)( 41,332)
( 42,331)( 43,329)( 44,330)( 45,327)( 46,328)( 47,326)( 48,325)( 49,324)
( 50,323)( 51,345)( 52,346)( 53,343)( 54,344)( 55,342)( 56,341)( 57,340)
( 58,339)( 59,361)( 60,362)( 61,359)( 62,360)( 63,358)( 64,357)( 65,356)
( 66,355)( 67,353)( 68,354)( 69,351)( 70,352)( 71,350)( 72,349)( 73,348)
( 74,347)( 75,369)( 76,370)( 77,367)( 78,368)( 79,366)( 80,365)( 81,364)
( 82,363)( 83,385)( 84,386)( 85,383)( 86,384)( 87,382)( 88,381)( 89,380)
( 90,379)( 91,377)( 92,378)( 93,375)( 94,376)( 95,374)( 96,373)( 97,372)
( 98,371)( 99,393)(100,394)(101,391)(102,392)(103,390)(104,389)(105,388)
(106,387)(107,409)(108,410)(109,407)(110,408)(111,406)(112,405)(113,404)
(114,403)(115,401)(116,402)(117,399)(118,400)(119,398)(120,397)(121,396)
(122,395)(123,417)(124,418)(125,415)(126,416)(127,414)(128,413)(129,412)
(130,411)(131,433)(132,434)(133,431)(134,432)(135,430)(136,429)(137,428)
(138,427)(139,425)(140,426)(141,423)(142,424)(143,422)(144,421)(145,420)
(146,419)(147,442)(148,441)(149,440)(150,439)(151,437)(152,438)(153,435)
(154,436)(155,458)(156,457)(157,456)(158,455)(159,453)(160,454)(161,451)
(162,452)(163,450)(164,449)(165,448)(166,447)(167,445)(168,446)(169,443)
(170,444)(171,466)(172,465)(173,464)(174,463)(175,461)(176,462)(177,459)
(178,460)(179,482)(180,481)(181,480)(182,479)(183,477)(184,478)(185,475)
(186,476)(187,474)(188,473)(189,472)(190,471)(191,469)(192,470)(193,467)
(194,468)(195,490)(196,489)(197,488)(198,487)(199,485)(200,486)(201,483)
(202,484)(203,506)(204,505)(205,504)(206,503)(207,501)(208,502)(209,499)
(210,500)(211,498)(212,497)(213,496)(214,495)(215,493)(216,494)(217,491)
(218,492)(219,514)(220,513)(221,512)(222,511)(223,509)(224,510)(225,507)
(226,508)(227,530)(228,529)(229,528)(230,527)(231,525)(232,526)(233,523)
(234,524)(235,522)(236,521)(237,520)(238,519)(239,517)(240,518)(241,515)
(242,516)(243,538)(244,537)(245,536)(246,535)(247,533)(248,534)(249,531)
(250,532)(251,554)(252,553)(253,552)(254,551)(255,549)(256,550)(257,547)
(258,548)(259,546)(260,545)(261,544)(262,543)(263,541)(264,542)(265,539)
(266,540)(267,562)(268,561)(269,560)(270,559)(271,557)(272,558)(273,555)
(274,556)(275,578)(276,577)(277,576)(278,575)(279,573)(280,574)(281,571)
(282,572)(283,570)(284,569)(285,568)(286,567)(287,565)(288,566)(289,563)
(290,564);
poly := sub<Sym(578)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >; 
 

to this polytope