Questions?
See the FAQ
or other info.

Polytope of Type {2,24,6}

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

to this polytope