Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*576b
if this polytope has a name.
Group : SmallGroup(576,8319)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 48, 144, 12
Order of s0s1s2 : 12
Order of s0s1s2s1 : 24
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {24,6,2} of size 1152
Vertex Figure Of :
   {2,24,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,3}*288, {12,6}*288b
   3-fold quotients : {8,6}*192b
   4-fold quotients : {12,3}*144
   6-fold quotients : {8,3}*96, {4,6}*96
   8-fold quotients : {6,6}*72b
   12-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   16-fold quotients : {6,3}*36
   24-fold quotients : {4,3}*24, {2,6}*24
   48-fold quotients : {2,3}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,12}*1152l, {24,12}*1152m, {24,6}*1152l
   3-fold covers : {24,18}*1728b, {24,6}*1728b, {24,6}*1728f
Permutation Representation (GAP) : 
s0 := (  1,293)(  2,294)(  3,296)(  4,295)(  5,290)(  6,289)(  7,291)(  8,292)
(  9,309)( 10,310)( 11,312)( 12,311)( 13,306)( 14,305)( 15,307)( 16,308)
( 17,301)( 18,302)( 19,304)( 20,303)( 21,298)( 22,297)( 23,299)( 24,300)
( 25,317)( 26,318)( 27,320)( 28,319)( 29,314)( 30,313)( 31,315)( 32,316)
( 33,333)( 34,334)( 35,336)( 36,335)( 37,330)( 38,329)( 39,331)( 40,332)
( 41,325)( 42,326)( 43,328)( 44,327)( 45,322)( 46,321)( 47,323)( 48,324)
( 49,341)( 50,342)( 51,344)( 52,343)( 53,338)( 54,337)( 55,339)( 56,340)
( 57,357)( 58,358)( 59,360)( 60,359)( 61,354)( 62,353)( 63,355)( 64,356)
( 65,349)( 66,350)( 67,352)( 68,351)( 69,346)( 70,345)( 71,347)( 72,348)
( 73,365)( 74,366)( 75,368)( 76,367)( 77,362)( 78,361)( 79,363)( 80,364)
( 81,381)( 82,382)( 83,384)( 84,383)( 85,378)( 86,377)( 87,379)( 88,380)
( 89,373)( 90,374)( 91,376)( 92,375)( 93,370)( 94,369)( 95,371)( 96,372)
( 97,389)( 98,390)( 99,392)(100,391)(101,386)(102,385)(103,387)(104,388)
(105,405)(106,406)(107,408)(108,407)(109,402)(110,401)(111,403)(112,404)
(113,397)(114,398)(115,400)(116,399)(117,394)(118,393)(119,395)(120,396)
(121,413)(122,414)(123,416)(124,415)(125,410)(126,409)(127,411)(128,412)
(129,429)(130,430)(131,432)(132,431)(133,426)(134,425)(135,427)(136,428)
(137,421)(138,422)(139,424)(140,423)(141,418)(142,417)(143,419)(144,420)
(145,438)(146,437)(147,439)(148,440)(149,433)(150,434)(151,436)(152,435)
(153,454)(154,453)(155,455)(156,456)(157,449)(158,450)(159,452)(160,451)
(161,446)(162,445)(163,447)(164,448)(165,441)(166,442)(167,444)(168,443)
(169,462)(170,461)(171,463)(172,464)(173,457)(174,458)(175,460)(176,459)
(177,478)(178,477)(179,479)(180,480)(181,473)(182,474)(183,476)(184,475)
(185,470)(186,469)(187,471)(188,472)(189,465)(190,466)(191,468)(192,467)
(193,486)(194,485)(195,487)(196,488)(197,481)(198,482)(199,484)(200,483)
(201,502)(202,501)(203,503)(204,504)(205,497)(206,498)(207,500)(208,499)
(209,494)(210,493)(211,495)(212,496)(213,489)(214,490)(215,492)(216,491)
(217,510)(218,509)(219,511)(220,512)(221,505)(222,506)(223,508)(224,507)
(225,526)(226,525)(227,527)(228,528)(229,521)(230,522)(231,524)(232,523)
(233,518)(234,517)(235,519)(236,520)(237,513)(238,514)(239,516)(240,515)
(241,534)(242,533)(243,535)(244,536)(245,529)(246,530)(247,532)(248,531)
(249,550)(250,549)(251,551)(252,552)(253,545)(254,546)(255,548)(256,547)
(257,542)(258,541)(259,543)(260,544)(261,537)(262,538)(263,540)(264,539)
(265,558)(266,557)(267,559)(268,560)(269,553)(270,554)(271,556)(272,555)
(273,574)(274,573)(275,575)(276,576)(277,569)(278,570)(279,572)(280,571)
(281,566)(282,565)(283,567)(284,568)(285,561)(286,562)(287,564)(288,563);;
s1 := (  1,441)(  2,442)(  3,446)(  4,445)(  5,444)(  6,443)(  7,448)(  8,447)
(  9,433)( 10,434)( 11,438)( 12,437)( 13,436)( 14,435)( 15,440)( 16,439)
( 17,449)( 18,450)( 19,454)( 20,453)( 21,452)( 22,451)( 23,456)( 24,455)
( 25,489)( 26,490)( 27,494)( 28,493)( 29,492)( 30,491)( 31,496)( 32,495)
( 33,481)( 34,482)( 35,486)( 36,485)( 37,484)( 38,483)( 39,488)( 40,487)
( 41,497)( 42,498)( 43,502)( 44,501)( 45,500)( 46,499)( 47,504)( 48,503)
( 49,465)( 50,466)( 51,470)( 52,469)( 53,468)( 54,467)( 55,472)( 56,471)
( 57,457)( 58,458)( 59,462)( 60,461)( 61,460)( 62,459)( 63,464)( 64,463)
( 65,473)( 66,474)( 67,478)( 68,477)( 69,476)( 70,475)( 71,480)( 72,479)
( 73,513)( 74,514)( 75,518)( 76,517)( 77,516)( 78,515)( 79,520)( 80,519)
( 81,505)( 82,506)( 83,510)( 84,509)( 85,508)( 86,507)( 87,512)( 88,511)
( 89,521)( 90,522)( 91,526)( 92,525)( 93,524)( 94,523)( 95,528)( 96,527)
( 97,561)( 98,562)( 99,566)(100,565)(101,564)(102,563)(103,568)(104,567)
(105,553)(106,554)(107,558)(108,557)(109,556)(110,555)(111,560)(112,559)
(113,569)(114,570)(115,574)(116,573)(117,572)(118,571)(119,576)(120,575)
(121,537)(122,538)(123,542)(124,541)(125,540)(126,539)(127,544)(128,543)
(129,529)(130,530)(131,534)(132,533)(133,532)(134,531)(135,536)(136,535)
(137,545)(138,546)(139,550)(140,549)(141,548)(142,547)(143,552)(144,551)
(145,298)(146,297)(147,301)(148,302)(149,299)(150,300)(151,303)(152,304)
(153,290)(154,289)(155,293)(156,294)(157,291)(158,292)(159,295)(160,296)
(161,306)(162,305)(163,309)(164,310)(165,307)(166,308)(167,311)(168,312)
(169,346)(170,345)(171,349)(172,350)(173,347)(174,348)(175,351)(176,352)
(177,338)(178,337)(179,341)(180,342)(181,339)(182,340)(183,343)(184,344)
(185,354)(186,353)(187,357)(188,358)(189,355)(190,356)(191,359)(192,360)
(193,322)(194,321)(195,325)(196,326)(197,323)(198,324)(199,327)(200,328)
(201,314)(202,313)(203,317)(204,318)(205,315)(206,316)(207,319)(208,320)
(209,330)(210,329)(211,333)(212,334)(213,331)(214,332)(215,335)(216,336)
(217,370)(218,369)(219,373)(220,374)(221,371)(222,372)(223,375)(224,376)
(225,362)(226,361)(227,365)(228,366)(229,363)(230,364)(231,367)(232,368)
(233,378)(234,377)(235,381)(236,382)(237,379)(238,380)(239,383)(240,384)
(241,418)(242,417)(243,421)(244,422)(245,419)(246,420)(247,423)(248,424)
(249,410)(250,409)(251,413)(252,414)(253,411)(254,412)(255,415)(256,416)
(257,426)(258,425)(259,429)(260,430)(261,427)(262,428)(263,431)(264,432)
(265,394)(266,393)(267,397)(268,398)(269,395)(270,396)(271,399)(272,400)
(273,386)(274,385)(275,389)(276,390)(277,387)(278,388)(279,391)(280,392)
(281,402)(282,401)(283,405)(284,406)(285,403)(286,404)(287,407)(288,408);;
s2 := (  1,553)(  2,554)(  3,559)(  4,560)(  5,558)(  6,557)(  7,555)(  8,556)
(  9,569)( 10,570)( 11,575)( 12,576)( 13,574)( 14,573)( 15,571)( 16,572)
( 17,561)( 18,562)( 19,567)( 20,568)( 21,566)( 22,565)( 23,563)( 24,564)
( 25,529)( 26,530)( 27,535)( 28,536)( 29,534)( 30,533)( 31,531)( 32,532)
( 33,545)( 34,546)( 35,551)( 36,552)( 37,550)( 38,549)( 39,547)( 40,548)
( 41,537)( 42,538)( 43,543)( 44,544)( 45,542)( 46,541)( 47,539)( 48,540)
( 49,505)( 50,506)( 51,511)( 52,512)( 53,510)( 54,509)( 55,507)( 56,508)
( 57,521)( 58,522)( 59,527)( 60,528)( 61,526)( 62,525)( 63,523)( 64,524)
( 65,513)( 66,514)( 67,519)( 68,520)( 69,518)( 70,517)( 71,515)( 72,516)
( 73,481)( 74,482)( 75,487)( 76,488)( 77,486)( 78,485)( 79,483)( 80,484)
( 81,497)( 82,498)( 83,503)( 84,504)( 85,502)( 86,501)( 87,499)( 88,500)
( 89,489)( 90,490)( 91,495)( 92,496)( 93,494)( 94,493)( 95,491)( 96,492)
( 97,457)( 98,458)( 99,463)(100,464)(101,462)(102,461)(103,459)(104,460)
(105,473)(106,474)(107,479)(108,480)(109,478)(110,477)(111,475)(112,476)
(113,465)(114,466)(115,471)(116,472)(117,470)(118,469)(119,467)(120,468)
(121,433)(122,434)(123,439)(124,440)(125,438)(126,437)(127,435)(128,436)
(129,449)(130,450)(131,455)(132,456)(133,454)(134,453)(135,451)(136,452)
(137,441)(138,442)(139,447)(140,448)(141,446)(142,445)(143,443)(144,444)
(145,410)(146,409)(147,416)(148,415)(149,413)(150,414)(151,412)(152,411)
(153,426)(154,425)(155,432)(156,431)(157,429)(158,430)(159,428)(160,427)
(161,418)(162,417)(163,424)(164,423)(165,421)(166,422)(167,420)(168,419)
(169,386)(170,385)(171,392)(172,391)(173,389)(174,390)(175,388)(176,387)
(177,402)(178,401)(179,408)(180,407)(181,405)(182,406)(183,404)(184,403)
(185,394)(186,393)(187,400)(188,399)(189,397)(190,398)(191,396)(192,395)
(193,362)(194,361)(195,368)(196,367)(197,365)(198,366)(199,364)(200,363)
(201,378)(202,377)(203,384)(204,383)(205,381)(206,382)(207,380)(208,379)
(209,370)(210,369)(211,376)(212,375)(213,373)(214,374)(215,372)(216,371)
(217,338)(218,337)(219,344)(220,343)(221,341)(222,342)(223,340)(224,339)
(225,354)(226,353)(227,360)(228,359)(229,357)(230,358)(231,356)(232,355)
(233,346)(234,345)(235,352)(236,351)(237,349)(238,350)(239,348)(240,347)
(241,314)(242,313)(243,320)(244,319)(245,317)(246,318)(247,316)(248,315)
(249,330)(250,329)(251,336)(252,335)(253,333)(254,334)(255,332)(256,331)
(257,322)(258,321)(259,328)(260,327)(261,325)(262,326)(263,324)(264,323)
(265,290)(266,289)(267,296)(268,295)(269,293)(270,294)(271,292)(272,291)
(273,306)(274,305)(275,312)(276,311)(277,309)(278,310)(279,308)(280,307)
(281,298)(282,297)(283,304)(284,303)(285,301)(286,302)(287,300)(288,299);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(576)!(  1,293)(  2,294)(  3,296)(  4,295)(  5,290)(  6,289)(  7,291)
(  8,292)(  9,309)( 10,310)( 11,312)( 12,311)( 13,306)( 14,305)( 15,307)
( 16,308)( 17,301)( 18,302)( 19,304)( 20,303)( 21,298)( 22,297)( 23,299)
( 24,300)( 25,317)( 26,318)( 27,320)( 28,319)( 29,314)( 30,313)( 31,315)
( 32,316)( 33,333)( 34,334)( 35,336)( 36,335)( 37,330)( 38,329)( 39,331)
( 40,332)( 41,325)( 42,326)( 43,328)( 44,327)( 45,322)( 46,321)( 47,323)
( 48,324)( 49,341)( 50,342)( 51,344)( 52,343)( 53,338)( 54,337)( 55,339)
( 56,340)( 57,357)( 58,358)( 59,360)( 60,359)( 61,354)( 62,353)( 63,355)
( 64,356)( 65,349)( 66,350)( 67,352)( 68,351)( 69,346)( 70,345)( 71,347)
( 72,348)( 73,365)( 74,366)( 75,368)( 76,367)( 77,362)( 78,361)( 79,363)
( 80,364)( 81,381)( 82,382)( 83,384)( 84,383)( 85,378)( 86,377)( 87,379)
( 88,380)( 89,373)( 90,374)( 91,376)( 92,375)( 93,370)( 94,369)( 95,371)
( 96,372)( 97,389)( 98,390)( 99,392)(100,391)(101,386)(102,385)(103,387)
(104,388)(105,405)(106,406)(107,408)(108,407)(109,402)(110,401)(111,403)
(112,404)(113,397)(114,398)(115,400)(116,399)(117,394)(118,393)(119,395)
(120,396)(121,413)(122,414)(123,416)(124,415)(125,410)(126,409)(127,411)
(128,412)(129,429)(130,430)(131,432)(132,431)(133,426)(134,425)(135,427)
(136,428)(137,421)(138,422)(139,424)(140,423)(141,418)(142,417)(143,419)
(144,420)(145,438)(146,437)(147,439)(148,440)(149,433)(150,434)(151,436)
(152,435)(153,454)(154,453)(155,455)(156,456)(157,449)(158,450)(159,452)
(160,451)(161,446)(162,445)(163,447)(164,448)(165,441)(166,442)(167,444)
(168,443)(169,462)(170,461)(171,463)(172,464)(173,457)(174,458)(175,460)
(176,459)(177,478)(178,477)(179,479)(180,480)(181,473)(182,474)(183,476)
(184,475)(185,470)(186,469)(187,471)(188,472)(189,465)(190,466)(191,468)
(192,467)(193,486)(194,485)(195,487)(196,488)(197,481)(198,482)(199,484)
(200,483)(201,502)(202,501)(203,503)(204,504)(205,497)(206,498)(207,500)
(208,499)(209,494)(210,493)(211,495)(212,496)(213,489)(214,490)(215,492)
(216,491)(217,510)(218,509)(219,511)(220,512)(221,505)(222,506)(223,508)
(224,507)(225,526)(226,525)(227,527)(228,528)(229,521)(230,522)(231,524)
(232,523)(233,518)(234,517)(235,519)(236,520)(237,513)(238,514)(239,516)
(240,515)(241,534)(242,533)(243,535)(244,536)(245,529)(246,530)(247,532)
(248,531)(249,550)(250,549)(251,551)(252,552)(253,545)(254,546)(255,548)
(256,547)(257,542)(258,541)(259,543)(260,544)(261,537)(262,538)(263,540)
(264,539)(265,558)(266,557)(267,559)(268,560)(269,553)(270,554)(271,556)
(272,555)(273,574)(274,573)(275,575)(276,576)(277,569)(278,570)(279,572)
(280,571)(281,566)(282,565)(283,567)(284,568)(285,561)(286,562)(287,564)
(288,563);
s1 := Sym(576)!(  1,441)(  2,442)(  3,446)(  4,445)(  5,444)(  6,443)(  7,448)
(  8,447)(  9,433)( 10,434)( 11,438)( 12,437)( 13,436)( 14,435)( 15,440)
( 16,439)( 17,449)( 18,450)( 19,454)( 20,453)( 21,452)( 22,451)( 23,456)
( 24,455)( 25,489)( 26,490)( 27,494)( 28,493)( 29,492)( 30,491)( 31,496)
( 32,495)( 33,481)( 34,482)( 35,486)( 36,485)( 37,484)( 38,483)( 39,488)
( 40,487)( 41,497)( 42,498)( 43,502)( 44,501)( 45,500)( 46,499)( 47,504)
( 48,503)( 49,465)( 50,466)( 51,470)( 52,469)( 53,468)( 54,467)( 55,472)
( 56,471)( 57,457)( 58,458)( 59,462)( 60,461)( 61,460)( 62,459)( 63,464)
( 64,463)( 65,473)( 66,474)( 67,478)( 68,477)( 69,476)( 70,475)( 71,480)
( 72,479)( 73,513)( 74,514)( 75,518)( 76,517)( 77,516)( 78,515)( 79,520)
( 80,519)( 81,505)( 82,506)( 83,510)( 84,509)( 85,508)( 86,507)( 87,512)
( 88,511)( 89,521)( 90,522)( 91,526)( 92,525)( 93,524)( 94,523)( 95,528)
( 96,527)( 97,561)( 98,562)( 99,566)(100,565)(101,564)(102,563)(103,568)
(104,567)(105,553)(106,554)(107,558)(108,557)(109,556)(110,555)(111,560)
(112,559)(113,569)(114,570)(115,574)(116,573)(117,572)(118,571)(119,576)
(120,575)(121,537)(122,538)(123,542)(124,541)(125,540)(126,539)(127,544)
(128,543)(129,529)(130,530)(131,534)(132,533)(133,532)(134,531)(135,536)
(136,535)(137,545)(138,546)(139,550)(140,549)(141,548)(142,547)(143,552)
(144,551)(145,298)(146,297)(147,301)(148,302)(149,299)(150,300)(151,303)
(152,304)(153,290)(154,289)(155,293)(156,294)(157,291)(158,292)(159,295)
(160,296)(161,306)(162,305)(163,309)(164,310)(165,307)(166,308)(167,311)
(168,312)(169,346)(170,345)(171,349)(172,350)(173,347)(174,348)(175,351)
(176,352)(177,338)(178,337)(179,341)(180,342)(181,339)(182,340)(183,343)
(184,344)(185,354)(186,353)(187,357)(188,358)(189,355)(190,356)(191,359)
(192,360)(193,322)(194,321)(195,325)(196,326)(197,323)(198,324)(199,327)
(200,328)(201,314)(202,313)(203,317)(204,318)(205,315)(206,316)(207,319)
(208,320)(209,330)(210,329)(211,333)(212,334)(213,331)(214,332)(215,335)
(216,336)(217,370)(218,369)(219,373)(220,374)(221,371)(222,372)(223,375)
(224,376)(225,362)(226,361)(227,365)(228,366)(229,363)(230,364)(231,367)
(232,368)(233,378)(234,377)(235,381)(236,382)(237,379)(238,380)(239,383)
(240,384)(241,418)(242,417)(243,421)(244,422)(245,419)(246,420)(247,423)
(248,424)(249,410)(250,409)(251,413)(252,414)(253,411)(254,412)(255,415)
(256,416)(257,426)(258,425)(259,429)(260,430)(261,427)(262,428)(263,431)
(264,432)(265,394)(266,393)(267,397)(268,398)(269,395)(270,396)(271,399)
(272,400)(273,386)(274,385)(275,389)(276,390)(277,387)(278,388)(279,391)
(280,392)(281,402)(282,401)(283,405)(284,406)(285,403)(286,404)(287,407)
(288,408);
s2 := Sym(576)!(  1,553)(  2,554)(  3,559)(  4,560)(  5,558)(  6,557)(  7,555)
(  8,556)(  9,569)( 10,570)( 11,575)( 12,576)( 13,574)( 14,573)( 15,571)
( 16,572)( 17,561)( 18,562)( 19,567)( 20,568)( 21,566)( 22,565)( 23,563)
( 24,564)( 25,529)( 26,530)( 27,535)( 28,536)( 29,534)( 30,533)( 31,531)
( 32,532)( 33,545)( 34,546)( 35,551)( 36,552)( 37,550)( 38,549)( 39,547)
( 40,548)( 41,537)( 42,538)( 43,543)( 44,544)( 45,542)( 46,541)( 47,539)
( 48,540)( 49,505)( 50,506)( 51,511)( 52,512)( 53,510)( 54,509)( 55,507)
( 56,508)( 57,521)( 58,522)( 59,527)( 60,528)( 61,526)( 62,525)( 63,523)
( 64,524)( 65,513)( 66,514)( 67,519)( 68,520)( 69,518)( 70,517)( 71,515)
( 72,516)( 73,481)( 74,482)( 75,487)( 76,488)( 77,486)( 78,485)( 79,483)
( 80,484)( 81,497)( 82,498)( 83,503)( 84,504)( 85,502)( 86,501)( 87,499)
( 88,500)( 89,489)( 90,490)( 91,495)( 92,496)( 93,494)( 94,493)( 95,491)
( 96,492)( 97,457)( 98,458)( 99,463)(100,464)(101,462)(102,461)(103,459)
(104,460)(105,473)(106,474)(107,479)(108,480)(109,478)(110,477)(111,475)
(112,476)(113,465)(114,466)(115,471)(116,472)(117,470)(118,469)(119,467)
(120,468)(121,433)(122,434)(123,439)(124,440)(125,438)(126,437)(127,435)
(128,436)(129,449)(130,450)(131,455)(132,456)(133,454)(134,453)(135,451)
(136,452)(137,441)(138,442)(139,447)(140,448)(141,446)(142,445)(143,443)
(144,444)(145,410)(146,409)(147,416)(148,415)(149,413)(150,414)(151,412)
(152,411)(153,426)(154,425)(155,432)(156,431)(157,429)(158,430)(159,428)
(160,427)(161,418)(162,417)(163,424)(164,423)(165,421)(166,422)(167,420)
(168,419)(169,386)(170,385)(171,392)(172,391)(173,389)(174,390)(175,388)
(176,387)(177,402)(178,401)(179,408)(180,407)(181,405)(182,406)(183,404)
(184,403)(185,394)(186,393)(187,400)(188,399)(189,397)(190,398)(191,396)
(192,395)(193,362)(194,361)(195,368)(196,367)(197,365)(198,366)(199,364)
(200,363)(201,378)(202,377)(203,384)(204,383)(205,381)(206,382)(207,380)
(208,379)(209,370)(210,369)(211,376)(212,375)(213,373)(214,374)(215,372)
(216,371)(217,338)(218,337)(219,344)(220,343)(221,341)(222,342)(223,340)
(224,339)(225,354)(226,353)(227,360)(228,359)(229,357)(230,358)(231,356)
(232,355)(233,346)(234,345)(235,352)(236,351)(237,349)(238,350)(239,348)
(240,347)(241,314)(242,313)(243,320)(244,319)(245,317)(246,318)(247,316)
(248,315)(249,330)(250,329)(251,336)(252,335)(253,333)(254,334)(255,332)
(256,331)(257,322)(258,321)(259,328)(260,327)(261,325)(262,326)(263,324)
(264,323)(265,290)(266,289)(267,296)(268,295)(269,293)(270,294)(271,292)
(272,291)(273,306)(274,305)(275,312)(276,311)(277,309)(278,310)(279,308)
(280,307)(281,298)(282,297)(283,304)(284,303)(285,301)(286,302)(287,300)
(288,299);
poly := sub<Sym(576)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope