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Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*1152c
if this polytope has a name.
Group : SmallGroup(1152,157570)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 24, 144, 48
Order of s0s1s2s3 : 24
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 : {2,3,12}*576, {2,6,6}*576b
   3-fold quotients : {2,6,12}*384b
   4-fold quotients : {2,3,6}*288
   6-fold quotients : {2,3,12}*192, {2,6,6}*192
   8-fold quotients : {2,6,6}*144c
   12-fold quotients : {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {2,3,3}*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 := (  3,153)(  4,154)(  5,149)(  6,150)(  7,152)(  8,151)(  9,147)( 10,148)
( 11,161)( 12,162)( 13,157)( 14,158)( 15,160)( 16,159)( 17,155)( 18,156)
( 19,169)( 20,170)( 21,165)( 22,166)( 23,168)( 24,167)( 25,163)( 26,164)
( 27,201)( 28,202)( 29,197)( 30,198)( 31,200)( 32,199)( 33,195)( 34,196)
( 35,209)( 36,210)( 37,205)( 38,206)( 39,208)( 40,207)( 41,203)( 42,204)
( 43,217)( 44,218)( 45,213)( 46,214)( 47,216)( 48,215)( 49,211)( 50,212)
( 51,177)( 52,178)( 53,173)( 54,174)( 55,176)( 56,175)( 57,171)( 58,172)
( 59,185)( 60,186)( 61,181)( 62,182)( 63,184)( 64,183)( 65,179)( 66,180)
( 67,193)( 68,194)( 69,189)( 70,190)( 71,192)( 72,191)( 73,187)( 74,188)
( 75,225)( 76,226)( 77,221)( 78,222)( 79,224)( 80,223)( 81,219)( 82,220)
( 83,233)( 84,234)( 85,229)( 86,230)( 87,232)( 88,231)( 89,227)( 90,228)
( 91,241)( 92,242)( 93,237)( 94,238)( 95,240)( 96,239)( 97,235)( 98,236)
( 99,273)(100,274)(101,269)(102,270)(103,272)(104,271)(105,267)(106,268)
(107,281)(108,282)(109,277)(110,278)(111,280)(112,279)(113,275)(114,276)
(115,289)(116,290)(117,285)(118,286)(119,288)(120,287)(121,283)(122,284)
(123,249)(124,250)(125,245)(126,246)(127,248)(128,247)(129,243)(130,244)
(131,257)(132,258)(133,253)(134,254)(135,256)(136,255)(137,251)(138,252)
(139,265)(140,266)(141,261)(142,262)(143,264)(144,263)(145,259)(146,260)
(291,441)(292,442)(293,437)(294,438)(295,440)(296,439)(297,435)(298,436)
(299,449)(300,450)(301,445)(302,446)(303,448)(304,447)(305,443)(306,444)
(307,457)(308,458)(309,453)(310,454)(311,456)(312,455)(313,451)(314,452)
(315,489)(316,490)(317,485)(318,486)(319,488)(320,487)(321,483)(322,484)
(323,497)(324,498)(325,493)(326,494)(327,496)(328,495)(329,491)(330,492)
(331,505)(332,506)(333,501)(334,502)(335,504)(336,503)(337,499)(338,500)
(339,465)(340,466)(341,461)(342,462)(343,464)(344,463)(345,459)(346,460)
(347,473)(348,474)(349,469)(350,470)(351,472)(352,471)(353,467)(354,468)
(355,481)(356,482)(357,477)(358,478)(359,480)(360,479)(361,475)(362,476)
(363,513)(364,514)(365,509)(366,510)(367,512)(368,511)(369,507)(370,508)
(371,521)(372,522)(373,517)(374,518)(375,520)(376,519)(377,515)(378,516)
(379,529)(380,530)(381,525)(382,526)(383,528)(384,527)(385,523)(386,524)
(387,561)(388,562)(389,557)(390,558)(391,560)(392,559)(393,555)(394,556)
(395,569)(396,570)(397,565)(398,566)(399,568)(400,567)(401,563)(402,564)
(403,577)(404,578)(405,573)(406,574)(407,576)(408,575)(409,571)(410,572)
(411,537)(412,538)(413,533)(414,534)(415,536)(416,535)(417,531)(418,532)
(419,545)(420,546)(421,541)(422,542)(423,544)(424,543)(425,539)(426,540)
(427,553)(428,554)(429,549)(430,550)(431,552)(432,551)(433,547)(434,548);;
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*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*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)!(  3,153)(  4,154)(  5,149)(  6,150)(  7,152)(  8,151)(  9,147)
( 10,148)( 11,161)( 12,162)( 13,157)( 14,158)( 15,160)( 16,159)( 17,155)
( 18,156)( 19,169)( 20,170)( 21,165)( 22,166)( 23,168)( 24,167)( 25,163)
( 26,164)( 27,201)( 28,202)( 29,197)( 30,198)( 31,200)( 32,199)( 33,195)
( 34,196)( 35,209)( 36,210)( 37,205)( 38,206)( 39,208)( 40,207)( 41,203)
( 42,204)( 43,217)( 44,218)( 45,213)( 46,214)( 47,216)( 48,215)( 49,211)
( 50,212)( 51,177)( 52,178)( 53,173)( 54,174)( 55,176)( 56,175)( 57,171)
( 58,172)( 59,185)( 60,186)( 61,181)( 62,182)( 63,184)( 64,183)( 65,179)
( 66,180)( 67,193)( 68,194)( 69,189)( 70,190)( 71,192)( 72,191)( 73,187)
( 74,188)( 75,225)( 76,226)( 77,221)( 78,222)( 79,224)( 80,223)( 81,219)
( 82,220)( 83,233)( 84,234)( 85,229)( 86,230)( 87,232)( 88,231)( 89,227)
( 90,228)( 91,241)( 92,242)( 93,237)( 94,238)( 95,240)( 96,239)( 97,235)
( 98,236)( 99,273)(100,274)(101,269)(102,270)(103,272)(104,271)(105,267)
(106,268)(107,281)(108,282)(109,277)(110,278)(111,280)(112,279)(113,275)
(114,276)(115,289)(116,290)(117,285)(118,286)(119,288)(120,287)(121,283)
(122,284)(123,249)(124,250)(125,245)(126,246)(127,248)(128,247)(129,243)
(130,244)(131,257)(132,258)(133,253)(134,254)(135,256)(136,255)(137,251)
(138,252)(139,265)(140,266)(141,261)(142,262)(143,264)(144,263)(145,259)
(146,260)(291,441)(292,442)(293,437)(294,438)(295,440)(296,439)(297,435)
(298,436)(299,449)(300,450)(301,445)(302,446)(303,448)(304,447)(305,443)
(306,444)(307,457)(308,458)(309,453)(310,454)(311,456)(312,455)(313,451)
(314,452)(315,489)(316,490)(317,485)(318,486)(319,488)(320,487)(321,483)
(322,484)(323,497)(324,498)(325,493)(326,494)(327,496)(328,495)(329,491)
(330,492)(331,505)(332,506)(333,501)(334,502)(335,504)(336,503)(337,499)
(338,500)(339,465)(340,466)(341,461)(342,462)(343,464)(344,463)(345,459)
(346,460)(347,473)(348,474)(349,469)(350,470)(351,472)(352,471)(353,467)
(354,468)(355,481)(356,482)(357,477)(358,478)(359,480)(360,479)(361,475)
(362,476)(363,513)(364,514)(365,509)(366,510)(367,512)(368,511)(369,507)
(370,508)(371,521)(372,522)(373,517)(374,518)(375,520)(376,519)(377,515)
(378,516)(379,529)(380,530)(381,525)(382,526)(383,528)(384,527)(385,523)
(386,524)(387,561)(388,562)(389,557)(390,558)(391,560)(392,559)(393,555)
(394,556)(395,569)(396,570)(397,565)(398,566)(399,568)(400,567)(401,563)
(402,564)(403,577)(404,578)(405,573)(406,574)(407,576)(408,575)(409,571)
(410,572)(411,537)(412,538)(413,533)(414,534)(415,536)(416,535)(417,531)
(418,532)(419,545)(420,546)(421,541)(422,542)(423,544)(424,543)(425,539)
(426,540)(427,553)(428,554)(429,549)(430,550)(431,552)(432,551)(433,547)
(434,548);
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*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 >; 
 

to this polytope