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