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