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Polytope of Type {20,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,6}*1440c
if this polytope has a name.
Group : SmallGroup(1440,5324)
Rank : 4
Schlafli Type : {20,6,6}
Number of vertices, edges, etc : 20, 60, 18, 6
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {20,6,3}*720, {10,6,6}*720b
   3-fold quotients : {20,2,6}*480
   4-fold quotients : {10,6,3}*360
   5-fold quotients : {4,6,6}*288c
   6-fold quotients : {20,2,3}*240, {10,2,6}*240
   9-fold quotients : {20,2,2}*160
   10-fold quotients : {4,6,3}*144, {2,6,6}*144b
   12-fold quotients : {5,2,6}*120, {10,2,3}*120
   15-fold quotients : {4,2,6}*96
   18-fold quotients : {10,2,2}*80
   20-fold quotients : {2,6,3}*72
   24-fold quotients : {5,2,3}*60
   30-fold quotients : {4,2,3}*48, {2,2,6}*48
   36-fold quotients : {5,2,2}*40
   45-fold quotients : {4,2,2}*32
   60-fold quotients : {2,2,3}*24
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)
(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)
(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)
(142,145)(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)
(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)
(181,226)(182,230)(183,229)(184,228)(185,227)(186,231)(187,235)(188,234)
(189,233)(190,232)(191,236)(192,240)(193,239)(194,238)(195,237)(196,241)
(197,245)(198,244)(199,243)(200,242)(201,246)(202,250)(203,249)(204,248)
(205,247)(206,251)(207,255)(208,254)(209,253)(210,252)(211,256)(212,260)
(213,259)(214,258)(215,257)(216,261)(217,265)(218,264)(219,263)(220,262)
(221,266)(222,270)(223,269)(224,268)(225,267)(271,316)(272,320)(273,319)
(274,318)(275,317)(276,321)(277,325)(278,324)(279,323)(280,322)(281,326)
(282,330)(283,329)(284,328)(285,327)(286,331)(287,335)(288,334)(289,333)
(290,332)(291,336)(292,340)(293,339)(294,338)(295,337)(296,341)(297,345)
(298,344)(299,343)(300,342)(301,346)(302,350)(303,349)(304,348)(305,347)
(306,351)(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)(313,359)
(314,358)(315,357)(361,406)(362,410)(363,409)(364,408)(365,407)(366,411)
(367,415)(368,414)(369,413)(370,412)(371,416)(372,420)(373,419)(374,418)
(375,417)(376,421)(377,425)(378,424)(379,423)(380,422)(381,426)(382,430)
(383,429)(384,428)(385,427)(386,431)(387,435)(388,434)(389,433)(390,432)
(391,436)(392,440)(393,439)(394,438)(395,437)(396,441)(397,445)(398,444)
(399,443)(400,442)(401,446)(402,450)(403,449)(404,448)(405,447)(451,496)
(452,500)(453,499)(454,498)(455,497)(456,501)(457,505)(458,504)(459,503)
(460,502)(461,506)(462,510)(463,509)(464,508)(465,507)(466,511)(467,515)
(468,514)(469,513)(470,512)(471,516)(472,520)(473,519)(474,518)(475,517)
(476,521)(477,525)(478,524)(479,523)(480,522)(481,526)(482,530)(483,529)
(484,528)(485,527)(486,531)(487,535)(488,534)(489,533)(490,532)(491,536)
(492,540)(493,539)(494,538)(495,537)(542,545)(543,544)(547,550)(548,549)
(552,555)(553,554)(557,560)(558,559)(562,565)(563,564)(567,570)(568,569)
(572,575)(573,574)(577,580)(578,579)(582,585)(583,584)(587,590)(588,589)
(592,595)(593,594)(597,600)(598,599)(602,605)(603,604)(607,610)(608,609)
(612,615)(613,614)(617,620)(618,619)(622,625)(623,624)(627,630)(628,629)
(632,635)(633,634)(637,640)(638,639)(642,645)(643,644)(647,650)(648,649)
(652,655)(653,654)(657,660)(658,659)(662,665)(663,664)(667,670)(668,669)
(672,675)(673,674)(677,680)(678,679)(682,685)(683,684)(687,690)(688,689)
(692,695)(693,694)(697,700)(698,699)(702,705)(703,704)(707,710)(708,709)
(712,715)(713,714)(717,720)(718,719);;
s1 := (  1,362)(  2,361)(  3,365)(  4,364)(  5,363)(  6,372)(  7,371)(  8,375)
(  9,374)( 10,373)( 11,367)( 12,366)( 13,370)( 14,369)( 15,368)( 16,377)
( 17,376)( 18,380)( 19,379)( 20,378)( 21,387)( 22,386)( 23,390)( 24,389)
( 25,388)( 26,382)( 27,381)( 28,385)( 29,384)( 30,383)( 31,392)( 32,391)
( 33,395)( 34,394)( 35,393)( 36,402)( 37,401)( 38,405)( 39,404)( 40,403)
( 41,397)( 42,396)( 43,400)( 44,399)( 45,398)( 46,407)( 47,406)( 48,410)
( 49,409)( 50,408)( 51,417)( 52,416)( 53,420)( 54,419)( 55,418)( 56,412)
( 57,411)( 58,415)( 59,414)( 60,413)( 61,422)( 62,421)( 63,425)( 64,424)
( 65,423)( 66,432)( 67,431)( 68,435)( 69,434)( 70,433)( 71,427)( 72,426)
( 73,430)( 74,429)( 75,428)( 76,437)( 77,436)( 78,440)( 79,439)( 80,438)
( 81,447)( 82,446)( 83,450)( 84,449)( 85,448)( 86,442)( 87,441)( 88,445)
( 89,444)( 90,443)( 91,452)( 92,451)( 93,455)( 94,454)( 95,453)( 96,462)
( 97,461)( 98,465)( 99,464)(100,463)(101,457)(102,456)(103,460)(104,459)
(105,458)(106,467)(107,466)(108,470)(109,469)(110,468)(111,477)(112,476)
(113,480)(114,479)(115,478)(116,472)(117,471)(118,475)(119,474)(120,473)
(121,482)(122,481)(123,485)(124,484)(125,483)(126,492)(127,491)(128,495)
(129,494)(130,493)(131,487)(132,486)(133,490)(134,489)(135,488)(136,497)
(137,496)(138,500)(139,499)(140,498)(141,507)(142,506)(143,510)(144,509)
(145,508)(146,502)(147,501)(148,505)(149,504)(150,503)(151,512)(152,511)
(153,515)(154,514)(155,513)(156,522)(157,521)(158,525)(159,524)(160,523)
(161,517)(162,516)(163,520)(164,519)(165,518)(166,527)(167,526)(168,530)
(169,529)(170,528)(171,537)(172,536)(173,540)(174,539)(175,538)(176,532)
(177,531)(178,535)(179,534)(180,533)(181,587)(182,586)(183,590)(184,589)
(185,588)(186,597)(187,596)(188,600)(189,599)(190,598)(191,592)(192,591)
(193,595)(194,594)(195,593)(196,602)(197,601)(198,605)(199,604)(200,603)
(201,612)(202,611)(203,615)(204,614)(205,613)(206,607)(207,606)(208,610)
(209,609)(210,608)(211,617)(212,616)(213,620)(214,619)(215,618)(216,627)
(217,626)(218,630)(219,629)(220,628)(221,622)(222,621)(223,625)(224,624)
(225,623)(226,542)(227,541)(228,545)(229,544)(230,543)(231,552)(232,551)
(233,555)(234,554)(235,553)(236,547)(237,546)(238,550)(239,549)(240,548)
(241,557)(242,556)(243,560)(244,559)(245,558)(246,567)(247,566)(248,570)
(249,569)(250,568)(251,562)(252,561)(253,565)(254,564)(255,563)(256,572)
(257,571)(258,575)(259,574)(260,573)(261,582)(262,581)(263,585)(264,584)
(265,583)(266,577)(267,576)(268,580)(269,579)(270,578)(271,677)(272,676)
(273,680)(274,679)(275,678)(276,687)(277,686)(278,690)(279,689)(280,688)
(281,682)(282,681)(283,685)(284,684)(285,683)(286,692)(287,691)(288,695)
(289,694)(290,693)(291,702)(292,701)(293,705)(294,704)(295,703)(296,697)
(297,696)(298,700)(299,699)(300,698)(301,707)(302,706)(303,710)(304,709)
(305,708)(306,717)(307,716)(308,720)(309,719)(310,718)(311,712)(312,711)
(313,715)(314,714)(315,713)(316,632)(317,631)(318,635)(319,634)(320,633)
(321,642)(322,641)(323,645)(324,644)(325,643)(326,637)(327,636)(328,640)
(329,639)(330,638)(331,647)(332,646)(333,650)(334,649)(335,648)(336,657)
(337,656)(338,660)(339,659)(340,658)(341,652)(342,651)(343,655)(344,654)
(345,653)(346,662)(347,661)(348,665)(349,664)(350,663)(351,672)(352,671)
(353,675)(354,674)(355,673)(356,667)(357,666)(358,670)(359,669)(360,668);;
s2 := (  1,546)(  2,547)(  3,548)(  4,549)(  5,550)(  6,541)(  7,542)(  8,543)
(  9,544)( 10,545)( 11,551)( 12,552)( 13,553)( 14,554)( 15,555)( 16,576)
( 17,577)( 18,578)( 19,579)( 20,580)( 21,571)( 22,572)( 23,573)( 24,574)
( 25,575)( 26,581)( 27,582)( 28,583)( 29,584)( 30,585)( 31,561)( 32,562)
( 33,563)( 34,564)( 35,565)( 36,556)( 37,557)( 38,558)( 39,559)( 40,560)
( 41,566)( 42,567)( 43,568)( 44,569)( 45,570)( 46,591)( 47,592)( 48,593)
( 49,594)( 50,595)( 51,586)( 52,587)( 53,588)( 54,589)( 55,590)( 56,596)
( 57,597)( 58,598)( 59,599)( 60,600)( 61,621)( 62,622)( 63,623)( 64,624)
( 65,625)( 66,616)( 67,617)( 68,618)( 69,619)( 70,620)( 71,626)( 72,627)
( 73,628)( 74,629)( 75,630)( 76,606)( 77,607)( 78,608)( 79,609)( 80,610)
( 81,601)( 82,602)( 83,603)( 84,604)( 85,605)( 86,611)( 87,612)( 88,613)
( 89,614)( 90,615)( 91,636)( 92,637)( 93,638)( 94,639)( 95,640)( 96,631)
( 97,632)( 98,633)( 99,634)(100,635)(101,641)(102,642)(103,643)(104,644)
(105,645)(106,666)(107,667)(108,668)(109,669)(110,670)(111,661)(112,662)
(113,663)(114,664)(115,665)(116,671)(117,672)(118,673)(119,674)(120,675)
(121,651)(122,652)(123,653)(124,654)(125,655)(126,646)(127,647)(128,648)
(129,649)(130,650)(131,656)(132,657)(133,658)(134,659)(135,660)(136,681)
(137,682)(138,683)(139,684)(140,685)(141,676)(142,677)(143,678)(144,679)
(145,680)(146,686)(147,687)(148,688)(149,689)(150,690)(151,711)(152,712)
(153,713)(154,714)(155,715)(156,706)(157,707)(158,708)(159,709)(160,710)
(161,716)(162,717)(163,718)(164,719)(165,720)(166,696)(167,697)(168,698)
(169,699)(170,700)(171,691)(172,692)(173,693)(174,694)(175,695)(176,701)
(177,702)(178,703)(179,704)(180,705)(181,411)(182,412)(183,413)(184,414)
(185,415)(186,406)(187,407)(188,408)(189,409)(190,410)(191,416)(192,417)
(193,418)(194,419)(195,420)(196,441)(197,442)(198,443)(199,444)(200,445)
(201,436)(202,437)(203,438)(204,439)(205,440)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,426)(212,427)(213,428)(214,429)(215,430)(216,421)
(217,422)(218,423)(219,424)(220,425)(221,431)(222,432)(223,433)(224,434)
(225,435)(226,366)(227,367)(228,368)(229,369)(230,370)(231,361)(232,362)
(233,363)(234,364)(235,365)(236,371)(237,372)(238,373)(239,374)(240,375)
(241,396)(242,397)(243,398)(244,399)(245,400)(246,391)(247,392)(248,393)
(249,394)(250,395)(251,401)(252,402)(253,403)(254,404)(255,405)(256,381)
(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)(264,379)
(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,501)(272,502)
(273,503)(274,504)(275,505)(276,496)(277,497)(278,498)(279,499)(280,500)
(281,506)(282,507)(283,508)(284,509)(285,510)(286,531)(287,532)(288,533)
(289,534)(290,535)(291,526)(292,527)(293,528)(294,529)(295,530)(296,536)
(297,537)(298,538)(299,539)(300,540)(301,516)(302,517)(303,518)(304,519)
(305,520)(306,511)(307,512)(308,513)(309,514)(310,515)(311,521)(312,522)
(313,523)(314,524)(315,525)(316,456)(317,457)(318,458)(319,459)(320,460)
(321,451)(322,452)(323,453)(324,454)(325,455)(326,461)(327,462)(328,463)
(329,464)(330,465)(331,486)(332,487)(333,488)(334,489)(335,490)(336,481)
(337,482)(338,483)(339,484)(340,485)(341,491)(342,492)(343,493)(344,494)
(345,495)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)(352,467)
(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)(360,480);;
s3 := (  1,646)(  2,647)(  3,648)(  4,649)(  5,650)(  6,656)(  7,657)(  8,658)
(  9,659)( 10,660)( 11,651)( 12,652)( 13,653)( 14,654)( 15,655)( 16,631)
( 17,632)( 18,633)( 19,634)( 20,635)( 21,641)( 22,642)( 23,643)( 24,644)
( 25,645)( 26,636)( 27,637)( 28,638)( 29,639)( 30,640)( 31,661)( 32,662)
( 33,663)( 34,664)( 35,665)( 36,671)( 37,672)( 38,673)( 39,674)( 40,675)
( 41,666)( 42,667)( 43,668)( 44,669)( 45,670)( 46,691)( 47,692)( 48,693)
( 49,694)( 50,695)( 51,701)( 52,702)( 53,703)( 54,704)( 55,705)( 56,696)
( 57,697)( 58,698)( 59,699)( 60,700)( 61,676)( 62,677)( 63,678)( 64,679)
( 65,680)( 66,686)( 67,687)( 68,688)( 69,689)( 70,690)( 71,681)( 72,682)
( 73,683)( 74,684)( 75,685)( 76,706)( 77,707)( 78,708)( 79,709)( 80,710)
( 81,716)( 82,717)( 83,718)( 84,719)( 85,720)( 86,711)( 87,712)( 88,713)
( 89,714)( 90,715)( 91,556)( 92,557)( 93,558)( 94,559)( 95,560)( 96,566)
( 97,567)( 98,568)( 99,569)(100,570)(101,561)(102,562)(103,563)(104,564)
(105,565)(106,541)(107,542)(108,543)(109,544)(110,545)(111,551)(112,552)
(113,553)(114,554)(115,555)(116,546)(117,547)(118,548)(119,549)(120,550)
(121,571)(122,572)(123,573)(124,574)(125,575)(126,581)(127,582)(128,583)
(129,584)(130,585)(131,576)(132,577)(133,578)(134,579)(135,580)(136,601)
(137,602)(138,603)(139,604)(140,605)(141,611)(142,612)(143,613)(144,614)
(145,615)(146,606)(147,607)(148,608)(149,609)(150,610)(151,586)(152,587)
(153,588)(154,589)(155,590)(156,596)(157,597)(158,598)(159,599)(160,600)
(161,591)(162,592)(163,593)(164,594)(165,595)(166,616)(167,617)(168,618)
(169,619)(170,620)(171,626)(172,627)(173,628)(174,629)(175,630)(176,621)
(177,622)(178,623)(179,624)(180,625)(181,511)(182,512)(183,513)(184,514)
(185,515)(186,521)(187,522)(188,523)(189,524)(190,525)(191,516)(192,517)
(193,518)(194,519)(195,520)(196,496)(197,497)(198,498)(199,499)(200,500)
(201,506)(202,507)(203,508)(204,509)(205,510)(206,501)(207,502)(208,503)
(209,504)(210,505)(211,526)(212,527)(213,528)(214,529)(215,530)(216,536)
(217,537)(218,538)(219,539)(220,540)(221,531)(222,532)(223,533)(224,534)
(225,535)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)(232,477)
(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)(240,475)
(241,451)(242,452)(243,453)(244,454)(245,455)(246,461)(247,462)(248,463)
(249,464)(250,465)(251,456)(252,457)(253,458)(254,459)(255,460)(256,481)
(257,482)(258,483)(259,484)(260,485)(261,491)(262,492)(263,493)(264,494)
(265,495)(266,486)(267,487)(268,488)(269,489)(270,490)(271,421)(272,422)
(273,423)(274,424)(275,425)(276,431)(277,432)(278,433)(279,434)(280,435)
(281,426)(282,427)(283,428)(284,429)(285,430)(286,406)(287,407)(288,408)
(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)(296,411)
(297,412)(298,413)(299,414)(300,415)(301,436)(302,437)(303,438)(304,439)
(305,440)(306,446)(307,447)(308,448)(309,449)(310,450)(311,441)(312,442)
(313,443)(314,444)(315,445)(316,376)(317,377)(318,378)(319,379)(320,380)
(321,386)(322,387)(323,388)(324,389)(325,390)(326,381)(327,382)(328,383)
(329,384)(330,385)(331,361)(332,362)(333,363)(334,364)(335,365)(336,371)
(337,372)(338,373)(339,374)(340,375)(341,366)(342,367)(343,368)(344,369)
(345,370)(346,391)(347,392)(348,393)(349,394)(350,395)(351,401)(352,402)
(353,403)(354,404)(355,405)(356,396)(357,397)(358,398)(359,399)(360,400);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(720)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)
(118,119)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)
(138,139)(142,145)(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)
(158,159)(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)
(178,179)(181,226)(182,230)(183,229)(184,228)(185,227)(186,231)(187,235)
(188,234)(189,233)(190,232)(191,236)(192,240)(193,239)(194,238)(195,237)
(196,241)(197,245)(198,244)(199,243)(200,242)(201,246)(202,250)(203,249)
(204,248)(205,247)(206,251)(207,255)(208,254)(209,253)(210,252)(211,256)
(212,260)(213,259)(214,258)(215,257)(216,261)(217,265)(218,264)(219,263)
(220,262)(221,266)(222,270)(223,269)(224,268)(225,267)(271,316)(272,320)
(273,319)(274,318)(275,317)(276,321)(277,325)(278,324)(279,323)(280,322)
(281,326)(282,330)(283,329)(284,328)(285,327)(286,331)(287,335)(288,334)
(289,333)(290,332)(291,336)(292,340)(293,339)(294,338)(295,337)(296,341)
(297,345)(298,344)(299,343)(300,342)(301,346)(302,350)(303,349)(304,348)
(305,347)(306,351)(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)
(313,359)(314,358)(315,357)(361,406)(362,410)(363,409)(364,408)(365,407)
(366,411)(367,415)(368,414)(369,413)(370,412)(371,416)(372,420)(373,419)
(374,418)(375,417)(376,421)(377,425)(378,424)(379,423)(380,422)(381,426)
(382,430)(383,429)(384,428)(385,427)(386,431)(387,435)(388,434)(389,433)
(390,432)(391,436)(392,440)(393,439)(394,438)(395,437)(396,441)(397,445)
(398,444)(399,443)(400,442)(401,446)(402,450)(403,449)(404,448)(405,447)
(451,496)(452,500)(453,499)(454,498)(455,497)(456,501)(457,505)(458,504)
(459,503)(460,502)(461,506)(462,510)(463,509)(464,508)(465,507)(466,511)
(467,515)(468,514)(469,513)(470,512)(471,516)(472,520)(473,519)(474,518)
(475,517)(476,521)(477,525)(478,524)(479,523)(480,522)(481,526)(482,530)
(483,529)(484,528)(485,527)(486,531)(487,535)(488,534)(489,533)(490,532)
(491,536)(492,540)(493,539)(494,538)(495,537)(542,545)(543,544)(547,550)
(548,549)(552,555)(553,554)(557,560)(558,559)(562,565)(563,564)(567,570)
(568,569)(572,575)(573,574)(577,580)(578,579)(582,585)(583,584)(587,590)
(588,589)(592,595)(593,594)(597,600)(598,599)(602,605)(603,604)(607,610)
(608,609)(612,615)(613,614)(617,620)(618,619)(622,625)(623,624)(627,630)
(628,629)(632,635)(633,634)(637,640)(638,639)(642,645)(643,644)(647,650)
(648,649)(652,655)(653,654)(657,660)(658,659)(662,665)(663,664)(667,670)
(668,669)(672,675)(673,674)(677,680)(678,679)(682,685)(683,684)(687,690)
(688,689)(692,695)(693,694)(697,700)(698,699)(702,705)(703,704)(707,710)
(708,709)(712,715)(713,714)(717,720)(718,719);
s1 := Sym(720)!(  1,362)(  2,361)(  3,365)(  4,364)(  5,363)(  6,372)(  7,371)
(  8,375)(  9,374)( 10,373)( 11,367)( 12,366)( 13,370)( 14,369)( 15,368)
( 16,377)( 17,376)( 18,380)( 19,379)( 20,378)( 21,387)( 22,386)( 23,390)
( 24,389)( 25,388)( 26,382)( 27,381)( 28,385)( 29,384)( 30,383)( 31,392)
( 32,391)( 33,395)( 34,394)( 35,393)( 36,402)( 37,401)( 38,405)( 39,404)
( 40,403)( 41,397)( 42,396)( 43,400)( 44,399)( 45,398)( 46,407)( 47,406)
( 48,410)( 49,409)( 50,408)( 51,417)( 52,416)( 53,420)( 54,419)( 55,418)
( 56,412)( 57,411)( 58,415)( 59,414)( 60,413)( 61,422)( 62,421)( 63,425)
( 64,424)( 65,423)( 66,432)( 67,431)( 68,435)( 69,434)( 70,433)( 71,427)
( 72,426)( 73,430)( 74,429)( 75,428)( 76,437)( 77,436)( 78,440)( 79,439)
( 80,438)( 81,447)( 82,446)( 83,450)( 84,449)( 85,448)( 86,442)( 87,441)
( 88,445)( 89,444)( 90,443)( 91,452)( 92,451)( 93,455)( 94,454)( 95,453)
( 96,462)( 97,461)( 98,465)( 99,464)(100,463)(101,457)(102,456)(103,460)
(104,459)(105,458)(106,467)(107,466)(108,470)(109,469)(110,468)(111,477)
(112,476)(113,480)(114,479)(115,478)(116,472)(117,471)(118,475)(119,474)
(120,473)(121,482)(122,481)(123,485)(124,484)(125,483)(126,492)(127,491)
(128,495)(129,494)(130,493)(131,487)(132,486)(133,490)(134,489)(135,488)
(136,497)(137,496)(138,500)(139,499)(140,498)(141,507)(142,506)(143,510)
(144,509)(145,508)(146,502)(147,501)(148,505)(149,504)(150,503)(151,512)
(152,511)(153,515)(154,514)(155,513)(156,522)(157,521)(158,525)(159,524)
(160,523)(161,517)(162,516)(163,520)(164,519)(165,518)(166,527)(167,526)
(168,530)(169,529)(170,528)(171,537)(172,536)(173,540)(174,539)(175,538)
(176,532)(177,531)(178,535)(179,534)(180,533)(181,587)(182,586)(183,590)
(184,589)(185,588)(186,597)(187,596)(188,600)(189,599)(190,598)(191,592)
(192,591)(193,595)(194,594)(195,593)(196,602)(197,601)(198,605)(199,604)
(200,603)(201,612)(202,611)(203,615)(204,614)(205,613)(206,607)(207,606)
(208,610)(209,609)(210,608)(211,617)(212,616)(213,620)(214,619)(215,618)
(216,627)(217,626)(218,630)(219,629)(220,628)(221,622)(222,621)(223,625)
(224,624)(225,623)(226,542)(227,541)(228,545)(229,544)(230,543)(231,552)
(232,551)(233,555)(234,554)(235,553)(236,547)(237,546)(238,550)(239,549)
(240,548)(241,557)(242,556)(243,560)(244,559)(245,558)(246,567)(247,566)
(248,570)(249,569)(250,568)(251,562)(252,561)(253,565)(254,564)(255,563)
(256,572)(257,571)(258,575)(259,574)(260,573)(261,582)(262,581)(263,585)
(264,584)(265,583)(266,577)(267,576)(268,580)(269,579)(270,578)(271,677)
(272,676)(273,680)(274,679)(275,678)(276,687)(277,686)(278,690)(279,689)
(280,688)(281,682)(282,681)(283,685)(284,684)(285,683)(286,692)(287,691)
(288,695)(289,694)(290,693)(291,702)(292,701)(293,705)(294,704)(295,703)
(296,697)(297,696)(298,700)(299,699)(300,698)(301,707)(302,706)(303,710)
(304,709)(305,708)(306,717)(307,716)(308,720)(309,719)(310,718)(311,712)
(312,711)(313,715)(314,714)(315,713)(316,632)(317,631)(318,635)(319,634)
(320,633)(321,642)(322,641)(323,645)(324,644)(325,643)(326,637)(327,636)
(328,640)(329,639)(330,638)(331,647)(332,646)(333,650)(334,649)(335,648)
(336,657)(337,656)(338,660)(339,659)(340,658)(341,652)(342,651)(343,655)
(344,654)(345,653)(346,662)(347,661)(348,665)(349,664)(350,663)(351,672)
(352,671)(353,675)(354,674)(355,673)(356,667)(357,666)(358,670)(359,669)
(360,668);
s2 := Sym(720)!(  1,546)(  2,547)(  3,548)(  4,549)(  5,550)(  6,541)(  7,542)
(  8,543)(  9,544)( 10,545)( 11,551)( 12,552)( 13,553)( 14,554)( 15,555)
( 16,576)( 17,577)( 18,578)( 19,579)( 20,580)( 21,571)( 22,572)( 23,573)
( 24,574)( 25,575)( 26,581)( 27,582)( 28,583)( 29,584)( 30,585)( 31,561)
( 32,562)( 33,563)( 34,564)( 35,565)( 36,556)( 37,557)( 38,558)( 39,559)
( 40,560)( 41,566)( 42,567)( 43,568)( 44,569)( 45,570)( 46,591)( 47,592)
( 48,593)( 49,594)( 50,595)( 51,586)( 52,587)( 53,588)( 54,589)( 55,590)
( 56,596)( 57,597)( 58,598)( 59,599)( 60,600)( 61,621)( 62,622)( 63,623)
( 64,624)( 65,625)( 66,616)( 67,617)( 68,618)( 69,619)( 70,620)( 71,626)
( 72,627)( 73,628)( 74,629)( 75,630)( 76,606)( 77,607)( 78,608)( 79,609)
( 80,610)( 81,601)( 82,602)( 83,603)( 84,604)( 85,605)( 86,611)( 87,612)
( 88,613)( 89,614)( 90,615)( 91,636)( 92,637)( 93,638)( 94,639)( 95,640)
( 96,631)( 97,632)( 98,633)( 99,634)(100,635)(101,641)(102,642)(103,643)
(104,644)(105,645)(106,666)(107,667)(108,668)(109,669)(110,670)(111,661)
(112,662)(113,663)(114,664)(115,665)(116,671)(117,672)(118,673)(119,674)
(120,675)(121,651)(122,652)(123,653)(124,654)(125,655)(126,646)(127,647)
(128,648)(129,649)(130,650)(131,656)(132,657)(133,658)(134,659)(135,660)
(136,681)(137,682)(138,683)(139,684)(140,685)(141,676)(142,677)(143,678)
(144,679)(145,680)(146,686)(147,687)(148,688)(149,689)(150,690)(151,711)
(152,712)(153,713)(154,714)(155,715)(156,706)(157,707)(158,708)(159,709)
(160,710)(161,716)(162,717)(163,718)(164,719)(165,720)(166,696)(167,697)
(168,698)(169,699)(170,700)(171,691)(172,692)(173,693)(174,694)(175,695)
(176,701)(177,702)(178,703)(179,704)(180,705)(181,411)(182,412)(183,413)
(184,414)(185,415)(186,406)(187,407)(188,408)(189,409)(190,410)(191,416)
(192,417)(193,418)(194,419)(195,420)(196,441)(197,442)(198,443)(199,444)
(200,445)(201,436)(202,437)(203,438)(204,439)(205,440)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,426)(212,427)(213,428)(214,429)(215,430)
(216,421)(217,422)(218,423)(219,424)(220,425)(221,431)(222,432)(223,433)
(224,434)(225,435)(226,366)(227,367)(228,368)(229,369)(230,370)(231,361)
(232,362)(233,363)(234,364)(235,365)(236,371)(237,372)(238,373)(239,374)
(240,375)(241,396)(242,397)(243,398)(244,399)(245,400)(246,391)(247,392)
(248,393)(249,394)(250,395)(251,401)(252,402)(253,403)(254,404)(255,405)
(256,381)(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)
(264,379)(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,501)
(272,502)(273,503)(274,504)(275,505)(276,496)(277,497)(278,498)(279,499)
(280,500)(281,506)(282,507)(283,508)(284,509)(285,510)(286,531)(287,532)
(288,533)(289,534)(290,535)(291,526)(292,527)(293,528)(294,529)(295,530)
(296,536)(297,537)(298,538)(299,539)(300,540)(301,516)(302,517)(303,518)
(304,519)(305,520)(306,511)(307,512)(308,513)(309,514)(310,515)(311,521)
(312,522)(313,523)(314,524)(315,525)(316,456)(317,457)(318,458)(319,459)
(320,460)(321,451)(322,452)(323,453)(324,454)(325,455)(326,461)(327,462)
(328,463)(329,464)(330,465)(331,486)(332,487)(333,488)(334,489)(335,490)
(336,481)(337,482)(338,483)(339,484)(340,485)(341,491)(342,492)(343,493)
(344,494)(345,495)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)
(352,467)(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)
(360,480);
s3 := Sym(720)!(  1,646)(  2,647)(  3,648)(  4,649)(  5,650)(  6,656)(  7,657)
(  8,658)(  9,659)( 10,660)( 11,651)( 12,652)( 13,653)( 14,654)( 15,655)
( 16,631)( 17,632)( 18,633)( 19,634)( 20,635)( 21,641)( 22,642)( 23,643)
( 24,644)( 25,645)( 26,636)( 27,637)( 28,638)( 29,639)( 30,640)( 31,661)
( 32,662)( 33,663)( 34,664)( 35,665)( 36,671)( 37,672)( 38,673)( 39,674)
( 40,675)( 41,666)( 42,667)( 43,668)( 44,669)( 45,670)( 46,691)( 47,692)
( 48,693)( 49,694)( 50,695)( 51,701)( 52,702)( 53,703)( 54,704)( 55,705)
( 56,696)( 57,697)( 58,698)( 59,699)( 60,700)( 61,676)( 62,677)( 63,678)
( 64,679)( 65,680)( 66,686)( 67,687)( 68,688)( 69,689)( 70,690)( 71,681)
( 72,682)( 73,683)( 74,684)( 75,685)( 76,706)( 77,707)( 78,708)( 79,709)
( 80,710)( 81,716)( 82,717)( 83,718)( 84,719)( 85,720)( 86,711)( 87,712)
( 88,713)( 89,714)( 90,715)( 91,556)( 92,557)( 93,558)( 94,559)( 95,560)
( 96,566)( 97,567)( 98,568)( 99,569)(100,570)(101,561)(102,562)(103,563)
(104,564)(105,565)(106,541)(107,542)(108,543)(109,544)(110,545)(111,551)
(112,552)(113,553)(114,554)(115,555)(116,546)(117,547)(118,548)(119,549)
(120,550)(121,571)(122,572)(123,573)(124,574)(125,575)(126,581)(127,582)
(128,583)(129,584)(130,585)(131,576)(132,577)(133,578)(134,579)(135,580)
(136,601)(137,602)(138,603)(139,604)(140,605)(141,611)(142,612)(143,613)
(144,614)(145,615)(146,606)(147,607)(148,608)(149,609)(150,610)(151,586)
(152,587)(153,588)(154,589)(155,590)(156,596)(157,597)(158,598)(159,599)
(160,600)(161,591)(162,592)(163,593)(164,594)(165,595)(166,616)(167,617)
(168,618)(169,619)(170,620)(171,626)(172,627)(173,628)(174,629)(175,630)
(176,621)(177,622)(178,623)(179,624)(180,625)(181,511)(182,512)(183,513)
(184,514)(185,515)(186,521)(187,522)(188,523)(189,524)(190,525)(191,516)
(192,517)(193,518)(194,519)(195,520)(196,496)(197,497)(198,498)(199,499)
(200,500)(201,506)(202,507)(203,508)(204,509)(205,510)(206,501)(207,502)
(208,503)(209,504)(210,505)(211,526)(212,527)(213,528)(214,529)(215,530)
(216,536)(217,537)(218,538)(219,539)(220,540)(221,531)(222,532)(223,533)
(224,534)(225,535)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)
(232,477)(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)
(240,475)(241,451)(242,452)(243,453)(244,454)(245,455)(246,461)(247,462)
(248,463)(249,464)(250,465)(251,456)(252,457)(253,458)(254,459)(255,460)
(256,481)(257,482)(258,483)(259,484)(260,485)(261,491)(262,492)(263,493)
(264,494)(265,495)(266,486)(267,487)(268,488)(269,489)(270,490)(271,421)
(272,422)(273,423)(274,424)(275,425)(276,431)(277,432)(278,433)(279,434)
(280,435)(281,426)(282,427)(283,428)(284,429)(285,430)(286,406)(287,407)
(288,408)(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)
(296,411)(297,412)(298,413)(299,414)(300,415)(301,436)(302,437)(303,438)
(304,439)(305,440)(306,446)(307,447)(308,448)(309,449)(310,450)(311,441)
(312,442)(313,443)(314,444)(315,445)(316,376)(317,377)(318,378)(319,379)
(320,380)(321,386)(322,387)(323,388)(324,389)(325,390)(326,381)(327,382)
(328,383)(329,384)(330,385)(331,361)(332,362)(333,363)(334,364)(335,365)
(336,371)(337,372)(338,373)(339,374)(340,375)(341,366)(342,367)(343,368)
(344,369)(345,370)(346,391)(347,392)(348,393)(349,394)(350,395)(351,401)
(352,402)(353,403)(354,404)(355,405)(356,396)(357,397)(358,398)(359,399)
(360,400);
poly := sub<Sym(720)|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, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope