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