Polytope of Type {12,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*1728x
if this polytope has a name.
Group : SmallGroup(1728,46356)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 72, 432, 72
Order of s0s1s2 : 6
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,12}*864c
3-fold quotients : {12,12}*576h, {12,12}*576j
6-fold quotients : {6,12}*288a, {6,12}*288b
8-fold quotients : {6,6}*216d
9-fold quotients : {12,4}*192c
12-fold quotients : {3,12}*144, {6,12}*144d
18-fold quotients : {6,4}*96
24-fold quotients : {6,6}*72a, {6,6}*72b, {6,6}*72c
36-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
48-fold quotients : {3,6}*36, {6,3}*36
72-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
144-fold quotients : {2,3}*12, {3,2}*12
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,217)( 2,218)( 3,220)( 4,219)( 5,221)( 6,222)( 7,224)( 8,223)
( 9,225)( 10,226)( 11,228)( 12,227)( 13,241)( 14,242)( 15,244)( 16,243)
( 17,245)( 18,246)( 19,248)( 20,247)( 21,249)( 22,250)( 23,252)( 24,251)
( 25,229)( 26,230)( 27,232)( 28,231)( 29,233)( 30,234)( 31,236)( 32,235)
( 33,237)( 34,238)( 35,240)( 36,239)( 37,289)( 38,290)( 39,292)( 40,291)
( 41,293)( 42,294)( 43,296)( 44,295)( 45,297)( 46,298)( 47,300)( 48,299)
( 49,313)( 50,314)( 51,316)( 52,315)( 53,317)( 54,318)( 55,320)( 56,319)
( 57,321)( 58,322)( 59,324)( 60,323)( 61,301)( 62,302)( 63,304)( 64,303)
( 65,305)( 66,306)( 67,308)( 68,307)( 69,309)( 70,310)( 71,312)( 72,311)
( 73,253)( 74,254)( 75,256)( 76,255)( 77,257)( 78,258)( 79,260)( 80,259)
( 81,261)( 82,262)( 83,264)( 84,263)( 85,277)( 86,278)( 87,280)( 88,279)
( 89,281)( 90,282)( 91,284)( 92,283)( 93,285)( 94,286)( 95,288)( 96,287)
( 97,265)( 98,266)( 99,268)(100,267)(101,269)(102,270)(103,272)(104,271)
(105,273)(106,274)(107,276)(108,275)(109,325)(110,326)(111,328)(112,327)
(113,329)(114,330)(115,332)(116,331)(117,333)(118,334)(119,336)(120,335)
(121,349)(122,350)(123,352)(124,351)(125,353)(126,354)(127,356)(128,355)
(129,357)(130,358)(131,360)(132,359)(133,337)(134,338)(135,340)(136,339)
(137,341)(138,342)(139,344)(140,343)(141,345)(142,346)(143,348)(144,347)
(145,397)(146,398)(147,400)(148,399)(149,401)(150,402)(151,404)(152,403)
(153,405)(154,406)(155,408)(156,407)(157,421)(158,422)(159,424)(160,423)
(161,425)(162,426)(163,428)(164,427)(165,429)(166,430)(167,432)(168,431)
(169,409)(170,410)(171,412)(172,411)(173,413)(174,414)(175,416)(176,415)
(177,417)(178,418)(179,420)(180,419)(181,361)(182,362)(183,364)(184,363)
(185,365)(186,366)(187,368)(188,367)(189,369)(190,370)(191,372)(192,371)
(193,385)(194,386)(195,388)(196,387)(197,389)(198,390)(199,392)(200,391)
(201,393)(202,394)(203,396)(204,395)(205,373)(206,374)(207,376)(208,375)
(209,377)(210,378)(211,380)(212,379)(213,381)(214,382)(215,384)(216,383)
(433,757)(434,758)(435,760)(436,759)(437,761)(438,762)(439,764)(440,763)
(441,765)(442,766)(443,768)(444,767)(445,781)(446,782)(447,784)(448,783)
(449,785)(450,786)(451,788)(452,787)(453,789)(454,790)(455,792)(456,791)
(457,769)(458,770)(459,772)(460,771)(461,773)(462,774)(463,776)(464,775)
(465,777)(466,778)(467,780)(468,779)(469,829)(470,830)(471,832)(472,831)
(473,833)(474,834)(475,836)(476,835)(477,837)(478,838)(479,840)(480,839)
(481,853)(482,854)(483,856)(484,855)(485,857)(486,858)(487,860)(488,859)
(489,861)(490,862)(491,864)(492,863)(493,841)(494,842)(495,844)(496,843)
(497,845)(498,846)(499,848)(500,847)(501,849)(502,850)(503,852)(504,851)
(505,793)(506,794)(507,796)(508,795)(509,797)(510,798)(511,800)(512,799)
(513,801)(514,802)(515,804)(516,803)(517,817)(518,818)(519,820)(520,819)
(521,821)(522,822)(523,824)(524,823)(525,825)(526,826)(527,828)(528,827)
(529,805)(530,806)(531,808)(532,807)(533,809)(534,810)(535,812)(536,811)
(537,813)(538,814)(539,816)(540,815)(541,649)(542,650)(543,652)(544,651)
(545,653)(546,654)(547,656)(548,655)(549,657)(550,658)(551,660)(552,659)
(553,673)(554,674)(555,676)(556,675)(557,677)(558,678)(559,680)(560,679)
(561,681)(562,682)(563,684)(564,683)(565,661)(566,662)(567,664)(568,663)
(569,665)(570,666)(571,668)(572,667)(573,669)(574,670)(575,672)(576,671)
(577,721)(578,722)(579,724)(580,723)(581,725)(582,726)(583,728)(584,727)
(585,729)(586,730)(587,732)(588,731)(589,745)(590,746)(591,748)(592,747)
(593,749)(594,750)(595,752)(596,751)(597,753)(598,754)(599,756)(600,755)
(601,733)(602,734)(603,736)(604,735)(605,737)(606,738)(607,740)(608,739)
(609,741)(610,742)(611,744)(612,743)(613,685)(614,686)(615,688)(616,687)
(617,689)(618,690)(619,692)(620,691)(621,693)(622,694)(623,696)(624,695)
(625,709)(626,710)(627,712)(628,711)(629,713)(630,714)(631,716)(632,715)
(633,717)(634,718)(635,720)(636,719)(637,697)(638,698)(639,700)(640,699)
(641,701)(642,702)(643,704)(644,703)(645,705)(646,706)(647,708)(648,707);;
s1 := ( 1,697)( 2,700)( 3,699)( 4,698)( 5,705)( 6,708)( 7,707)( 8,706)
( 9,701)( 10,704)( 11,703)( 12,702)( 13,685)( 14,688)( 15,687)( 16,686)
( 17,693)( 18,696)( 19,695)( 20,694)( 21,689)( 22,692)( 23,691)( 24,690)
( 25,709)( 26,712)( 27,711)( 28,710)( 29,717)( 30,720)( 31,719)( 32,718)
( 33,713)( 34,716)( 35,715)( 36,714)( 37,661)( 38,664)( 39,663)( 40,662)
( 41,669)( 42,672)( 43,671)( 44,670)( 45,665)( 46,668)( 47,667)( 48,666)
( 49,649)( 50,652)( 51,651)( 52,650)( 53,657)( 54,660)( 55,659)( 56,658)
( 57,653)( 58,656)( 59,655)( 60,654)( 61,673)( 62,676)( 63,675)( 64,674)
( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)( 72,678)
( 73,733)( 74,736)( 75,735)( 76,734)( 77,741)( 78,744)( 79,743)( 80,742)
( 81,737)( 82,740)( 83,739)( 84,738)( 85,721)( 86,724)( 87,723)( 88,722)
( 89,729)( 90,732)( 91,731)( 92,730)( 93,725)( 94,728)( 95,727)( 96,726)
( 97,745)( 98,748)( 99,747)(100,746)(101,753)(102,756)(103,755)(104,754)
(105,749)(106,752)(107,751)(108,750)(109,805)(110,808)(111,807)(112,806)
(113,813)(114,816)(115,815)(116,814)(117,809)(118,812)(119,811)(120,810)
(121,793)(122,796)(123,795)(124,794)(125,801)(126,804)(127,803)(128,802)
(129,797)(130,800)(131,799)(132,798)(133,817)(134,820)(135,819)(136,818)
(137,825)(138,828)(139,827)(140,826)(141,821)(142,824)(143,823)(144,822)
(145,769)(146,772)(147,771)(148,770)(149,777)(150,780)(151,779)(152,778)
(153,773)(154,776)(155,775)(156,774)(157,757)(158,760)(159,759)(160,758)
(161,765)(162,768)(163,767)(164,766)(165,761)(166,764)(167,763)(168,762)
(169,781)(170,784)(171,783)(172,782)(173,789)(174,792)(175,791)(176,790)
(177,785)(178,788)(179,787)(180,786)(181,841)(182,844)(183,843)(184,842)
(185,849)(186,852)(187,851)(188,850)(189,845)(190,848)(191,847)(192,846)
(193,829)(194,832)(195,831)(196,830)(197,837)(198,840)(199,839)(200,838)
(201,833)(202,836)(203,835)(204,834)(205,853)(206,856)(207,855)(208,854)
(209,861)(210,864)(211,863)(212,862)(213,857)(214,860)(215,859)(216,858)
(217,481)(218,484)(219,483)(220,482)(221,489)(222,492)(223,491)(224,490)
(225,485)(226,488)(227,487)(228,486)(229,469)(230,472)(231,471)(232,470)
(233,477)(234,480)(235,479)(236,478)(237,473)(238,476)(239,475)(240,474)
(241,493)(242,496)(243,495)(244,494)(245,501)(246,504)(247,503)(248,502)
(249,497)(250,500)(251,499)(252,498)(253,445)(254,448)(255,447)(256,446)
(257,453)(258,456)(259,455)(260,454)(261,449)(262,452)(263,451)(264,450)
(265,433)(266,436)(267,435)(268,434)(269,441)(270,444)(271,443)(272,442)
(273,437)(274,440)(275,439)(276,438)(277,457)(278,460)(279,459)(280,458)
(281,465)(282,468)(283,467)(284,466)(285,461)(286,464)(287,463)(288,462)
(289,517)(290,520)(291,519)(292,518)(293,525)(294,528)(295,527)(296,526)
(297,521)(298,524)(299,523)(300,522)(301,505)(302,508)(303,507)(304,506)
(305,513)(306,516)(307,515)(308,514)(309,509)(310,512)(311,511)(312,510)
(313,529)(314,532)(315,531)(316,530)(317,537)(318,540)(319,539)(320,538)
(321,533)(322,536)(323,535)(324,534)(325,589)(326,592)(327,591)(328,590)
(329,597)(330,600)(331,599)(332,598)(333,593)(334,596)(335,595)(336,594)
(337,577)(338,580)(339,579)(340,578)(341,585)(342,588)(343,587)(344,586)
(345,581)(346,584)(347,583)(348,582)(349,601)(350,604)(351,603)(352,602)
(353,609)(354,612)(355,611)(356,610)(357,605)(358,608)(359,607)(360,606)
(361,553)(362,556)(363,555)(364,554)(365,561)(366,564)(367,563)(368,562)
(369,557)(370,560)(371,559)(372,558)(373,541)(374,544)(375,543)(376,542)
(377,549)(378,552)(379,551)(380,550)(381,545)(382,548)(383,547)(384,546)
(385,565)(386,568)(387,567)(388,566)(389,573)(390,576)(391,575)(392,574)
(393,569)(394,572)(395,571)(396,570)(397,625)(398,628)(399,627)(400,626)
(401,633)(402,636)(403,635)(404,634)(405,629)(406,632)(407,631)(408,630)
(409,613)(410,616)(411,615)(412,614)(413,621)(414,624)(415,623)(416,622)
(417,617)(418,620)(419,619)(420,618)(421,637)(422,640)(423,639)(424,638)
(425,645)(426,648)(427,647)(428,646)(429,641)(430,644)(431,643)(432,642);;
s2 := ( 1,438)( 2,437)( 3,440)( 4,439)( 5,434)( 6,433)( 7,436)( 8,435)
( 9,442)( 10,441)( 11,444)( 12,443)( 13,462)( 14,461)( 15,464)( 16,463)
( 17,458)( 18,457)( 19,460)( 20,459)( 21,466)( 22,465)( 23,468)( 24,467)
( 25,450)( 26,449)( 27,452)( 28,451)( 29,446)( 30,445)( 31,448)( 32,447)
( 33,454)( 34,453)( 35,456)( 36,455)( 37,474)( 38,473)( 39,476)( 40,475)
( 41,470)( 42,469)( 43,472)( 44,471)( 45,478)( 46,477)( 47,480)( 48,479)
( 49,498)( 50,497)( 51,500)( 52,499)( 53,494)( 54,493)( 55,496)( 56,495)
( 57,502)( 58,501)( 59,504)( 60,503)( 61,486)( 62,485)( 63,488)( 64,487)
( 65,482)( 66,481)( 67,484)( 68,483)( 69,490)( 70,489)( 71,492)( 72,491)
( 73,510)( 74,509)( 75,512)( 76,511)( 77,506)( 78,505)( 79,508)( 80,507)
( 81,514)( 82,513)( 83,516)( 84,515)( 85,534)( 86,533)( 87,536)( 88,535)
( 89,530)( 90,529)( 91,532)( 92,531)( 93,538)( 94,537)( 95,540)( 96,539)
( 97,522)( 98,521)( 99,524)(100,523)(101,518)(102,517)(103,520)(104,519)
(105,526)(106,525)(107,528)(108,527)(109,546)(110,545)(111,548)(112,547)
(113,542)(114,541)(115,544)(116,543)(117,550)(118,549)(119,552)(120,551)
(121,570)(122,569)(123,572)(124,571)(125,566)(126,565)(127,568)(128,567)
(129,574)(130,573)(131,576)(132,575)(133,558)(134,557)(135,560)(136,559)
(137,554)(138,553)(139,556)(140,555)(141,562)(142,561)(143,564)(144,563)
(145,582)(146,581)(147,584)(148,583)(149,578)(150,577)(151,580)(152,579)
(153,586)(154,585)(155,588)(156,587)(157,606)(158,605)(159,608)(160,607)
(161,602)(162,601)(163,604)(164,603)(165,610)(166,609)(167,612)(168,611)
(169,594)(170,593)(171,596)(172,595)(173,590)(174,589)(175,592)(176,591)
(177,598)(178,597)(179,600)(180,599)(181,618)(182,617)(183,620)(184,619)
(185,614)(186,613)(187,616)(188,615)(189,622)(190,621)(191,624)(192,623)
(193,642)(194,641)(195,644)(196,643)(197,638)(198,637)(199,640)(200,639)
(201,646)(202,645)(203,648)(204,647)(205,630)(206,629)(207,632)(208,631)
(209,626)(210,625)(211,628)(212,627)(213,634)(214,633)(215,636)(216,635)
(217,762)(218,761)(219,764)(220,763)(221,758)(222,757)(223,760)(224,759)
(225,766)(226,765)(227,768)(228,767)(229,786)(230,785)(231,788)(232,787)
(233,782)(234,781)(235,784)(236,783)(237,790)(238,789)(239,792)(240,791)
(241,774)(242,773)(243,776)(244,775)(245,770)(246,769)(247,772)(248,771)
(249,778)(250,777)(251,780)(252,779)(253,798)(254,797)(255,800)(256,799)
(257,794)(258,793)(259,796)(260,795)(261,802)(262,801)(263,804)(264,803)
(265,822)(266,821)(267,824)(268,823)(269,818)(270,817)(271,820)(272,819)
(273,826)(274,825)(275,828)(276,827)(277,810)(278,809)(279,812)(280,811)
(281,806)(282,805)(283,808)(284,807)(285,814)(286,813)(287,816)(288,815)
(289,834)(290,833)(291,836)(292,835)(293,830)(294,829)(295,832)(296,831)
(297,838)(298,837)(299,840)(300,839)(301,858)(302,857)(303,860)(304,859)
(305,854)(306,853)(307,856)(308,855)(309,862)(310,861)(311,864)(312,863)
(313,846)(314,845)(315,848)(316,847)(317,842)(318,841)(319,844)(320,843)
(321,850)(322,849)(323,852)(324,851)(325,654)(326,653)(327,656)(328,655)
(329,650)(330,649)(331,652)(332,651)(333,658)(334,657)(335,660)(336,659)
(337,678)(338,677)(339,680)(340,679)(341,674)(342,673)(343,676)(344,675)
(345,682)(346,681)(347,684)(348,683)(349,666)(350,665)(351,668)(352,667)
(353,662)(354,661)(355,664)(356,663)(357,670)(358,669)(359,672)(360,671)
(361,690)(362,689)(363,692)(364,691)(365,686)(366,685)(367,688)(368,687)
(369,694)(370,693)(371,696)(372,695)(373,714)(374,713)(375,716)(376,715)
(377,710)(378,709)(379,712)(380,711)(381,718)(382,717)(383,720)(384,719)
(385,702)(386,701)(387,704)(388,703)(389,698)(390,697)(391,700)(392,699)
(393,706)(394,705)(395,708)(396,707)(397,726)(398,725)(399,728)(400,727)
(401,722)(402,721)(403,724)(404,723)(405,730)(406,729)(407,732)(408,731)
(409,750)(410,749)(411,752)(412,751)(413,746)(414,745)(415,748)(416,747)
(417,754)(418,753)(419,756)(420,755)(421,738)(422,737)(423,740)(424,739)
(425,734)(426,733)(427,736)(428,735)(429,742)(430,741)(431,744)(432,743);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*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(864)!( 1,217)( 2,218)( 3,220)( 4,219)( 5,221)( 6,222)( 7,224)
( 8,223)( 9,225)( 10,226)( 11,228)( 12,227)( 13,241)( 14,242)( 15,244)
( 16,243)( 17,245)( 18,246)( 19,248)( 20,247)( 21,249)( 22,250)( 23,252)
( 24,251)( 25,229)( 26,230)( 27,232)( 28,231)( 29,233)( 30,234)( 31,236)
( 32,235)( 33,237)( 34,238)( 35,240)( 36,239)( 37,289)( 38,290)( 39,292)
( 40,291)( 41,293)( 42,294)( 43,296)( 44,295)( 45,297)( 46,298)( 47,300)
( 48,299)( 49,313)( 50,314)( 51,316)( 52,315)( 53,317)( 54,318)( 55,320)
( 56,319)( 57,321)( 58,322)( 59,324)( 60,323)( 61,301)( 62,302)( 63,304)
( 64,303)( 65,305)( 66,306)( 67,308)( 68,307)( 69,309)( 70,310)( 71,312)
( 72,311)( 73,253)( 74,254)( 75,256)( 76,255)( 77,257)( 78,258)( 79,260)
( 80,259)( 81,261)( 82,262)( 83,264)( 84,263)( 85,277)( 86,278)( 87,280)
( 88,279)( 89,281)( 90,282)( 91,284)( 92,283)( 93,285)( 94,286)( 95,288)
( 96,287)( 97,265)( 98,266)( 99,268)(100,267)(101,269)(102,270)(103,272)
(104,271)(105,273)(106,274)(107,276)(108,275)(109,325)(110,326)(111,328)
(112,327)(113,329)(114,330)(115,332)(116,331)(117,333)(118,334)(119,336)
(120,335)(121,349)(122,350)(123,352)(124,351)(125,353)(126,354)(127,356)
(128,355)(129,357)(130,358)(131,360)(132,359)(133,337)(134,338)(135,340)
(136,339)(137,341)(138,342)(139,344)(140,343)(141,345)(142,346)(143,348)
(144,347)(145,397)(146,398)(147,400)(148,399)(149,401)(150,402)(151,404)
(152,403)(153,405)(154,406)(155,408)(156,407)(157,421)(158,422)(159,424)
(160,423)(161,425)(162,426)(163,428)(164,427)(165,429)(166,430)(167,432)
(168,431)(169,409)(170,410)(171,412)(172,411)(173,413)(174,414)(175,416)
(176,415)(177,417)(178,418)(179,420)(180,419)(181,361)(182,362)(183,364)
(184,363)(185,365)(186,366)(187,368)(188,367)(189,369)(190,370)(191,372)
(192,371)(193,385)(194,386)(195,388)(196,387)(197,389)(198,390)(199,392)
(200,391)(201,393)(202,394)(203,396)(204,395)(205,373)(206,374)(207,376)
(208,375)(209,377)(210,378)(211,380)(212,379)(213,381)(214,382)(215,384)
(216,383)(433,757)(434,758)(435,760)(436,759)(437,761)(438,762)(439,764)
(440,763)(441,765)(442,766)(443,768)(444,767)(445,781)(446,782)(447,784)
(448,783)(449,785)(450,786)(451,788)(452,787)(453,789)(454,790)(455,792)
(456,791)(457,769)(458,770)(459,772)(460,771)(461,773)(462,774)(463,776)
(464,775)(465,777)(466,778)(467,780)(468,779)(469,829)(470,830)(471,832)
(472,831)(473,833)(474,834)(475,836)(476,835)(477,837)(478,838)(479,840)
(480,839)(481,853)(482,854)(483,856)(484,855)(485,857)(486,858)(487,860)
(488,859)(489,861)(490,862)(491,864)(492,863)(493,841)(494,842)(495,844)
(496,843)(497,845)(498,846)(499,848)(500,847)(501,849)(502,850)(503,852)
(504,851)(505,793)(506,794)(507,796)(508,795)(509,797)(510,798)(511,800)
(512,799)(513,801)(514,802)(515,804)(516,803)(517,817)(518,818)(519,820)
(520,819)(521,821)(522,822)(523,824)(524,823)(525,825)(526,826)(527,828)
(528,827)(529,805)(530,806)(531,808)(532,807)(533,809)(534,810)(535,812)
(536,811)(537,813)(538,814)(539,816)(540,815)(541,649)(542,650)(543,652)
(544,651)(545,653)(546,654)(547,656)(548,655)(549,657)(550,658)(551,660)
(552,659)(553,673)(554,674)(555,676)(556,675)(557,677)(558,678)(559,680)
(560,679)(561,681)(562,682)(563,684)(564,683)(565,661)(566,662)(567,664)
(568,663)(569,665)(570,666)(571,668)(572,667)(573,669)(574,670)(575,672)
(576,671)(577,721)(578,722)(579,724)(580,723)(581,725)(582,726)(583,728)
(584,727)(585,729)(586,730)(587,732)(588,731)(589,745)(590,746)(591,748)
(592,747)(593,749)(594,750)(595,752)(596,751)(597,753)(598,754)(599,756)
(600,755)(601,733)(602,734)(603,736)(604,735)(605,737)(606,738)(607,740)
(608,739)(609,741)(610,742)(611,744)(612,743)(613,685)(614,686)(615,688)
(616,687)(617,689)(618,690)(619,692)(620,691)(621,693)(622,694)(623,696)
(624,695)(625,709)(626,710)(627,712)(628,711)(629,713)(630,714)(631,716)
(632,715)(633,717)(634,718)(635,720)(636,719)(637,697)(638,698)(639,700)
(640,699)(641,701)(642,702)(643,704)(644,703)(645,705)(646,706)(647,708)
(648,707);
s1 := Sym(864)!( 1,697)( 2,700)( 3,699)( 4,698)( 5,705)( 6,708)( 7,707)
( 8,706)( 9,701)( 10,704)( 11,703)( 12,702)( 13,685)( 14,688)( 15,687)
( 16,686)( 17,693)( 18,696)( 19,695)( 20,694)( 21,689)( 22,692)( 23,691)
( 24,690)( 25,709)( 26,712)( 27,711)( 28,710)( 29,717)( 30,720)( 31,719)
( 32,718)( 33,713)( 34,716)( 35,715)( 36,714)( 37,661)( 38,664)( 39,663)
( 40,662)( 41,669)( 42,672)( 43,671)( 44,670)( 45,665)( 46,668)( 47,667)
( 48,666)( 49,649)( 50,652)( 51,651)( 52,650)( 53,657)( 54,660)( 55,659)
( 56,658)( 57,653)( 58,656)( 59,655)( 60,654)( 61,673)( 62,676)( 63,675)
( 64,674)( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)
( 72,678)( 73,733)( 74,736)( 75,735)( 76,734)( 77,741)( 78,744)( 79,743)
( 80,742)( 81,737)( 82,740)( 83,739)( 84,738)( 85,721)( 86,724)( 87,723)
( 88,722)( 89,729)( 90,732)( 91,731)( 92,730)( 93,725)( 94,728)( 95,727)
( 96,726)( 97,745)( 98,748)( 99,747)(100,746)(101,753)(102,756)(103,755)
(104,754)(105,749)(106,752)(107,751)(108,750)(109,805)(110,808)(111,807)
(112,806)(113,813)(114,816)(115,815)(116,814)(117,809)(118,812)(119,811)
(120,810)(121,793)(122,796)(123,795)(124,794)(125,801)(126,804)(127,803)
(128,802)(129,797)(130,800)(131,799)(132,798)(133,817)(134,820)(135,819)
(136,818)(137,825)(138,828)(139,827)(140,826)(141,821)(142,824)(143,823)
(144,822)(145,769)(146,772)(147,771)(148,770)(149,777)(150,780)(151,779)
(152,778)(153,773)(154,776)(155,775)(156,774)(157,757)(158,760)(159,759)
(160,758)(161,765)(162,768)(163,767)(164,766)(165,761)(166,764)(167,763)
(168,762)(169,781)(170,784)(171,783)(172,782)(173,789)(174,792)(175,791)
(176,790)(177,785)(178,788)(179,787)(180,786)(181,841)(182,844)(183,843)
(184,842)(185,849)(186,852)(187,851)(188,850)(189,845)(190,848)(191,847)
(192,846)(193,829)(194,832)(195,831)(196,830)(197,837)(198,840)(199,839)
(200,838)(201,833)(202,836)(203,835)(204,834)(205,853)(206,856)(207,855)
(208,854)(209,861)(210,864)(211,863)(212,862)(213,857)(214,860)(215,859)
(216,858)(217,481)(218,484)(219,483)(220,482)(221,489)(222,492)(223,491)
(224,490)(225,485)(226,488)(227,487)(228,486)(229,469)(230,472)(231,471)
(232,470)(233,477)(234,480)(235,479)(236,478)(237,473)(238,476)(239,475)
(240,474)(241,493)(242,496)(243,495)(244,494)(245,501)(246,504)(247,503)
(248,502)(249,497)(250,500)(251,499)(252,498)(253,445)(254,448)(255,447)
(256,446)(257,453)(258,456)(259,455)(260,454)(261,449)(262,452)(263,451)
(264,450)(265,433)(266,436)(267,435)(268,434)(269,441)(270,444)(271,443)
(272,442)(273,437)(274,440)(275,439)(276,438)(277,457)(278,460)(279,459)
(280,458)(281,465)(282,468)(283,467)(284,466)(285,461)(286,464)(287,463)
(288,462)(289,517)(290,520)(291,519)(292,518)(293,525)(294,528)(295,527)
(296,526)(297,521)(298,524)(299,523)(300,522)(301,505)(302,508)(303,507)
(304,506)(305,513)(306,516)(307,515)(308,514)(309,509)(310,512)(311,511)
(312,510)(313,529)(314,532)(315,531)(316,530)(317,537)(318,540)(319,539)
(320,538)(321,533)(322,536)(323,535)(324,534)(325,589)(326,592)(327,591)
(328,590)(329,597)(330,600)(331,599)(332,598)(333,593)(334,596)(335,595)
(336,594)(337,577)(338,580)(339,579)(340,578)(341,585)(342,588)(343,587)
(344,586)(345,581)(346,584)(347,583)(348,582)(349,601)(350,604)(351,603)
(352,602)(353,609)(354,612)(355,611)(356,610)(357,605)(358,608)(359,607)
(360,606)(361,553)(362,556)(363,555)(364,554)(365,561)(366,564)(367,563)
(368,562)(369,557)(370,560)(371,559)(372,558)(373,541)(374,544)(375,543)
(376,542)(377,549)(378,552)(379,551)(380,550)(381,545)(382,548)(383,547)
(384,546)(385,565)(386,568)(387,567)(388,566)(389,573)(390,576)(391,575)
(392,574)(393,569)(394,572)(395,571)(396,570)(397,625)(398,628)(399,627)
(400,626)(401,633)(402,636)(403,635)(404,634)(405,629)(406,632)(407,631)
(408,630)(409,613)(410,616)(411,615)(412,614)(413,621)(414,624)(415,623)
(416,622)(417,617)(418,620)(419,619)(420,618)(421,637)(422,640)(423,639)
(424,638)(425,645)(426,648)(427,647)(428,646)(429,641)(430,644)(431,643)
(432,642);
s2 := Sym(864)!( 1,438)( 2,437)( 3,440)( 4,439)( 5,434)( 6,433)( 7,436)
( 8,435)( 9,442)( 10,441)( 11,444)( 12,443)( 13,462)( 14,461)( 15,464)
( 16,463)( 17,458)( 18,457)( 19,460)( 20,459)( 21,466)( 22,465)( 23,468)
( 24,467)( 25,450)( 26,449)( 27,452)( 28,451)( 29,446)( 30,445)( 31,448)
( 32,447)( 33,454)( 34,453)( 35,456)( 36,455)( 37,474)( 38,473)( 39,476)
( 40,475)( 41,470)( 42,469)( 43,472)( 44,471)( 45,478)( 46,477)( 47,480)
( 48,479)( 49,498)( 50,497)( 51,500)( 52,499)( 53,494)( 54,493)( 55,496)
( 56,495)( 57,502)( 58,501)( 59,504)( 60,503)( 61,486)( 62,485)( 63,488)
( 64,487)( 65,482)( 66,481)( 67,484)( 68,483)( 69,490)( 70,489)( 71,492)
( 72,491)( 73,510)( 74,509)( 75,512)( 76,511)( 77,506)( 78,505)( 79,508)
( 80,507)( 81,514)( 82,513)( 83,516)( 84,515)( 85,534)( 86,533)( 87,536)
( 88,535)( 89,530)( 90,529)( 91,532)( 92,531)( 93,538)( 94,537)( 95,540)
( 96,539)( 97,522)( 98,521)( 99,524)(100,523)(101,518)(102,517)(103,520)
(104,519)(105,526)(106,525)(107,528)(108,527)(109,546)(110,545)(111,548)
(112,547)(113,542)(114,541)(115,544)(116,543)(117,550)(118,549)(119,552)
(120,551)(121,570)(122,569)(123,572)(124,571)(125,566)(126,565)(127,568)
(128,567)(129,574)(130,573)(131,576)(132,575)(133,558)(134,557)(135,560)
(136,559)(137,554)(138,553)(139,556)(140,555)(141,562)(142,561)(143,564)
(144,563)(145,582)(146,581)(147,584)(148,583)(149,578)(150,577)(151,580)
(152,579)(153,586)(154,585)(155,588)(156,587)(157,606)(158,605)(159,608)
(160,607)(161,602)(162,601)(163,604)(164,603)(165,610)(166,609)(167,612)
(168,611)(169,594)(170,593)(171,596)(172,595)(173,590)(174,589)(175,592)
(176,591)(177,598)(178,597)(179,600)(180,599)(181,618)(182,617)(183,620)
(184,619)(185,614)(186,613)(187,616)(188,615)(189,622)(190,621)(191,624)
(192,623)(193,642)(194,641)(195,644)(196,643)(197,638)(198,637)(199,640)
(200,639)(201,646)(202,645)(203,648)(204,647)(205,630)(206,629)(207,632)
(208,631)(209,626)(210,625)(211,628)(212,627)(213,634)(214,633)(215,636)
(216,635)(217,762)(218,761)(219,764)(220,763)(221,758)(222,757)(223,760)
(224,759)(225,766)(226,765)(227,768)(228,767)(229,786)(230,785)(231,788)
(232,787)(233,782)(234,781)(235,784)(236,783)(237,790)(238,789)(239,792)
(240,791)(241,774)(242,773)(243,776)(244,775)(245,770)(246,769)(247,772)
(248,771)(249,778)(250,777)(251,780)(252,779)(253,798)(254,797)(255,800)
(256,799)(257,794)(258,793)(259,796)(260,795)(261,802)(262,801)(263,804)
(264,803)(265,822)(266,821)(267,824)(268,823)(269,818)(270,817)(271,820)
(272,819)(273,826)(274,825)(275,828)(276,827)(277,810)(278,809)(279,812)
(280,811)(281,806)(282,805)(283,808)(284,807)(285,814)(286,813)(287,816)
(288,815)(289,834)(290,833)(291,836)(292,835)(293,830)(294,829)(295,832)
(296,831)(297,838)(298,837)(299,840)(300,839)(301,858)(302,857)(303,860)
(304,859)(305,854)(306,853)(307,856)(308,855)(309,862)(310,861)(311,864)
(312,863)(313,846)(314,845)(315,848)(316,847)(317,842)(318,841)(319,844)
(320,843)(321,850)(322,849)(323,852)(324,851)(325,654)(326,653)(327,656)
(328,655)(329,650)(330,649)(331,652)(332,651)(333,658)(334,657)(335,660)
(336,659)(337,678)(338,677)(339,680)(340,679)(341,674)(342,673)(343,676)
(344,675)(345,682)(346,681)(347,684)(348,683)(349,666)(350,665)(351,668)
(352,667)(353,662)(354,661)(355,664)(356,663)(357,670)(358,669)(359,672)
(360,671)(361,690)(362,689)(363,692)(364,691)(365,686)(366,685)(367,688)
(368,687)(369,694)(370,693)(371,696)(372,695)(373,714)(374,713)(375,716)
(376,715)(377,710)(378,709)(379,712)(380,711)(381,718)(382,717)(383,720)
(384,719)(385,702)(386,701)(387,704)(388,703)(389,698)(390,697)(391,700)
(392,699)(393,706)(394,705)(395,708)(396,707)(397,726)(398,725)(399,728)
(400,727)(401,722)(402,721)(403,724)(404,723)(405,730)(406,729)(407,732)
(408,731)(409,750)(410,749)(411,752)(412,751)(413,746)(414,745)(415,748)
(416,747)(417,754)(418,753)(419,756)(420,755)(421,738)(422,737)(423,740)
(424,739)(425,734)(426,733)(427,736)(428,735)(429,742)(430,741)(431,744)
(432,743);
poly := sub<Sym(864)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*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