Polytope of Type {108,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {108,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,11356)
Rank : 3
Schlafli Type : {108,4}
Number of vertices, edges, etc : 216, 432, 8
Order of s0s1s2 : 108
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {108,4}*864b, {108,4}*864c, {54,4}*864
3-fold quotients : {36,4}*576b
4-fold quotients : {108,2}*432, {27,4}*432, {54,4}*432b, {54,4}*432c
6-fold quotients : {36,4}*288b, {36,4}*288c, {18,4}*288
8-fold quotients : {27,4}*216, {54,2}*216
9-fold quotients : {12,4}*192b
12-fold quotients : {36,2}*144, {9,4}*144, {18,4}*144b, {18,4}*144c
16-fold quotients : {27,2}*108
18-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
24-fold quotients : {9,4}*72, {18,2}*72
36-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
48-fold quotients : {9,2}*36
72-fold quotients : {3,4}*24, {6,2}*24
108-fold quotients : {4,2}*16
144-fold quotients : {3,2}*12
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)
( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)( 51, 96)
( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)
( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)
( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)(114,118)
(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)(146,214)
(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)(154,206)
(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)
(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)(170,190)
(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)(178,182)
(179,184)(180,183)(217,325)(218,326)(219,328)(220,327)(221,333)(222,334)
(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,357)(230,358)
(231,360)(232,359)(233,353)(234,354)(235,356)(236,355)(237,349)(238,350)
(239,352)(240,351)(241,345)(242,346)(243,348)(244,347)(245,341)(246,342)
(247,344)(248,343)(249,337)(250,338)(251,340)(252,339)(253,429)(254,430)
(255,432)(256,431)(257,425)(258,426)(259,428)(260,427)(261,421)(262,422)
(263,424)(264,423)(265,417)(266,418)(267,420)(268,419)(269,413)(270,414)
(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)(278,406)
(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)(286,398)
(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)
(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)(302,382)
(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)(310,374)
(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)(318,366)
(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(435,436)(437,441)
(438,442)(439,444)(440,443)(445,465)(446,466)(447,468)(448,467)(449,461)
(450,462)(451,464)(452,463)(453,457)(454,458)(455,460)(456,459)(469,537)
(470,538)(471,540)(472,539)(473,533)(474,534)(475,536)(476,535)(477,529)
(478,530)(479,532)(480,531)(481,525)(482,526)(483,528)(484,527)(485,521)
(486,522)(487,524)(488,523)(489,517)(490,518)(491,520)(492,519)(493,513)
(494,514)(495,516)(496,515)(497,509)(498,510)(499,512)(500,511)(501,505)
(502,506)(503,508)(504,507)(543,544)(545,549)(546,550)(547,552)(548,551)
(553,573)(554,574)(555,576)(556,575)(557,569)(558,570)(559,572)(560,571)
(561,565)(562,566)(563,568)(564,567)(577,645)(578,646)(579,648)(580,647)
(581,641)(582,642)(583,644)(584,643)(585,637)(586,638)(587,640)(588,639)
(589,633)(590,634)(591,636)(592,635)(593,629)(594,630)(595,632)(596,631)
(597,625)(598,626)(599,628)(600,627)(601,621)(602,622)(603,624)(604,623)
(605,617)(606,618)(607,620)(608,619)(609,613)(610,614)(611,616)(612,615)
(649,757)(650,758)(651,760)(652,759)(653,765)(654,766)(655,768)(656,767)
(657,761)(658,762)(659,764)(660,763)(661,789)(662,790)(663,792)(664,791)
(665,785)(666,786)(667,788)(668,787)(669,781)(670,782)(671,784)(672,783)
(673,777)(674,778)(675,780)(676,779)(677,773)(678,774)(679,776)(680,775)
(681,769)(682,770)(683,772)(684,771)(685,861)(686,862)(687,864)(688,863)
(689,857)(690,858)(691,860)(692,859)(693,853)(694,854)(695,856)(696,855)
(697,849)(698,850)(699,852)(700,851)(701,845)(702,846)(703,848)(704,847)
(705,841)(706,842)(707,844)(708,843)(709,837)(710,838)(711,840)(712,839)
(713,833)(714,834)(715,836)(716,835)(717,829)(718,830)(719,832)(720,831)
(721,825)(722,826)(723,828)(724,827)(725,821)(726,822)(727,824)(728,823)
(729,817)(730,818)(731,820)(732,819)(733,813)(734,814)(735,816)(736,815)
(737,809)(738,810)(739,812)(740,811)(741,805)(742,806)(743,808)(744,807)
(745,801)(746,802)(747,804)(748,803)(749,797)(750,798)(751,800)(752,799)
(753,793)(754,794)(755,796)(756,795);;
s1 := ( 1,253)( 2,256)( 3,255)( 4,254)( 5,261)( 6,264)( 7,263)( 8,262)
( 9,257)( 10,260)( 11,259)( 12,258)( 13,285)( 14,288)( 15,287)( 16,286)
( 17,281)( 18,284)( 19,283)( 20,282)( 21,277)( 22,280)( 23,279)( 24,278)
( 25,273)( 26,276)( 27,275)( 28,274)( 29,269)( 30,272)( 31,271)( 32,270)
( 33,265)( 34,268)( 35,267)( 36,266)( 37,217)( 38,220)( 39,219)( 40,218)
( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)( 48,222)
( 49,249)( 50,252)( 51,251)( 52,250)( 53,245)( 54,248)( 55,247)( 56,246)
( 57,241)( 58,244)( 59,243)( 60,242)( 61,237)( 62,240)( 63,239)( 64,238)
( 65,233)( 66,236)( 67,235)( 68,234)( 69,229)( 70,232)( 71,231)( 72,230)
( 73,321)( 74,324)( 75,323)( 76,322)( 77,317)( 78,320)( 79,319)( 80,318)
( 81,313)( 82,316)( 83,315)( 84,314)( 85,309)( 86,312)( 87,311)( 88,310)
( 89,305)( 90,308)( 91,307)( 92,306)( 93,301)( 94,304)( 95,303)( 96,302)
( 97,297)( 98,300)( 99,299)(100,298)(101,293)(102,296)(103,295)(104,294)
(105,289)(106,292)(107,291)(108,290)(109,361)(110,364)(111,363)(112,362)
(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)(120,366)
(121,393)(122,396)(123,395)(124,394)(125,389)(126,392)(127,391)(128,390)
(129,385)(130,388)(131,387)(132,386)(133,381)(134,384)(135,383)(136,382)
(137,377)(138,380)(139,379)(140,378)(141,373)(142,376)(143,375)(144,374)
(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)(152,334)
(153,329)(154,332)(155,331)(156,330)(157,357)(158,360)(159,359)(160,358)
(161,353)(162,356)(163,355)(164,354)(165,349)(166,352)(167,351)(168,350)
(169,345)(170,348)(171,347)(172,346)(173,341)(174,344)(175,343)(176,342)
(177,337)(178,340)(179,339)(180,338)(181,429)(182,432)(183,431)(184,430)
(185,425)(186,428)(187,427)(188,426)(189,421)(190,424)(191,423)(192,422)
(193,417)(194,420)(195,419)(196,418)(197,413)(198,416)(199,415)(200,414)
(201,409)(202,412)(203,411)(204,410)(205,405)(206,408)(207,407)(208,406)
(209,401)(210,404)(211,403)(212,402)(213,397)(214,400)(215,399)(216,398)
(433,685)(434,688)(435,687)(436,686)(437,693)(438,696)(439,695)(440,694)
(441,689)(442,692)(443,691)(444,690)(445,717)(446,720)(447,719)(448,718)
(449,713)(450,716)(451,715)(452,714)(453,709)(454,712)(455,711)(456,710)
(457,705)(458,708)(459,707)(460,706)(461,701)(462,704)(463,703)(464,702)
(465,697)(466,700)(467,699)(468,698)(469,649)(470,652)(471,651)(472,650)
(473,657)(474,660)(475,659)(476,658)(477,653)(478,656)(479,655)(480,654)
(481,681)(482,684)(483,683)(484,682)(485,677)(486,680)(487,679)(488,678)
(489,673)(490,676)(491,675)(492,674)(493,669)(494,672)(495,671)(496,670)
(497,665)(498,668)(499,667)(500,666)(501,661)(502,664)(503,663)(504,662)
(505,753)(506,756)(507,755)(508,754)(509,749)(510,752)(511,751)(512,750)
(513,745)(514,748)(515,747)(516,746)(517,741)(518,744)(519,743)(520,742)
(521,737)(522,740)(523,739)(524,738)(525,733)(526,736)(527,735)(528,734)
(529,729)(530,732)(531,731)(532,730)(533,725)(534,728)(535,727)(536,726)
(537,721)(538,724)(539,723)(540,722)(541,793)(542,796)(543,795)(544,794)
(545,801)(546,804)(547,803)(548,802)(549,797)(550,800)(551,799)(552,798)
(553,825)(554,828)(555,827)(556,826)(557,821)(558,824)(559,823)(560,822)
(561,817)(562,820)(563,819)(564,818)(565,813)(566,816)(567,815)(568,814)
(569,809)(570,812)(571,811)(572,810)(573,805)(574,808)(575,807)(576,806)
(577,757)(578,760)(579,759)(580,758)(581,765)(582,768)(583,767)(584,766)
(585,761)(586,764)(587,763)(588,762)(589,789)(590,792)(591,791)(592,790)
(593,785)(594,788)(595,787)(596,786)(597,781)(598,784)(599,783)(600,782)
(601,777)(602,780)(603,779)(604,778)(605,773)(606,776)(607,775)(608,774)
(609,769)(610,772)(611,771)(612,770)(613,861)(614,864)(615,863)(616,862)
(617,857)(618,860)(619,859)(620,858)(621,853)(622,856)(623,855)(624,854)
(625,849)(626,852)(627,851)(628,850)(629,845)(630,848)(631,847)(632,846)
(633,841)(634,844)(635,843)(636,842)(637,837)(638,840)(639,839)(640,838)
(641,833)(642,836)(643,835)(644,834)(645,829)(646,832)(647,831)(648,830);;
s2 := ( 1,434)( 2,433)( 3,436)( 4,435)( 5,438)( 6,437)( 7,440)( 8,439)
( 9,442)( 10,441)( 11,444)( 12,443)( 13,446)( 14,445)( 15,448)( 16,447)
( 17,450)( 18,449)( 19,452)( 20,451)( 21,454)( 22,453)( 23,456)( 24,455)
( 25,458)( 26,457)( 27,460)( 28,459)( 29,462)( 30,461)( 31,464)( 32,463)
( 33,466)( 34,465)( 35,468)( 36,467)( 37,470)( 38,469)( 39,472)( 40,471)
( 41,474)( 42,473)( 43,476)( 44,475)( 45,478)( 46,477)( 47,480)( 48,479)
( 49,482)( 50,481)( 51,484)( 52,483)( 53,486)( 54,485)( 55,488)( 56,487)
( 57,490)( 58,489)( 59,492)( 60,491)( 61,494)( 62,493)( 63,496)( 64,495)
( 65,498)( 66,497)( 67,500)( 68,499)( 69,502)( 70,501)( 71,504)( 72,503)
( 73,506)( 74,505)( 75,508)( 76,507)( 77,510)( 78,509)( 79,512)( 80,511)
( 81,514)( 82,513)( 83,516)( 84,515)( 85,518)( 86,517)( 87,520)( 88,519)
( 89,522)( 90,521)( 91,524)( 92,523)( 93,526)( 94,525)( 95,528)( 96,527)
( 97,530)( 98,529)( 99,532)(100,531)(101,534)(102,533)(103,536)(104,535)
(105,538)(106,537)(107,540)(108,539)(109,542)(110,541)(111,544)(112,543)
(113,546)(114,545)(115,548)(116,547)(117,550)(118,549)(119,552)(120,551)
(121,554)(122,553)(123,556)(124,555)(125,558)(126,557)(127,560)(128,559)
(129,562)(130,561)(131,564)(132,563)(133,566)(134,565)(135,568)(136,567)
(137,570)(138,569)(139,572)(140,571)(141,574)(142,573)(143,576)(144,575)
(145,578)(146,577)(147,580)(148,579)(149,582)(150,581)(151,584)(152,583)
(153,586)(154,585)(155,588)(156,587)(157,590)(158,589)(159,592)(160,591)
(161,594)(162,593)(163,596)(164,595)(165,598)(166,597)(167,600)(168,599)
(169,602)(170,601)(171,604)(172,603)(173,606)(174,605)(175,608)(176,607)
(177,610)(178,609)(179,612)(180,611)(181,614)(182,613)(183,616)(184,615)
(185,618)(186,617)(187,620)(188,619)(189,622)(190,621)(191,624)(192,623)
(193,626)(194,625)(195,628)(196,627)(197,630)(198,629)(199,632)(200,631)
(201,634)(202,633)(203,636)(204,635)(205,638)(206,637)(207,640)(208,639)
(209,642)(210,641)(211,644)(212,643)(213,646)(214,645)(215,648)(216,647)
(217,650)(218,649)(219,652)(220,651)(221,654)(222,653)(223,656)(224,655)
(225,658)(226,657)(227,660)(228,659)(229,662)(230,661)(231,664)(232,663)
(233,666)(234,665)(235,668)(236,667)(237,670)(238,669)(239,672)(240,671)
(241,674)(242,673)(243,676)(244,675)(245,678)(246,677)(247,680)(248,679)
(249,682)(250,681)(251,684)(252,683)(253,686)(254,685)(255,688)(256,687)
(257,690)(258,689)(259,692)(260,691)(261,694)(262,693)(263,696)(264,695)
(265,698)(266,697)(267,700)(268,699)(269,702)(270,701)(271,704)(272,703)
(273,706)(274,705)(275,708)(276,707)(277,710)(278,709)(279,712)(280,711)
(281,714)(282,713)(283,716)(284,715)(285,718)(286,717)(287,720)(288,719)
(289,722)(290,721)(291,724)(292,723)(293,726)(294,725)(295,728)(296,727)
(297,730)(298,729)(299,732)(300,731)(301,734)(302,733)(303,736)(304,735)
(305,738)(306,737)(307,740)(308,739)(309,742)(310,741)(311,744)(312,743)
(313,746)(314,745)(315,748)(316,747)(317,750)(318,749)(319,752)(320,751)
(321,754)(322,753)(323,756)(324,755)(325,758)(326,757)(327,760)(328,759)
(329,762)(330,761)(331,764)(332,763)(333,766)(334,765)(335,768)(336,767)
(337,770)(338,769)(339,772)(340,771)(341,774)(342,773)(343,776)(344,775)
(345,778)(346,777)(347,780)(348,779)(349,782)(350,781)(351,784)(352,783)
(353,786)(354,785)(355,788)(356,787)(357,790)(358,789)(359,792)(360,791)
(361,794)(362,793)(363,796)(364,795)(365,798)(366,797)(367,800)(368,799)
(369,802)(370,801)(371,804)(372,803)(373,806)(374,805)(375,808)(376,807)
(377,810)(378,809)(379,812)(380,811)(381,814)(382,813)(383,816)(384,815)
(385,818)(386,817)(387,820)(388,819)(389,822)(390,821)(391,824)(392,823)
(393,826)(394,825)(395,828)(396,827)(397,830)(398,829)(399,832)(400,831)
(401,834)(402,833)(403,836)(404,835)(405,838)(406,837)(407,840)(408,839)
(409,842)(410,841)(411,844)(412,843)(413,846)(414,845)(415,848)(416,847)
(417,850)(418,849)(419,852)(420,851)(421,854)(422,853)(423,856)(424,855)
(425,858)(426,857)(427,860)(428,859)(429,862)(430,861)(431,864)(432,863);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*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*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*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*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*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*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(864)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)
( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)
( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)
( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)
(114,118)(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)
(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)
(146,214)(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)
(154,206)(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)
(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)
(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)
(178,182)(179,184)(180,183)(217,325)(218,326)(219,328)(220,327)(221,333)
(222,334)(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,357)
(230,358)(231,360)(232,359)(233,353)(234,354)(235,356)(236,355)(237,349)
(238,350)(239,352)(240,351)(241,345)(242,346)(243,348)(244,347)(245,341)
(246,342)(247,344)(248,343)(249,337)(250,338)(251,340)(252,339)(253,429)
(254,430)(255,432)(256,431)(257,425)(258,426)(259,428)(260,427)(261,421)
(262,422)(263,424)(264,423)(265,417)(266,418)(267,420)(268,419)(269,413)
(270,414)(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)
(278,406)(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)
(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)
(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)
(302,382)(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)
(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)
(318,366)(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(435,436)
(437,441)(438,442)(439,444)(440,443)(445,465)(446,466)(447,468)(448,467)
(449,461)(450,462)(451,464)(452,463)(453,457)(454,458)(455,460)(456,459)
(469,537)(470,538)(471,540)(472,539)(473,533)(474,534)(475,536)(476,535)
(477,529)(478,530)(479,532)(480,531)(481,525)(482,526)(483,528)(484,527)
(485,521)(486,522)(487,524)(488,523)(489,517)(490,518)(491,520)(492,519)
(493,513)(494,514)(495,516)(496,515)(497,509)(498,510)(499,512)(500,511)
(501,505)(502,506)(503,508)(504,507)(543,544)(545,549)(546,550)(547,552)
(548,551)(553,573)(554,574)(555,576)(556,575)(557,569)(558,570)(559,572)
(560,571)(561,565)(562,566)(563,568)(564,567)(577,645)(578,646)(579,648)
(580,647)(581,641)(582,642)(583,644)(584,643)(585,637)(586,638)(587,640)
(588,639)(589,633)(590,634)(591,636)(592,635)(593,629)(594,630)(595,632)
(596,631)(597,625)(598,626)(599,628)(600,627)(601,621)(602,622)(603,624)
(604,623)(605,617)(606,618)(607,620)(608,619)(609,613)(610,614)(611,616)
(612,615)(649,757)(650,758)(651,760)(652,759)(653,765)(654,766)(655,768)
(656,767)(657,761)(658,762)(659,764)(660,763)(661,789)(662,790)(663,792)
(664,791)(665,785)(666,786)(667,788)(668,787)(669,781)(670,782)(671,784)
(672,783)(673,777)(674,778)(675,780)(676,779)(677,773)(678,774)(679,776)
(680,775)(681,769)(682,770)(683,772)(684,771)(685,861)(686,862)(687,864)
(688,863)(689,857)(690,858)(691,860)(692,859)(693,853)(694,854)(695,856)
(696,855)(697,849)(698,850)(699,852)(700,851)(701,845)(702,846)(703,848)
(704,847)(705,841)(706,842)(707,844)(708,843)(709,837)(710,838)(711,840)
(712,839)(713,833)(714,834)(715,836)(716,835)(717,829)(718,830)(719,832)
(720,831)(721,825)(722,826)(723,828)(724,827)(725,821)(726,822)(727,824)
(728,823)(729,817)(730,818)(731,820)(732,819)(733,813)(734,814)(735,816)
(736,815)(737,809)(738,810)(739,812)(740,811)(741,805)(742,806)(743,808)
(744,807)(745,801)(746,802)(747,804)(748,803)(749,797)(750,798)(751,800)
(752,799)(753,793)(754,794)(755,796)(756,795);
s1 := Sym(864)!( 1,253)( 2,256)( 3,255)( 4,254)( 5,261)( 6,264)( 7,263)
( 8,262)( 9,257)( 10,260)( 11,259)( 12,258)( 13,285)( 14,288)( 15,287)
( 16,286)( 17,281)( 18,284)( 19,283)( 20,282)( 21,277)( 22,280)( 23,279)
( 24,278)( 25,273)( 26,276)( 27,275)( 28,274)( 29,269)( 30,272)( 31,271)
( 32,270)( 33,265)( 34,268)( 35,267)( 36,266)( 37,217)( 38,220)( 39,219)
( 40,218)( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)
( 48,222)( 49,249)( 50,252)( 51,251)( 52,250)( 53,245)( 54,248)( 55,247)
( 56,246)( 57,241)( 58,244)( 59,243)( 60,242)( 61,237)( 62,240)( 63,239)
( 64,238)( 65,233)( 66,236)( 67,235)( 68,234)( 69,229)( 70,232)( 71,231)
( 72,230)( 73,321)( 74,324)( 75,323)( 76,322)( 77,317)( 78,320)( 79,319)
( 80,318)( 81,313)( 82,316)( 83,315)( 84,314)( 85,309)( 86,312)( 87,311)
( 88,310)( 89,305)( 90,308)( 91,307)( 92,306)( 93,301)( 94,304)( 95,303)
( 96,302)( 97,297)( 98,300)( 99,299)(100,298)(101,293)(102,296)(103,295)
(104,294)(105,289)(106,292)(107,291)(108,290)(109,361)(110,364)(111,363)
(112,362)(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)
(120,366)(121,393)(122,396)(123,395)(124,394)(125,389)(126,392)(127,391)
(128,390)(129,385)(130,388)(131,387)(132,386)(133,381)(134,384)(135,383)
(136,382)(137,377)(138,380)(139,379)(140,378)(141,373)(142,376)(143,375)
(144,374)(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)
(152,334)(153,329)(154,332)(155,331)(156,330)(157,357)(158,360)(159,359)
(160,358)(161,353)(162,356)(163,355)(164,354)(165,349)(166,352)(167,351)
(168,350)(169,345)(170,348)(171,347)(172,346)(173,341)(174,344)(175,343)
(176,342)(177,337)(178,340)(179,339)(180,338)(181,429)(182,432)(183,431)
(184,430)(185,425)(186,428)(187,427)(188,426)(189,421)(190,424)(191,423)
(192,422)(193,417)(194,420)(195,419)(196,418)(197,413)(198,416)(199,415)
(200,414)(201,409)(202,412)(203,411)(204,410)(205,405)(206,408)(207,407)
(208,406)(209,401)(210,404)(211,403)(212,402)(213,397)(214,400)(215,399)
(216,398)(433,685)(434,688)(435,687)(436,686)(437,693)(438,696)(439,695)
(440,694)(441,689)(442,692)(443,691)(444,690)(445,717)(446,720)(447,719)
(448,718)(449,713)(450,716)(451,715)(452,714)(453,709)(454,712)(455,711)
(456,710)(457,705)(458,708)(459,707)(460,706)(461,701)(462,704)(463,703)
(464,702)(465,697)(466,700)(467,699)(468,698)(469,649)(470,652)(471,651)
(472,650)(473,657)(474,660)(475,659)(476,658)(477,653)(478,656)(479,655)
(480,654)(481,681)(482,684)(483,683)(484,682)(485,677)(486,680)(487,679)
(488,678)(489,673)(490,676)(491,675)(492,674)(493,669)(494,672)(495,671)
(496,670)(497,665)(498,668)(499,667)(500,666)(501,661)(502,664)(503,663)
(504,662)(505,753)(506,756)(507,755)(508,754)(509,749)(510,752)(511,751)
(512,750)(513,745)(514,748)(515,747)(516,746)(517,741)(518,744)(519,743)
(520,742)(521,737)(522,740)(523,739)(524,738)(525,733)(526,736)(527,735)
(528,734)(529,729)(530,732)(531,731)(532,730)(533,725)(534,728)(535,727)
(536,726)(537,721)(538,724)(539,723)(540,722)(541,793)(542,796)(543,795)
(544,794)(545,801)(546,804)(547,803)(548,802)(549,797)(550,800)(551,799)
(552,798)(553,825)(554,828)(555,827)(556,826)(557,821)(558,824)(559,823)
(560,822)(561,817)(562,820)(563,819)(564,818)(565,813)(566,816)(567,815)
(568,814)(569,809)(570,812)(571,811)(572,810)(573,805)(574,808)(575,807)
(576,806)(577,757)(578,760)(579,759)(580,758)(581,765)(582,768)(583,767)
(584,766)(585,761)(586,764)(587,763)(588,762)(589,789)(590,792)(591,791)
(592,790)(593,785)(594,788)(595,787)(596,786)(597,781)(598,784)(599,783)
(600,782)(601,777)(602,780)(603,779)(604,778)(605,773)(606,776)(607,775)
(608,774)(609,769)(610,772)(611,771)(612,770)(613,861)(614,864)(615,863)
(616,862)(617,857)(618,860)(619,859)(620,858)(621,853)(622,856)(623,855)
(624,854)(625,849)(626,852)(627,851)(628,850)(629,845)(630,848)(631,847)
(632,846)(633,841)(634,844)(635,843)(636,842)(637,837)(638,840)(639,839)
(640,838)(641,833)(642,836)(643,835)(644,834)(645,829)(646,832)(647,831)
(648,830);
s2 := Sym(864)!( 1,434)( 2,433)( 3,436)( 4,435)( 5,438)( 6,437)( 7,440)
( 8,439)( 9,442)( 10,441)( 11,444)( 12,443)( 13,446)( 14,445)( 15,448)
( 16,447)( 17,450)( 18,449)( 19,452)( 20,451)( 21,454)( 22,453)( 23,456)
( 24,455)( 25,458)( 26,457)( 27,460)( 28,459)( 29,462)( 30,461)( 31,464)
( 32,463)( 33,466)( 34,465)( 35,468)( 36,467)( 37,470)( 38,469)( 39,472)
( 40,471)( 41,474)( 42,473)( 43,476)( 44,475)( 45,478)( 46,477)( 47,480)
( 48,479)( 49,482)( 50,481)( 51,484)( 52,483)( 53,486)( 54,485)( 55,488)
( 56,487)( 57,490)( 58,489)( 59,492)( 60,491)( 61,494)( 62,493)( 63,496)
( 64,495)( 65,498)( 66,497)( 67,500)( 68,499)( 69,502)( 70,501)( 71,504)
( 72,503)( 73,506)( 74,505)( 75,508)( 76,507)( 77,510)( 78,509)( 79,512)
( 80,511)( 81,514)( 82,513)( 83,516)( 84,515)( 85,518)( 86,517)( 87,520)
( 88,519)( 89,522)( 90,521)( 91,524)( 92,523)( 93,526)( 94,525)( 95,528)
( 96,527)( 97,530)( 98,529)( 99,532)(100,531)(101,534)(102,533)(103,536)
(104,535)(105,538)(106,537)(107,540)(108,539)(109,542)(110,541)(111,544)
(112,543)(113,546)(114,545)(115,548)(116,547)(117,550)(118,549)(119,552)
(120,551)(121,554)(122,553)(123,556)(124,555)(125,558)(126,557)(127,560)
(128,559)(129,562)(130,561)(131,564)(132,563)(133,566)(134,565)(135,568)
(136,567)(137,570)(138,569)(139,572)(140,571)(141,574)(142,573)(143,576)
(144,575)(145,578)(146,577)(147,580)(148,579)(149,582)(150,581)(151,584)
(152,583)(153,586)(154,585)(155,588)(156,587)(157,590)(158,589)(159,592)
(160,591)(161,594)(162,593)(163,596)(164,595)(165,598)(166,597)(167,600)
(168,599)(169,602)(170,601)(171,604)(172,603)(173,606)(174,605)(175,608)
(176,607)(177,610)(178,609)(179,612)(180,611)(181,614)(182,613)(183,616)
(184,615)(185,618)(186,617)(187,620)(188,619)(189,622)(190,621)(191,624)
(192,623)(193,626)(194,625)(195,628)(196,627)(197,630)(198,629)(199,632)
(200,631)(201,634)(202,633)(203,636)(204,635)(205,638)(206,637)(207,640)
(208,639)(209,642)(210,641)(211,644)(212,643)(213,646)(214,645)(215,648)
(216,647)(217,650)(218,649)(219,652)(220,651)(221,654)(222,653)(223,656)
(224,655)(225,658)(226,657)(227,660)(228,659)(229,662)(230,661)(231,664)
(232,663)(233,666)(234,665)(235,668)(236,667)(237,670)(238,669)(239,672)
(240,671)(241,674)(242,673)(243,676)(244,675)(245,678)(246,677)(247,680)
(248,679)(249,682)(250,681)(251,684)(252,683)(253,686)(254,685)(255,688)
(256,687)(257,690)(258,689)(259,692)(260,691)(261,694)(262,693)(263,696)
(264,695)(265,698)(266,697)(267,700)(268,699)(269,702)(270,701)(271,704)
(272,703)(273,706)(274,705)(275,708)(276,707)(277,710)(278,709)(279,712)
(280,711)(281,714)(282,713)(283,716)(284,715)(285,718)(286,717)(287,720)
(288,719)(289,722)(290,721)(291,724)(292,723)(293,726)(294,725)(295,728)
(296,727)(297,730)(298,729)(299,732)(300,731)(301,734)(302,733)(303,736)
(304,735)(305,738)(306,737)(307,740)(308,739)(309,742)(310,741)(311,744)
(312,743)(313,746)(314,745)(315,748)(316,747)(317,750)(318,749)(319,752)
(320,751)(321,754)(322,753)(323,756)(324,755)(325,758)(326,757)(327,760)
(328,759)(329,762)(330,761)(331,764)(332,763)(333,766)(334,765)(335,768)
(336,767)(337,770)(338,769)(339,772)(340,771)(341,774)(342,773)(343,776)
(344,775)(345,778)(346,777)(347,780)(348,779)(349,782)(350,781)(351,784)
(352,783)(353,786)(354,785)(355,788)(356,787)(357,790)(358,789)(359,792)
(360,791)(361,794)(362,793)(363,796)(364,795)(365,798)(366,797)(367,800)
(368,799)(369,802)(370,801)(371,804)(372,803)(373,806)(374,805)(375,808)
(376,807)(377,810)(378,809)(379,812)(380,811)(381,814)(382,813)(383,816)
(384,815)(385,818)(386,817)(387,820)(388,819)(389,822)(390,821)(391,824)
(392,823)(393,826)(394,825)(395,828)(396,827)(397,830)(398,829)(399,832)
(400,831)(401,834)(402,833)(403,836)(404,835)(405,838)(406,837)(407,840)
(408,839)(409,842)(410,841)(411,844)(412,843)(413,846)(414,845)(415,848)
(416,847)(417,850)(418,849)(419,852)(420,851)(421,854)(422,853)(423,856)
(424,855)(425,858)(426,857)(427,860)(428,859)(429,862)(430,861)(431,864)
(432,863);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*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*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*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*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*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*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