Polytope of Type {48,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6,3}*1728b
if this polytope has a name.
Group : SmallGroup(1728,21263)
Rank : 4
Schlafli Type : {48,6,3}
Number of vertices, edges, etc : 48, 144, 9, 3
Order of s0s1s2s3 : 48
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 : {24,6,3}*864b
3-fold quotients : {48,2,3}*576, {16,6,3}*576
4-fold quotients : {12,6,3}*432b
6-fold quotients : {24,2,3}*288, {8,6,3}*288
8-fold quotients : {6,6,3}*216b
9-fold quotients : {16,2,3}*192
12-fold quotients : {12,2,3}*144, {4,6,3}*144
18-fold quotients : {8,2,3}*96
24-fold quotients : {2,6,3}*72, {6,2,3}*72
36-fold quotients : {4,2,3}*48
48-fold quotients : {3,2,3}*36
72-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)
( 50, 51)( 53, 54)( 55, 82)( 56, 84)( 57, 83)( 58, 85)( 59, 87)( 60, 86)
( 61, 88)( 62, 90)( 63, 89)( 64, 91)( 65, 93)( 66, 92)( 67, 94)( 68, 96)
( 69, 95)( 70, 97)( 71, 99)( 72, 98)( 73,100)( 74,102)( 75,101)( 76,103)
( 77,105)( 78,104)( 79,106)( 80,108)( 81,107)(109,163)(110,165)(111,164)
(112,166)(113,168)(114,167)(115,169)(116,171)(117,170)(118,172)(119,174)
(120,173)(121,175)(122,177)(123,176)(124,178)(125,180)(126,179)(127,181)
(128,183)(129,182)(130,184)(131,186)(132,185)(133,187)(134,189)(135,188)
(136,190)(137,192)(138,191)(139,193)(140,195)(141,194)(142,196)(143,198)
(144,197)(145,199)(146,201)(147,200)(148,202)(149,204)(150,203)(151,205)
(152,207)(153,206)(154,208)(155,210)(156,209)(157,211)(158,213)(159,212)
(160,214)(161,216)(162,215)(217,379)(218,381)(219,380)(220,382)(221,384)
(222,383)(223,385)(224,387)(225,386)(226,388)(227,390)(228,389)(229,391)
(230,393)(231,392)(232,394)(233,396)(234,395)(235,397)(236,399)(237,398)
(238,400)(239,402)(240,401)(241,403)(242,405)(243,404)(244,406)(245,408)
(246,407)(247,409)(248,411)(249,410)(250,412)(251,414)(252,413)(253,415)
(254,417)(255,416)(256,418)(257,420)(258,419)(259,421)(260,423)(261,422)
(262,424)(263,426)(264,425)(265,427)(266,429)(267,428)(268,430)(269,432)
(270,431)(271,325)(272,327)(273,326)(274,328)(275,330)(276,329)(277,331)
(278,333)(279,332)(280,334)(281,336)(282,335)(283,337)(284,339)(285,338)
(286,340)(287,342)(288,341)(289,343)(290,345)(291,344)(292,346)(293,348)
(294,347)(295,349)(296,351)(297,350)(298,352)(299,354)(300,353)(301,355)
(302,357)(303,356)(304,358)(305,360)(306,359)(307,361)(308,363)(309,362)
(310,364)(311,366)(312,365)(313,367)(314,369)(315,368)(316,370)(317,372)
(318,371)(319,373)(320,375)(321,374)(322,376)(323,378)(324,377)(433,541)
(434,543)(435,542)(436,544)(437,546)(438,545)(439,547)(440,549)(441,548)
(442,550)(443,552)(444,551)(445,553)(446,555)(447,554)(448,556)(449,558)
(450,557)(451,559)(452,561)(453,560)(454,562)(455,564)(456,563)(457,565)
(458,567)(459,566)(460,568)(461,570)(462,569)(463,571)(464,573)(465,572)
(466,574)(467,576)(468,575)(469,577)(470,579)(471,578)(472,580)(473,582)
(474,581)(475,583)(476,585)(477,584)(478,586)(479,588)(480,587)(481,589)
(482,591)(483,590)(484,592)(485,594)(486,593)(487,622)(488,624)(489,623)
(490,625)(491,627)(492,626)(493,628)(494,630)(495,629)(496,631)(497,633)
(498,632)(499,634)(500,636)(501,635)(502,637)(503,639)(504,638)(505,640)
(506,642)(507,641)(508,643)(509,645)(510,644)(511,646)(512,648)(513,647)
(514,595)(515,597)(516,596)(517,598)(518,600)(519,599)(520,601)(521,603)
(522,602)(523,604)(524,606)(525,605)(526,607)(527,609)(528,608)(529,610)
(530,612)(531,611)(532,613)(533,615)(534,614)(535,616)(536,618)(537,617)
(538,619)(539,621)(540,620)(650,651)(653,654)(656,657)(659,660)(662,663)
(665,666)(668,669)(671,672)(674,675)(677,678)(680,681)(683,684)(686,687)
(689,690)(692,693)(695,696)(698,699)(701,702)(703,730)(704,732)(705,731)
(706,733)(707,735)(708,734)(709,736)(710,738)(711,737)(712,739)(713,741)
(714,740)(715,742)(716,744)(717,743)(718,745)(719,747)(720,746)(721,748)
(722,750)(723,749)(724,751)(725,753)(726,752)(727,754)(728,756)(729,755)
(757,811)(758,813)(759,812)(760,814)(761,816)(762,815)(763,817)(764,819)
(765,818)(766,820)(767,822)(768,821)(769,823)(770,825)(771,824)(772,826)
(773,828)(774,827)(775,829)(776,831)(777,830)(778,832)(779,834)(780,833)
(781,835)(782,837)(783,836)(784,838)(785,840)(786,839)(787,841)(788,843)
(789,842)(790,844)(791,846)(792,845)(793,847)(794,849)(795,848)(796,850)
(797,852)(798,851)(799,853)(800,855)(801,854)(802,856)(803,858)(804,857)
(805,859)(806,861)(807,860)(808,862)(809,864)(810,863);;
s1 := ( 1,434)( 2,433)( 3,435)( 4,437)( 5,436)( 6,438)( 7,440)( 8,439)
( 9,441)( 10,452)( 11,451)( 12,453)( 13,455)( 14,454)( 15,456)( 16,458)
( 17,457)( 18,459)( 19,443)( 20,442)( 21,444)( 22,446)( 23,445)( 24,447)
( 25,449)( 26,448)( 27,450)( 28,461)( 29,460)( 30,462)( 31,464)( 32,463)
( 33,465)( 34,467)( 35,466)( 36,468)( 37,479)( 38,478)( 39,480)( 40,482)
( 41,481)( 42,483)( 43,485)( 44,484)( 45,486)( 46,470)( 47,469)( 48,471)
( 49,473)( 50,472)( 51,474)( 52,476)( 53,475)( 54,477)( 55,515)( 56,514)
( 57,516)( 58,518)( 59,517)( 60,519)( 61,521)( 62,520)( 63,522)( 64,533)
( 65,532)( 66,534)( 67,536)( 68,535)( 69,537)( 70,539)( 71,538)( 72,540)
( 73,524)( 74,523)( 75,525)( 76,527)( 77,526)( 78,528)( 79,530)( 80,529)
( 81,531)( 82,488)( 83,487)( 84,489)( 85,491)( 86,490)( 87,492)( 88,494)
( 89,493)( 90,495)( 91,506)( 92,505)( 93,507)( 94,509)( 95,508)( 96,510)
( 97,512)( 98,511)( 99,513)(100,497)(101,496)(102,498)(103,500)(104,499)
(105,501)(106,503)(107,502)(108,504)(109,596)(110,595)(111,597)(112,599)
(113,598)(114,600)(115,602)(116,601)(117,603)(118,614)(119,613)(120,615)
(121,617)(122,616)(123,618)(124,620)(125,619)(126,621)(127,605)(128,604)
(129,606)(130,608)(131,607)(132,609)(133,611)(134,610)(135,612)(136,623)
(137,622)(138,624)(139,626)(140,625)(141,627)(142,629)(143,628)(144,630)
(145,641)(146,640)(147,642)(148,644)(149,643)(150,645)(151,647)(152,646)
(153,648)(154,632)(155,631)(156,633)(157,635)(158,634)(159,636)(160,638)
(161,637)(162,639)(163,542)(164,541)(165,543)(166,545)(167,544)(168,546)
(169,548)(170,547)(171,549)(172,560)(173,559)(174,561)(175,563)(176,562)
(177,564)(178,566)(179,565)(180,567)(181,551)(182,550)(183,552)(184,554)
(185,553)(186,555)(187,557)(188,556)(189,558)(190,569)(191,568)(192,570)
(193,572)(194,571)(195,573)(196,575)(197,574)(198,576)(199,587)(200,586)
(201,588)(202,590)(203,589)(204,591)(205,593)(206,592)(207,594)(208,578)
(209,577)(210,579)(211,581)(212,580)(213,582)(214,584)(215,583)(216,585)
(217,812)(218,811)(219,813)(220,815)(221,814)(222,816)(223,818)(224,817)
(225,819)(226,830)(227,829)(228,831)(229,833)(230,832)(231,834)(232,836)
(233,835)(234,837)(235,821)(236,820)(237,822)(238,824)(239,823)(240,825)
(241,827)(242,826)(243,828)(244,839)(245,838)(246,840)(247,842)(248,841)
(249,843)(250,845)(251,844)(252,846)(253,857)(254,856)(255,858)(256,860)
(257,859)(258,861)(259,863)(260,862)(261,864)(262,848)(263,847)(264,849)
(265,851)(266,850)(267,852)(268,854)(269,853)(270,855)(271,758)(272,757)
(273,759)(274,761)(275,760)(276,762)(277,764)(278,763)(279,765)(280,776)
(281,775)(282,777)(283,779)(284,778)(285,780)(286,782)(287,781)(288,783)
(289,767)(290,766)(291,768)(292,770)(293,769)(294,771)(295,773)(296,772)
(297,774)(298,785)(299,784)(300,786)(301,788)(302,787)(303,789)(304,791)
(305,790)(306,792)(307,803)(308,802)(309,804)(310,806)(311,805)(312,807)
(313,809)(314,808)(315,810)(316,794)(317,793)(318,795)(319,797)(320,796)
(321,798)(322,800)(323,799)(324,801)(325,704)(326,703)(327,705)(328,707)
(329,706)(330,708)(331,710)(332,709)(333,711)(334,722)(335,721)(336,723)
(337,725)(338,724)(339,726)(340,728)(341,727)(342,729)(343,713)(344,712)
(345,714)(346,716)(347,715)(348,717)(349,719)(350,718)(351,720)(352,731)
(353,730)(354,732)(355,734)(356,733)(357,735)(358,737)(359,736)(360,738)
(361,749)(362,748)(363,750)(364,752)(365,751)(366,753)(367,755)(368,754)
(369,756)(370,740)(371,739)(372,741)(373,743)(374,742)(375,744)(376,746)
(377,745)(378,747)(379,650)(380,649)(381,651)(382,653)(383,652)(384,654)
(385,656)(386,655)(387,657)(388,668)(389,667)(390,669)(391,671)(392,670)
(393,672)(394,674)(395,673)(396,675)(397,659)(398,658)(399,660)(400,662)
(401,661)(402,663)(403,665)(404,664)(405,666)(406,677)(407,676)(408,678)
(409,680)(410,679)(411,681)(412,683)(413,682)(414,684)(415,695)(416,694)
(417,696)(418,698)(419,697)(420,699)(421,701)(422,700)(423,702)(424,686)
(425,685)(426,687)(427,689)(428,688)(429,690)(430,692)(431,691)(432,693);;
s2 := ( 1,658)( 2,659)( 3,660)( 4,664)( 5,665)( 6,666)( 7,661)( 8,662)
( 9,663)( 10,649)( 11,650)( 12,651)( 13,655)( 14,656)( 15,657)( 16,652)
( 17,653)( 18,654)( 19,667)( 20,668)( 21,669)( 22,673)( 23,674)( 24,675)
( 25,670)( 26,671)( 27,672)( 28,685)( 29,686)( 30,687)( 31,691)( 32,692)
( 33,693)( 34,688)( 35,689)( 36,690)( 37,676)( 38,677)( 39,678)( 40,682)
( 41,683)( 42,684)( 43,679)( 44,680)( 45,681)( 46,694)( 47,695)( 48,696)
( 49,700)( 50,701)( 51,702)( 52,697)( 53,698)( 54,699)( 55,712)( 56,713)
( 57,714)( 58,718)( 59,719)( 60,720)( 61,715)( 62,716)( 63,717)( 64,703)
( 65,704)( 66,705)( 67,709)( 68,710)( 69,711)( 70,706)( 71,707)( 72,708)
( 73,721)( 74,722)( 75,723)( 76,727)( 77,728)( 78,729)( 79,724)( 80,725)
( 81,726)( 82,739)( 83,740)( 84,741)( 85,745)( 86,746)( 87,747)( 88,742)
( 89,743)( 90,744)( 91,730)( 92,731)( 93,732)( 94,736)( 95,737)( 96,738)
( 97,733)( 98,734)( 99,735)(100,748)(101,749)(102,750)(103,754)(104,755)
(105,756)(106,751)(107,752)(108,753)(109,766)(110,767)(111,768)(112,772)
(113,773)(114,774)(115,769)(116,770)(117,771)(118,757)(119,758)(120,759)
(121,763)(122,764)(123,765)(124,760)(125,761)(126,762)(127,775)(128,776)
(129,777)(130,781)(131,782)(132,783)(133,778)(134,779)(135,780)(136,793)
(137,794)(138,795)(139,799)(140,800)(141,801)(142,796)(143,797)(144,798)
(145,784)(146,785)(147,786)(148,790)(149,791)(150,792)(151,787)(152,788)
(153,789)(154,802)(155,803)(156,804)(157,808)(158,809)(159,810)(160,805)
(161,806)(162,807)(163,820)(164,821)(165,822)(166,826)(167,827)(168,828)
(169,823)(170,824)(171,825)(172,811)(173,812)(174,813)(175,817)(176,818)
(177,819)(178,814)(179,815)(180,816)(181,829)(182,830)(183,831)(184,835)
(185,836)(186,837)(187,832)(188,833)(189,834)(190,847)(191,848)(192,849)
(193,853)(194,854)(195,855)(196,850)(197,851)(198,852)(199,838)(200,839)
(201,840)(202,844)(203,845)(204,846)(205,841)(206,842)(207,843)(208,856)
(209,857)(210,858)(211,862)(212,863)(213,864)(214,859)(215,860)(216,861)
(217,550)(218,551)(219,552)(220,556)(221,557)(222,558)(223,553)(224,554)
(225,555)(226,541)(227,542)(228,543)(229,547)(230,548)(231,549)(232,544)
(233,545)(234,546)(235,559)(236,560)(237,561)(238,565)(239,566)(240,567)
(241,562)(242,563)(243,564)(244,577)(245,578)(246,579)(247,583)(248,584)
(249,585)(250,580)(251,581)(252,582)(253,568)(254,569)(255,570)(256,574)
(257,575)(258,576)(259,571)(260,572)(261,573)(262,586)(263,587)(264,588)
(265,592)(266,593)(267,594)(268,589)(269,590)(270,591)(271,604)(272,605)
(273,606)(274,610)(275,611)(276,612)(277,607)(278,608)(279,609)(280,595)
(281,596)(282,597)(283,601)(284,602)(285,603)(286,598)(287,599)(288,600)
(289,613)(290,614)(291,615)(292,619)(293,620)(294,621)(295,616)(296,617)
(297,618)(298,631)(299,632)(300,633)(301,637)(302,638)(303,639)(304,634)
(305,635)(306,636)(307,622)(308,623)(309,624)(310,628)(311,629)(312,630)
(313,625)(314,626)(315,627)(316,640)(317,641)(318,642)(319,646)(320,647)
(321,648)(322,643)(323,644)(324,645)(325,523)(326,524)(327,525)(328,529)
(329,530)(330,531)(331,526)(332,527)(333,528)(334,514)(335,515)(336,516)
(337,520)(338,521)(339,522)(340,517)(341,518)(342,519)(343,532)(344,533)
(345,534)(346,538)(347,539)(348,540)(349,535)(350,536)(351,537)(352,496)
(353,497)(354,498)(355,502)(356,503)(357,504)(358,499)(359,500)(360,501)
(361,487)(362,488)(363,489)(364,493)(365,494)(366,495)(367,490)(368,491)
(369,492)(370,505)(371,506)(372,507)(373,511)(374,512)(375,513)(376,508)
(377,509)(378,510)(379,442)(380,443)(381,444)(382,448)(383,449)(384,450)
(385,445)(386,446)(387,447)(388,433)(389,434)(390,435)(391,439)(392,440)
(393,441)(394,436)(395,437)(396,438)(397,451)(398,452)(399,453)(400,457)
(401,458)(402,459)(403,454)(404,455)(405,456)(406,469)(407,470)(408,471)
(409,475)(410,476)(411,477)(412,472)(413,473)(414,474)(415,460)(416,461)
(417,462)(418,466)(419,467)(420,468)(421,463)(422,464)(423,465)(424,478)
(425,479)(426,480)(427,484)(428,485)(429,486)(430,481)(431,482)(432,483);;
s3 := ( 1,652)( 2,653)( 3,654)( 4,649)( 5,650)( 6,651)( 7,655)( 8,656)
( 9,657)( 10,670)( 11,671)( 12,672)( 13,667)( 14,668)( 15,669)( 16,673)
( 17,674)( 18,675)( 19,661)( 20,662)( 21,663)( 22,658)( 23,659)( 24,660)
( 25,664)( 26,665)( 27,666)( 28,679)( 29,680)( 30,681)( 31,676)( 32,677)
( 33,678)( 34,682)( 35,683)( 36,684)( 37,697)( 38,698)( 39,699)( 40,694)
( 41,695)( 42,696)( 43,700)( 44,701)( 45,702)( 46,688)( 47,689)( 48,690)
( 49,685)( 50,686)( 51,687)( 52,691)( 53,692)( 54,693)( 55,706)( 56,707)
( 57,708)( 58,703)( 59,704)( 60,705)( 61,709)( 62,710)( 63,711)( 64,724)
( 65,725)( 66,726)( 67,721)( 68,722)( 69,723)( 70,727)( 71,728)( 72,729)
( 73,715)( 74,716)( 75,717)( 76,712)( 77,713)( 78,714)( 79,718)( 80,719)
( 81,720)( 82,733)( 83,734)( 84,735)( 85,730)( 86,731)( 87,732)( 88,736)
( 89,737)( 90,738)( 91,751)( 92,752)( 93,753)( 94,748)( 95,749)( 96,750)
( 97,754)( 98,755)( 99,756)(100,742)(101,743)(102,744)(103,739)(104,740)
(105,741)(106,745)(107,746)(108,747)(109,760)(110,761)(111,762)(112,757)
(113,758)(114,759)(115,763)(116,764)(117,765)(118,778)(119,779)(120,780)
(121,775)(122,776)(123,777)(124,781)(125,782)(126,783)(127,769)(128,770)
(129,771)(130,766)(131,767)(132,768)(133,772)(134,773)(135,774)(136,787)
(137,788)(138,789)(139,784)(140,785)(141,786)(142,790)(143,791)(144,792)
(145,805)(146,806)(147,807)(148,802)(149,803)(150,804)(151,808)(152,809)
(153,810)(154,796)(155,797)(156,798)(157,793)(158,794)(159,795)(160,799)
(161,800)(162,801)(163,814)(164,815)(165,816)(166,811)(167,812)(168,813)
(169,817)(170,818)(171,819)(172,832)(173,833)(174,834)(175,829)(176,830)
(177,831)(178,835)(179,836)(180,837)(181,823)(182,824)(183,825)(184,820)
(185,821)(186,822)(187,826)(188,827)(189,828)(190,841)(191,842)(192,843)
(193,838)(194,839)(195,840)(196,844)(197,845)(198,846)(199,859)(200,860)
(201,861)(202,856)(203,857)(204,858)(205,862)(206,863)(207,864)(208,850)
(209,851)(210,852)(211,847)(212,848)(213,849)(214,853)(215,854)(216,855)
(217,544)(218,545)(219,546)(220,541)(221,542)(222,543)(223,547)(224,548)
(225,549)(226,562)(227,563)(228,564)(229,559)(230,560)(231,561)(232,565)
(233,566)(234,567)(235,553)(236,554)(237,555)(238,550)(239,551)(240,552)
(241,556)(242,557)(243,558)(244,571)(245,572)(246,573)(247,568)(248,569)
(249,570)(250,574)(251,575)(252,576)(253,589)(254,590)(255,591)(256,586)
(257,587)(258,588)(259,592)(260,593)(261,594)(262,580)(263,581)(264,582)
(265,577)(266,578)(267,579)(268,583)(269,584)(270,585)(271,598)(272,599)
(273,600)(274,595)(275,596)(276,597)(277,601)(278,602)(279,603)(280,616)
(281,617)(282,618)(283,613)(284,614)(285,615)(286,619)(287,620)(288,621)
(289,607)(290,608)(291,609)(292,604)(293,605)(294,606)(295,610)(296,611)
(297,612)(298,625)(299,626)(300,627)(301,622)(302,623)(303,624)(304,628)
(305,629)(306,630)(307,643)(308,644)(309,645)(310,640)(311,641)(312,642)
(313,646)(314,647)(315,648)(316,634)(317,635)(318,636)(319,631)(320,632)
(321,633)(322,637)(323,638)(324,639)(325,517)(326,518)(327,519)(328,514)
(329,515)(330,516)(331,520)(332,521)(333,522)(334,535)(335,536)(336,537)
(337,532)(338,533)(339,534)(340,538)(341,539)(342,540)(343,526)(344,527)
(345,528)(346,523)(347,524)(348,525)(349,529)(350,530)(351,531)(352,490)
(353,491)(354,492)(355,487)(356,488)(357,489)(358,493)(359,494)(360,495)
(361,508)(362,509)(363,510)(364,505)(365,506)(366,507)(367,511)(368,512)
(369,513)(370,499)(371,500)(372,501)(373,496)(374,497)(375,498)(376,502)
(377,503)(378,504)(379,436)(380,437)(381,438)(382,433)(383,434)(384,435)
(385,439)(386,440)(387,441)(388,454)(389,455)(390,456)(391,451)(392,452)
(393,453)(394,457)(395,458)(396,459)(397,445)(398,446)(399,447)(400,442)
(401,443)(402,444)(403,448)(404,449)(405,450)(406,463)(407,464)(408,465)
(409,460)(410,461)(411,462)(412,466)(413,467)(414,468)(415,481)(416,482)
(417,483)(418,478)(419,479)(420,480)(421,484)(422,485)(423,486)(424,472)
(425,473)(426,474)(427,469)(428,470)(429,471)(430,475)(431,476)(432,477);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
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)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)
( 47, 48)( 50, 51)( 53, 54)( 55, 82)( 56, 84)( 57, 83)( 58, 85)( 59, 87)
( 60, 86)( 61, 88)( 62, 90)( 63, 89)( 64, 91)( 65, 93)( 66, 92)( 67, 94)
( 68, 96)( 69, 95)( 70, 97)( 71, 99)( 72, 98)( 73,100)( 74,102)( 75,101)
( 76,103)( 77,105)( 78,104)( 79,106)( 80,108)( 81,107)(109,163)(110,165)
(111,164)(112,166)(113,168)(114,167)(115,169)(116,171)(117,170)(118,172)
(119,174)(120,173)(121,175)(122,177)(123,176)(124,178)(125,180)(126,179)
(127,181)(128,183)(129,182)(130,184)(131,186)(132,185)(133,187)(134,189)
(135,188)(136,190)(137,192)(138,191)(139,193)(140,195)(141,194)(142,196)
(143,198)(144,197)(145,199)(146,201)(147,200)(148,202)(149,204)(150,203)
(151,205)(152,207)(153,206)(154,208)(155,210)(156,209)(157,211)(158,213)
(159,212)(160,214)(161,216)(162,215)(217,379)(218,381)(219,380)(220,382)
(221,384)(222,383)(223,385)(224,387)(225,386)(226,388)(227,390)(228,389)
(229,391)(230,393)(231,392)(232,394)(233,396)(234,395)(235,397)(236,399)
(237,398)(238,400)(239,402)(240,401)(241,403)(242,405)(243,404)(244,406)
(245,408)(246,407)(247,409)(248,411)(249,410)(250,412)(251,414)(252,413)
(253,415)(254,417)(255,416)(256,418)(257,420)(258,419)(259,421)(260,423)
(261,422)(262,424)(263,426)(264,425)(265,427)(266,429)(267,428)(268,430)
(269,432)(270,431)(271,325)(272,327)(273,326)(274,328)(275,330)(276,329)
(277,331)(278,333)(279,332)(280,334)(281,336)(282,335)(283,337)(284,339)
(285,338)(286,340)(287,342)(288,341)(289,343)(290,345)(291,344)(292,346)
(293,348)(294,347)(295,349)(296,351)(297,350)(298,352)(299,354)(300,353)
(301,355)(302,357)(303,356)(304,358)(305,360)(306,359)(307,361)(308,363)
(309,362)(310,364)(311,366)(312,365)(313,367)(314,369)(315,368)(316,370)
(317,372)(318,371)(319,373)(320,375)(321,374)(322,376)(323,378)(324,377)
(433,541)(434,543)(435,542)(436,544)(437,546)(438,545)(439,547)(440,549)
(441,548)(442,550)(443,552)(444,551)(445,553)(446,555)(447,554)(448,556)
(449,558)(450,557)(451,559)(452,561)(453,560)(454,562)(455,564)(456,563)
(457,565)(458,567)(459,566)(460,568)(461,570)(462,569)(463,571)(464,573)
(465,572)(466,574)(467,576)(468,575)(469,577)(470,579)(471,578)(472,580)
(473,582)(474,581)(475,583)(476,585)(477,584)(478,586)(479,588)(480,587)
(481,589)(482,591)(483,590)(484,592)(485,594)(486,593)(487,622)(488,624)
(489,623)(490,625)(491,627)(492,626)(493,628)(494,630)(495,629)(496,631)
(497,633)(498,632)(499,634)(500,636)(501,635)(502,637)(503,639)(504,638)
(505,640)(506,642)(507,641)(508,643)(509,645)(510,644)(511,646)(512,648)
(513,647)(514,595)(515,597)(516,596)(517,598)(518,600)(519,599)(520,601)
(521,603)(522,602)(523,604)(524,606)(525,605)(526,607)(527,609)(528,608)
(529,610)(530,612)(531,611)(532,613)(533,615)(534,614)(535,616)(536,618)
(537,617)(538,619)(539,621)(540,620)(650,651)(653,654)(656,657)(659,660)
(662,663)(665,666)(668,669)(671,672)(674,675)(677,678)(680,681)(683,684)
(686,687)(689,690)(692,693)(695,696)(698,699)(701,702)(703,730)(704,732)
(705,731)(706,733)(707,735)(708,734)(709,736)(710,738)(711,737)(712,739)
(713,741)(714,740)(715,742)(716,744)(717,743)(718,745)(719,747)(720,746)
(721,748)(722,750)(723,749)(724,751)(725,753)(726,752)(727,754)(728,756)
(729,755)(757,811)(758,813)(759,812)(760,814)(761,816)(762,815)(763,817)
(764,819)(765,818)(766,820)(767,822)(768,821)(769,823)(770,825)(771,824)
(772,826)(773,828)(774,827)(775,829)(776,831)(777,830)(778,832)(779,834)
(780,833)(781,835)(782,837)(783,836)(784,838)(785,840)(786,839)(787,841)
(788,843)(789,842)(790,844)(791,846)(792,845)(793,847)(794,849)(795,848)
(796,850)(797,852)(798,851)(799,853)(800,855)(801,854)(802,856)(803,858)
(804,857)(805,859)(806,861)(807,860)(808,862)(809,864)(810,863);
s1 := Sym(864)!( 1,434)( 2,433)( 3,435)( 4,437)( 5,436)( 6,438)( 7,440)
( 8,439)( 9,441)( 10,452)( 11,451)( 12,453)( 13,455)( 14,454)( 15,456)
( 16,458)( 17,457)( 18,459)( 19,443)( 20,442)( 21,444)( 22,446)( 23,445)
( 24,447)( 25,449)( 26,448)( 27,450)( 28,461)( 29,460)( 30,462)( 31,464)
( 32,463)( 33,465)( 34,467)( 35,466)( 36,468)( 37,479)( 38,478)( 39,480)
( 40,482)( 41,481)( 42,483)( 43,485)( 44,484)( 45,486)( 46,470)( 47,469)
( 48,471)( 49,473)( 50,472)( 51,474)( 52,476)( 53,475)( 54,477)( 55,515)
( 56,514)( 57,516)( 58,518)( 59,517)( 60,519)( 61,521)( 62,520)( 63,522)
( 64,533)( 65,532)( 66,534)( 67,536)( 68,535)( 69,537)( 70,539)( 71,538)
( 72,540)( 73,524)( 74,523)( 75,525)( 76,527)( 77,526)( 78,528)( 79,530)
( 80,529)( 81,531)( 82,488)( 83,487)( 84,489)( 85,491)( 86,490)( 87,492)
( 88,494)( 89,493)( 90,495)( 91,506)( 92,505)( 93,507)( 94,509)( 95,508)
( 96,510)( 97,512)( 98,511)( 99,513)(100,497)(101,496)(102,498)(103,500)
(104,499)(105,501)(106,503)(107,502)(108,504)(109,596)(110,595)(111,597)
(112,599)(113,598)(114,600)(115,602)(116,601)(117,603)(118,614)(119,613)
(120,615)(121,617)(122,616)(123,618)(124,620)(125,619)(126,621)(127,605)
(128,604)(129,606)(130,608)(131,607)(132,609)(133,611)(134,610)(135,612)
(136,623)(137,622)(138,624)(139,626)(140,625)(141,627)(142,629)(143,628)
(144,630)(145,641)(146,640)(147,642)(148,644)(149,643)(150,645)(151,647)
(152,646)(153,648)(154,632)(155,631)(156,633)(157,635)(158,634)(159,636)
(160,638)(161,637)(162,639)(163,542)(164,541)(165,543)(166,545)(167,544)
(168,546)(169,548)(170,547)(171,549)(172,560)(173,559)(174,561)(175,563)
(176,562)(177,564)(178,566)(179,565)(180,567)(181,551)(182,550)(183,552)
(184,554)(185,553)(186,555)(187,557)(188,556)(189,558)(190,569)(191,568)
(192,570)(193,572)(194,571)(195,573)(196,575)(197,574)(198,576)(199,587)
(200,586)(201,588)(202,590)(203,589)(204,591)(205,593)(206,592)(207,594)
(208,578)(209,577)(210,579)(211,581)(212,580)(213,582)(214,584)(215,583)
(216,585)(217,812)(218,811)(219,813)(220,815)(221,814)(222,816)(223,818)
(224,817)(225,819)(226,830)(227,829)(228,831)(229,833)(230,832)(231,834)
(232,836)(233,835)(234,837)(235,821)(236,820)(237,822)(238,824)(239,823)
(240,825)(241,827)(242,826)(243,828)(244,839)(245,838)(246,840)(247,842)
(248,841)(249,843)(250,845)(251,844)(252,846)(253,857)(254,856)(255,858)
(256,860)(257,859)(258,861)(259,863)(260,862)(261,864)(262,848)(263,847)
(264,849)(265,851)(266,850)(267,852)(268,854)(269,853)(270,855)(271,758)
(272,757)(273,759)(274,761)(275,760)(276,762)(277,764)(278,763)(279,765)
(280,776)(281,775)(282,777)(283,779)(284,778)(285,780)(286,782)(287,781)
(288,783)(289,767)(290,766)(291,768)(292,770)(293,769)(294,771)(295,773)
(296,772)(297,774)(298,785)(299,784)(300,786)(301,788)(302,787)(303,789)
(304,791)(305,790)(306,792)(307,803)(308,802)(309,804)(310,806)(311,805)
(312,807)(313,809)(314,808)(315,810)(316,794)(317,793)(318,795)(319,797)
(320,796)(321,798)(322,800)(323,799)(324,801)(325,704)(326,703)(327,705)
(328,707)(329,706)(330,708)(331,710)(332,709)(333,711)(334,722)(335,721)
(336,723)(337,725)(338,724)(339,726)(340,728)(341,727)(342,729)(343,713)
(344,712)(345,714)(346,716)(347,715)(348,717)(349,719)(350,718)(351,720)
(352,731)(353,730)(354,732)(355,734)(356,733)(357,735)(358,737)(359,736)
(360,738)(361,749)(362,748)(363,750)(364,752)(365,751)(366,753)(367,755)
(368,754)(369,756)(370,740)(371,739)(372,741)(373,743)(374,742)(375,744)
(376,746)(377,745)(378,747)(379,650)(380,649)(381,651)(382,653)(383,652)
(384,654)(385,656)(386,655)(387,657)(388,668)(389,667)(390,669)(391,671)
(392,670)(393,672)(394,674)(395,673)(396,675)(397,659)(398,658)(399,660)
(400,662)(401,661)(402,663)(403,665)(404,664)(405,666)(406,677)(407,676)
(408,678)(409,680)(410,679)(411,681)(412,683)(413,682)(414,684)(415,695)
(416,694)(417,696)(418,698)(419,697)(420,699)(421,701)(422,700)(423,702)
(424,686)(425,685)(426,687)(427,689)(428,688)(429,690)(430,692)(431,691)
(432,693);
s2 := Sym(864)!( 1,658)( 2,659)( 3,660)( 4,664)( 5,665)( 6,666)( 7,661)
( 8,662)( 9,663)( 10,649)( 11,650)( 12,651)( 13,655)( 14,656)( 15,657)
( 16,652)( 17,653)( 18,654)( 19,667)( 20,668)( 21,669)( 22,673)( 23,674)
( 24,675)( 25,670)( 26,671)( 27,672)( 28,685)( 29,686)( 30,687)( 31,691)
( 32,692)( 33,693)( 34,688)( 35,689)( 36,690)( 37,676)( 38,677)( 39,678)
( 40,682)( 41,683)( 42,684)( 43,679)( 44,680)( 45,681)( 46,694)( 47,695)
( 48,696)( 49,700)( 50,701)( 51,702)( 52,697)( 53,698)( 54,699)( 55,712)
( 56,713)( 57,714)( 58,718)( 59,719)( 60,720)( 61,715)( 62,716)( 63,717)
( 64,703)( 65,704)( 66,705)( 67,709)( 68,710)( 69,711)( 70,706)( 71,707)
( 72,708)( 73,721)( 74,722)( 75,723)( 76,727)( 77,728)( 78,729)( 79,724)
( 80,725)( 81,726)( 82,739)( 83,740)( 84,741)( 85,745)( 86,746)( 87,747)
( 88,742)( 89,743)( 90,744)( 91,730)( 92,731)( 93,732)( 94,736)( 95,737)
( 96,738)( 97,733)( 98,734)( 99,735)(100,748)(101,749)(102,750)(103,754)
(104,755)(105,756)(106,751)(107,752)(108,753)(109,766)(110,767)(111,768)
(112,772)(113,773)(114,774)(115,769)(116,770)(117,771)(118,757)(119,758)
(120,759)(121,763)(122,764)(123,765)(124,760)(125,761)(126,762)(127,775)
(128,776)(129,777)(130,781)(131,782)(132,783)(133,778)(134,779)(135,780)
(136,793)(137,794)(138,795)(139,799)(140,800)(141,801)(142,796)(143,797)
(144,798)(145,784)(146,785)(147,786)(148,790)(149,791)(150,792)(151,787)
(152,788)(153,789)(154,802)(155,803)(156,804)(157,808)(158,809)(159,810)
(160,805)(161,806)(162,807)(163,820)(164,821)(165,822)(166,826)(167,827)
(168,828)(169,823)(170,824)(171,825)(172,811)(173,812)(174,813)(175,817)
(176,818)(177,819)(178,814)(179,815)(180,816)(181,829)(182,830)(183,831)
(184,835)(185,836)(186,837)(187,832)(188,833)(189,834)(190,847)(191,848)
(192,849)(193,853)(194,854)(195,855)(196,850)(197,851)(198,852)(199,838)
(200,839)(201,840)(202,844)(203,845)(204,846)(205,841)(206,842)(207,843)
(208,856)(209,857)(210,858)(211,862)(212,863)(213,864)(214,859)(215,860)
(216,861)(217,550)(218,551)(219,552)(220,556)(221,557)(222,558)(223,553)
(224,554)(225,555)(226,541)(227,542)(228,543)(229,547)(230,548)(231,549)
(232,544)(233,545)(234,546)(235,559)(236,560)(237,561)(238,565)(239,566)
(240,567)(241,562)(242,563)(243,564)(244,577)(245,578)(246,579)(247,583)
(248,584)(249,585)(250,580)(251,581)(252,582)(253,568)(254,569)(255,570)
(256,574)(257,575)(258,576)(259,571)(260,572)(261,573)(262,586)(263,587)
(264,588)(265,592)(266,593)(267,594)(268,589)(269,590)(270,591)(271,604)
(272,605)(273,606)(274,610)(275,611)(276,612)(277,607)(278,608)(279,609)
(280,595)(281,596)(282,597)(283,601)(284,602)(285,603)(286,598)(287,599)
(288,600)(289,613)(290,614)(291,615)(292,619)(293,620)(294,621)(295,616)
(296,617)(297,618)(298,631)(299,632)(300,633)(301,637)(302,638)(303,639)
(304,634)(305,635)(306,636)(307,622)(308,623)(309,624)(310,628)(311,629)
(312,630)(313,625)(314,626)(315,627)(316,640)(317,641)(318,642)(319,646)
(320,647)(321,648)(322,643)(323,644)(324,645)(325,523)(326,524)(327,525)
(328,529)(329,530)(330,531)(331,526)(332,527)(333,528)(334,514)(335,515)
(336,516)(337,520)(338,521)(339,522)(340,517)(341,518)(342,519)(343,532)
(344,533)(345,534)(346,538)(347,539)(348,540)(349,535)(350,536)(351,537)
(352,496)(353,497)(354,498)(355,502)(356,503)(357,504)(358,499)(359,500)
(360,501)(361,487)(362,488)(363,489)(364,493)(365,494)(366,495)(367,490)
(368,491)(369,492)(370,505)(371,506)(372,507)(373,511)(374,512)(375,513)
(376,508)(377,509)(378,510)(379,442)(380,443)(381,444)(382,448)(383,449)
(384,450)(385,445)(386,446)(387,447)(388,433)(389,434)(390,435)(391,439)
(392,440)(393,441)(394,436)(395,437)(396,438)(397,451)(398,452)(399,453)
(400,457)(401,458)(402,459)(403,454)(404,455)(405,456)(406,469)(407,470)
(408,471)(409,475)(410,476)(411,477)(412,472)(413,473)(414,474)(415,460)
(416,461)(417,462)(418,466)(419,467)(420,468)(421,463)(422,464)(423,465)
(424,478)(425,479)(426,480)(427,484)(428,485)(429,486)(430,481)(431,482)
(432,483);
s3 := Sym(864)!( 1,652)( 2,653)( 3,654)( 4,649)( 5,650)( 6,651)( 7,655)
( 8,656)( 9,657)( 10,670)( 11,671)( 12,672)( 13,667)( 14,668)( 15,669)
( 16,673)( 17,674)( 18,675)( 19,661)( 20,662)( 21,663)( 22,658)( 23,659)
( 24,660)( 25,664)( 26,665)( 27,666)( 28,679)( 29,680)( 30,681)( 31,676)
( 32,677)( 33,678)( 34,682)( 35,683)( 36,684)( 37,697)( 38,698)( 39,699)
( 40,694)( 41,695)( 42,696)( 43,700)( 44,701)( 45,702)( 46,688)( 47,689)
( 48,690)( 49,685)( 50,686)( 51,687)( 52,691)( 53,692)( 54,693)( 55,706)
( 56,707)( 57,708)( 58,703)( 59,704)( 60,705)( 61,709)( 62,710)( 63,711)
( 64,724)( 65,725)( 66,726)( 67,721)( 68,722)( 69,723)( 70,727)( 71,728)
( 72,729)( 73,715)( 74,716)( 75,717)( 76,712)( 77,713)( 78,714)( 79,718)
( 80,719)( 81,720)( 82,733)( 83,734)( 84,735)( 85,730)( 86,731)( 87,732)
( 88,736)( 89,737)( 90,738)( 91,751)( 92,752)( 93,753)( 94,748)( 95,749)
( 96,750)( 97,754)( 98,755)( 99,756)(100,742)(101,743)(102,744)(103,739)
(104,740)(105,741)(106,745)(107,746)(108,747)(109,760)(110,761)(111,762)
(112,757)(113,758)(114,759)(115,763)(116,764)(117,765)(118,778)(119,779)
(120,780)(121,775)(122,776)(123,777)(124,781)(125,782)(126,783)(127,769)
(128,770)(129,771)(130,766)(131,767)(132,768)(133,772)(134,773)(135,774)
(136,787)(137,788)(138,789)(139,784)(140,785)(141,786)(142,790)(143,791)
(144,792)(145,805)(146,806)(147,807)(148,802)(149,803)(150,804)(151,808)
(152,809)(153,810)(154,796)(155,797)(156,798)(157,793)(158,794)(159,795)
(160,799)(161,800)(162,801)(163,814)(164,815)(165,816)(166,811)(167,812)
(168,813)(169,817)(170,818)(171,819)(172,832)(173,833)(174,834)(175,829)
(176,830)(177,831)(178,835)(179,836)(180,837)(181,823)(182,824)(183,825)
(184,820)(185,821)(186,822)(187,826)(188,827)(189,828)(190,841)(191,842)
(192,843)(193,838)(194,839)(195,840)(196,844)(197,845)(198,846)(199,859)
(200,860)(201,861)(202,856)(203,857)(204,858)(205,862)(206,863)(207,864)
(208,850)(209,851)(210,852)(211,847)(212,848)(213,849)(214,853)(215,854)
(216,855)(217,544)(218,545)(219,546)(220,541)(221,542)(222,543)(223,547)
(224,548)(225,549)(226,562)(227,563)(228,564)(229,559)(230,560)(231,561)
(232,565)(233,566)(234,567)(235,553)(236,554)(237,555)(238,550)(239,551)
(240,552)(241,556)(242,557)(243,558)(244,571)(245,572)(246,573)(247,568)
(248,569)(249,570)(250,574)(251,575)(252,576)(253,589)(254,590)(255,591)
(256,586)(257,587)(258,588)(259,592)(260,593)(261,594)(262,580)(263,581)
(264,582)(265,577)(266,578)(267,579)(268,583)(269,584)(270,585)(271,598)
(272,599)(273,600)(274,595)(275,596)(276,597)(277,601)(278,602)(279,603)
(280,616)(281,617)(282,618)(283,613)(284,614)(285,615)(286,619)(287,620)
(288,621)(289,607)(290,608)(291,609)(292,604)(293,605)(294,606)(295,610)
(296,611)(297,612)(298,625)(299,626)(300,627)(301,622)(302,623)(303,624)
(304,628)(305,629)(306,630)(307,643)(308,644)(309,645)(310,640)(311,641)
(312,642)(313,646)(314,647)(315,648)(316,634)(317,635)(318,636)(319,631)
(320,632)(321,633)(322,637)(323,638)(324,639)(325,517)(326,518)(327,519)
(328,514)(329,515)(330,516)(331,520)(332,521)(333,522)(334,535)(335,536)
(336,537)(337,532)(338,533)(339,534)(340,538)(341,539)(342,540)(343,526)
(344,527)(345,528)(346,523)(347,524)(348,525)(349,529)(350,530)(351,531)
(352,490)(353,491)(354,492)(355,487)(356,488)(357,489)(358,493)(359,494)
(360,495)(361,508)(362,509)(363,510)(364,505)(365,506)(366,507)(367,511)
(368,512)(369,513)(370,499)(371,500)(372,501)(373,496)(374,497)(375,498)
(376,502)(377,503)(378,504)(379,436)(380,437)(381,438)(382,433)(383,434)
(384,435)(385,439)(386,440)(387,441)(388,454)(389,455)(390,456)(391,451)
(392,452)(393,453)(394,457)(395,458)(396,459)(397,445)(398,446)(399,447)
(400,442)(401,443)(402,444)(403,448)(404,449)(405,450)(406,463)(407,464)
(408,465)(409,460)(410,461)(411,462)(412,466)(413,467)(414,468)(415,481)
(416,482)(417,483)(418,478)(419,479)(420,480)(421,484)(422,485)(423,486)
(424,472)(425,473)(426,474)(427,469)(428,470)(429,471)(430,475)(431,476)
(432,477);
poly := sub<Sym(864)|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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 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