Polytope of Type {36,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,6,3}*1296b
if this polytope has a name.
Group : SmallGroup(1296,2007)
Rank : 4
Schlafli Type : {36,6,3}
Number of vertices, edges, etc : 36, 108, 9, 3
Order of s0s1s2s3 : 36
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 : {18,6,3}*648b
3-fold quotients : {36,2,3}*432, {12,6,3}*432b
6-fold quotients : {18,2,3}*216, {6,6,3}*216b
9-fold quotients : {12,2,3}*144, {4,6,3}*144
12-fold quotients : {9,2,3}*108
18-fold quotients : {2,6,3}*72, {6,2,3}*72
27-fold quotients : {4,2,3}*48
36-fold quotients : {3,2,3}*36
54-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)( 15, 16)
( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)( 33, 34)
( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)( 50, 53)( 51, 52)
( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 65, 66)( 67, 72)( 68, 71)( 69, 70)
( 74, 75)( 76, 81)( 77, 80)( 78, 79)( 83, 84)( 85, 90)( 86, 89)( 87, 88)
( 92, 93)( 94, 99)( 95, 98)( 96, 97)(101,102)(103,108)(104,107)(105,106)
(110,111)(112,117)(113,116)(114,115)(119,120)(121,126)(122,125)(123,124)
(128,129)(130,135)(131,134)(132,133)(137,138)(139,144)(140,143)(141,142)
(146,147)(148,153)(149,152)(150,151)(155,156)(157,162)(158,161)(159,160)
(163,244)(164,246)(165,245)(166,252)(167,251)(168,250)(169,249)(170,248)
(171,247)(172,253)(173,255)(174,254)(175,261)(176,260)(177,259)(178,258)
(179,257)(180,256)(181,262)(182,264)(183,263)(184,270)(185,269)(186,268)
(187,267)(188,266)(189,265)(190,271)(191,273)(192,272)(193,279)(194,278)
(195,277)(196,276)(197,275)(198,274)(199,280)(200,282)(201,281)(202,288)
(203,287)(204,286)(205,285)(206,284)(207,283)(208,289)(209,291)(210,290)
(211,297)(212,296)(213,295)(214,294)(215,293)(216,292)(217,298)(218,300)
(219,299)(220,306)(221,305)(222,304)(223,303)(224,302)(225,301)(226,307)
(227,309)(228,308)(229,315)(230,314)(231,313)(232,312)(233,311)(234,310)
(235,316)(236,318)(237,317)(238,324)(239,323)(240,322)(241,321)(242,320)
(243,319)(325,406)(326,408)(327,407)(328,414)(329,413)(330,412)(331,411)
(332,410)(333,409)(334,415)(335,417)(336,416)(337,423)(338,422)(339,421)
(340,420)(341,419)(342,418)(343,424)(344,426)(345,425)(346,432)(347,431)
(348,430)(349,429)(350,428)(351,427)(352,433)(353,435)(354,434)(355,441)
(356,440)(357,439)(358,438)(359,437)(360,436)(361,442)(362,444)(363,443)
(364,450)(365,449)(366,448)(367,447)(368,446)(369,445)(370,451)(371,453)
(372,452)(373,459)(374,458)(375,457)(376,456)(377,455)(378,454)(379,460)
(380,462)(381,461)(382,468)(383,467)(384,466)(385,465)(386,464)(387,463)
(388,469)(389,471)(390,470)(391,477)(392,476)(393,475)(394,474)(395,473)
(396,472)(397,478)(398,480)(399,479)(400,486)(401,485)(402,484)(403,483)
(404,482)(405,481)(488,489)(490,495)(491,494)(492,493)(497,498)(499,504)
(500,503)(501,502)(506,507)(508,513)(509,512)(510,511)(515,516)(517,522)
(518,521)(519,520)(524,525)(526,531)(527,530)(528,529)(533,534)(535,540)
(536,539)(537,538)(542,543)(544,549)(545,548)(546,547)(551,552)(553,558)
(554,557)(555,556)(560,561)(562,567)(563,566)(564,565)(569,570)(571,576)
(572,575)(573,574)(578,579)(580,585)(581,584)(582,583)(587,588)(589,594)
(590,593)(591,592)(596,597)(598,603)(599,602)(600,601)(605,606)(607,612)
(608,611)(609,610)(614,615)(616,621)(617,620)(618,619)(623,624)(625,630)
(626,629)(627,628)(632,633)(634,639)(635,638)(636,637)(641,642)(643,648)
(644,647)(645,646);;
s1 := ( 1,328)( 2,330)( 3,329)( 4,325)( 5,327)( 6,326)( 7,333)( 8,332)
( 9,331)( 10,337)( 11,339)( 12,338)( 13,334)( 14,336)( 15,335)( 16,342)
( 17,341)( 18,340)( 19,346)( 20,348)( 21,347)( 22,343)( 23,345)( 24,344)
( 25,351)( 26,350)( 27,349)( 28,382)( 29,384)( 30,383)( 31,379)( 32,381)
( 33,380)( 34,387)( 35,386)( 36,385)( 37,391)( 38,393)( 39,392)( 40,388)
( 41,390)( 42,389)( 43,396)( 44,395)( 45,394)( 46,400)( 47,402)( 48,401)
( 49,397)( 50,399)( 51,398)( 52,405)( 53,404)( 54,403)( 55,355)( 56,357)
( 57,356)( 58,352)( 59,354)( 60,353)( 61,360)( 62,359)( 63,358)( 64,364)
( 65,366)( 66,365)( 67,361)( 68,363)( 69,362)( 70,369)( 71,368)( 72,367)
( 73,373)( 74,375)( 75,374)( 76,370)( 77,372)( 78,371)( 79,378)( 80,377)
( 81,376)( 82,409)( 83,411)( 84,410)( 85,406)( 86,408)( 87,407)( 88,414)
( 89,413)( 90,412)( 91,418)( 92,420)( 93,419)( 94,415)( 95,417)( 96,416)
( 97,423)( 98,422)( 99,421)(100,427)(101,429)(102,428)(103,424)(104,426)
(105,425)(106,432)(107,431)(108,430)(109,463)(110,465)(111,464)(112,460)
(113,462)(114,461)(115,468)(116,467)(117,466)(118,472)(119,474)(120,473)
(121,469)(122,471)(123,470)(124,477)(125,476)(126,475)(127,481)(128,483)
(129,482)(130,478)(131,480)(132,479)(133,486)(134,485)(135,484)(136,436)
(137,438)(138,437)(139,433)(140,435)(141,434)(142,441)(143,440)(144,439)
(145,445)(146,447)(147,446)(148,442)(149,444)(150,443)(151,450)(152,449)
(153,448)(154,454)(155,456)(156,455)(157,451)(158,453)(159,452)(160,459)
(161,458)(162,457)(163,571)(164,573)(165,572)(166,568)(167,570)(168,569)
(169,576)(170,575)(171,574)(172,580)(173,582)(174,581)(175,577)(176,579)
(177,578)(178,585)(179,584)(180,583)(181,589)(182,591)(183,590)(184,586)
(185,588)(186,587)(187,594)(188,593)(189,592)(190,625)(191,627)(192,626)
(193,622)(194,624)(195,623)(196,630)(197,629)(198,628)(199,634)(200,636)
(201,635)(202,631)(203,633)(204,632)(205,639)(206,638)(207,637)(208,643)
(209,645)(210,644)(211,640)(212,642)(213,641)(214,648)(215,647)(216,646)
(217,598)(218,600)(219,599)(220,595)(221,597)(222,596)(223,603)(224,602)
(225,601)(226,607)(227,609)(228,608)(229,604)(230,606)(231,605)(232,612)
(233,611)(234,610)(235,616)(236,618)(237,617)(238,613)(239,615)(240,614)
(241,621)(242,620)(243,619)(244,490)(245,492)(246,491)(247,487)(248,489)
(249,488)(250,495)(251,494)(252,493)(253,499)(254,501)(255,500)(256,496)
(257,498)(258,497)(259,504)(260,503)(261,502)(262,508)(263,510)(264,509)
(265,505)(266,507)(267,506)(268,513)(269,512)(270,511)(271,544)(272,546)
(273,545)(274,541)(275,543)(276,542)(277,549)(278,548)(279,547)(280,553)
(281,555)(282,554)(283,550)(284,552)(285,551)(286,558)(287,557)(288,556)
(289,562)(290,564)(291,563)(292,559)(293,561)(294,560)(295,567)(296,566)
(297,565)(298,517)(299,519)(300,518)(301,514)(302,516)(303,515)(304,522)
(305,521)(306,520)(307,526)(308,528)(309,527)(310,523)(311,525)(312,524)
(313,531)(314,530)(315,529)(316,535)(317,537)(318,536)(319,532)(320,534)
(321,533)(322,540)(323,539)(324,538);;
s2 := ( 1,514)( 2,515)( 3,516)( 4,517)( 5,518)( 6,519)( 7,520)( 8,521)
( 9,522)( 10,532)( 11,533)( 12,534)( 13,535)( 14,536)( 15,537)( 16,538)
( 17,539)( 18,540)( 19,523)( 20,524)( 21,525)( 22,526)( 23,527)( 24,528)
( 25,529)( 26,530)( 27,531)( 28,487)( 29,488)( 30,489)( 31,490)( 32,491)
( 33,492)( 34,493)( 35,494)( 36,495)( 37,505)( 38,506)( 39,507)( 40,508)
( 41,509)( 42,510)( 43,511)( 44,512)( 45,513)( 46,496)( 47,497)( 48,498)
( 49,499)( 50,500)( 51,501)( 52,502)( 53,503)( 54,504)( 55,541)( 56,542)
( 57,543)( 58,544)( 59,545)( 60,546)( 61,547)( 62,548)( 63,549)( 64,559)
( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)( 72,567)
( 73,550)( 74,551)( 75,552)( 76,553)( 77,554)( 78,555)( 79,556)( 80,557)
( 81,558)( 82,595)( 83,596)( 84,597)( 85,598)( 86,599)( 87,600)( 88,601)
( 89,602)( 90,603)( 91,613)( 92,614)( 93,615)( 94,616)( 95,617)( 96,618)
( 97,619)( 98,620)( 99,621)(100,604)(101,605)(102,606)(103,607)(104,608)
(105,609)(106,610)(107,611)(108,612)(109,568)(110,569)(111,570)(112,571)
(113,572)(114,573)(115,574)(116,575)(117,576)(118,586)(119,587)(120,588)
(121,589)(122,590)(123,591)(124,592)(125,593)(126,594)(127,577)(128,578)
(129,579)(130,580)(131,581)(132,582)(133,583)(134,584)(135,585)(136,622)
(137,623)(138,624)(139,625)(140,626)(141,627)(142,628)(143,629)(144,630)
(145,640)(146,641)(147,642)(148,643)(149,644)(150,645)(151,646)(152,647)
(153,648)(154,631)(155,632)(156,633)(157,634)(158,635)(159,636)(160,637)
(161,638)(162,639)(163,433)(164,434)(165,435)(166,436)(167,437)(168,438)
(169,439)(170,440)(171,441)(172,451)(173,452)(174,453)(175,454)(176,455)
(177,456)(178,457)(179,458)(180,459)(181,442)(182,443)(183,444)(184,445)
(185,446)(186,447)(187,448)(188,449)(189,450)(190,406)(191,407)(192,408)
(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,424)(200,425)
(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)(208,415)
(209,416)(210,417)(211,418)(212,419)(213,420)(214,421)(215,422)(216,423)
(217,460)(218,461)(219,462)(220,463)(221,464)(222,465)(223,466)(224,467)
(225,468)(226,478)(227,479)(228,480)(229,481)(230,482)(231,483)(232,484)
(233,485)(234,486)(235,469)(236,470)(237,471)(238,472)(239,473)(240,474)
(241,475)(242,476)(243,477)(244,352)(245,353)(246,354)(247,355)(248,356)
(249,357)(250,358)(251,359)(252,360)(253,370)(254,371)(255,372)(256,373)
(257,374)(258,375)(259,376)(260,377)(261,378)(262,361)(263,362)(264,363)
(265,364)(266,365)(267,366)(268,367)(269,368)(270,369)(271,325)(272,326)
(273,327)(274,328)(275,329)(276,330)(277,331)(278,332)(279,333)(280,343)
(281,344)(282,345)(283,346)(284,347)(285,348)(286,349)(287,350)(288,351)
(289,334)(290,335)(291,336)(292,337)(293,338)(294,339)(295,340)(296,341)
(297,342)(298,379)(299,380)(300,381)(301,382)(302,383)(303,384)(304,385)
(305,386)(306,387)(307,397)(308,398)(309,399)(310,400)(311,401)(312,402)
(313,403)(314,404)(315,405)(316,388)(317,389)(318,390)(319,391)(320,392)
(321,393)(322,394)(323,395)(324,396);;
s3 := ( 1,496)( 2,497)( 3,498)( 4,499)( 5,500)( 6,501)( 7,502)( 8,503)
( 9,504)( 10,487)( 11,488)( 12,489)( 13,490)( 14,491)( 15,492)( 16,493)
( 17,494)( 18,495)( 19,505)( 20,506)( 21,507)( 22,508)( 23,509)( 24,510)
( 25,511)( 26,512)( 27,513)( 28,550)( 29,551)( 30,552)( 31,553)( 32,554)
( 33,555)( 34,556)( 35,557)( 36,558)( 37,541)( 38,542)( 39,543)( 40,544)
( 41,545)( 42,546)( 43,547)( 44,548)( 45,549)( 46,559)( 47,560)( 48,561)
( 49,562)( 50,563)( 51,564)( 52,565)( 53,566)( 54,567)( 55,523)( 56,524)
( 57,525)( 58,526)( 59,527)( 60,528)( 61,529)( 62,530)( 63,531)( 64,514)
( 65,515)( 66,516)( 67,517)( 68,518)( 69,519)( 70,520)( 71,521)( 72,522)
( 73,532)( 74,533)( 75,534)( 76,535)( 77,536)( 78,537)( 79,538)( 80,539)
( 81,540)( 82,577)( 83,578)( 84,579)( 85,580)( 86,581)( 87,582)( 88,583)
( 89,584)( 90,585)( 91,568)( 92,569)( 93,570)( 94,571)( 95,572)( 96,573)
( 97,574)( 98,575)( 99,576)(100,586)(101,587)(102,588)(103,589)(104,590)
(105,591)(106,592)(107,593)(108,594)(109,631)(110,632)(111,633)(112,634)
(113,635)(114,636)(115,637)(116,638)(117,639)(118,622)(119,623)(120,624)
(121,625)(122,626)(123,627)(124,628)(125,629)(126,630)(127,640)(128,641)
(129,642)(130,643)(131,644)(132,645)(133,646)(134,647)(135,648)(136,604)
(137,605)(138,606)(139,607)(140,608)(141,609)(142,610)(143,611)(144,612)
(145,595)(146,596)(147,597)(148,598)(149,599)(150,600)(151,601)(152,602)
(153,603)(154,613)(155,614)(156,615)(157,616)(158,617)(159,618)(160,619)
(161,620)(162,621)(163,415)(164,416)(165,417)(166,418)(167,419)(168,420)
(169,421)(170,422)(171,423)(172,406)(173,407)(174,408)(175,409)(176,410)
(177,411)(178,412)(179,413)(180,414)(181,424)(182,425)(183,426)(184,427)
(185,428)(186,429)(187,430)(188,431)(189,432)(190,469)(191,470)(192,471)
(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,460)(200,461)
(201,462)(202,463)(203,464)(204,465)(205,466)(206,467)(207,468)(208,478)
(209,479)(210,480)(211,481)(212,482)(213,483)(214,484)(215,485)(216,486)
(217,442)(218,443)(219,444)(220,445)(221,446)(222,447)(223,448)(224,449)
(225,450)(226,433)(227,434)(228,435)(229,436)(230,437)(231,438)(232,439)
(233,440)(234,441)(235,451)(236,452)(237,453)(238,454)(239,455)(240,456)
(241,457)(242,458)(243,459)(244,334)(245,335)(246,336)(247,337)(248,338)
(249,339)(250,340)(251,341)(252,342)(253,325)(254,326)(255,327)(256,328)
(257,329)(258,330)(259,331)(260,332)(261,333)(262,343)(263,344)(264,345)
(265,346)(266,347)(267,348)(268,349)(269,350)(270,351)(271,388)(272,389)
(273,390)(274,391)(275,392)(276,393)(277,394)(278,395)(279,396)(280,379)
(281,380)(282,381)(283,382)(284,383)(285,384)(286,385)(287,386)(288,387)
(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)(296,404)
(297,405)(298,361)(299,362)(300,363)(301,364)(302,365)(303,366)(304,367)
(305,368)(306,369)(307,352)(308,353)(309,354)(310,355)(311,356)(312,357)
(313,358)(314,359)(315,360)(316,370)(317,371)(318,372)(319,373)(320,374)
(321,375)(322,376)(323,377)(324,378);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(648)!( 2, 3)( 4, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)
( 15, 16)( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)
( 33, 34)( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)( 50, 53)
( 51, 52)( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 65, 66)( 67, 72)( 68, 71)
( 69, 70)( 74, 75)( 76, 81)( 77, 80)( 78, 79)( 83, 84)( 85, 90)( 86, 89)
( 87, 88)( 92, 93)( 94, 99)( 95, 98)( 96, 97)(101,102)(103,108)(104,107)
(105,106)(110,111)(112,117)(113,116)(114,115)(119,120)(121,126)(122,125)
(123,124)(128,129)(130,135)(131,134)(132,133)(137,138)(139,144)(140,143)
(141,142)(146,147)(148,153)(149,152)(150,151)(155,156)(157,162)(158,161)
(159,160)(163,244)(164,246)(165,245)(166,252)(167,251)(168,250)(169,249)
(170,248)(171,247)(172,253)(173,255)(174,254)(175,261)(176,260)(177,259)
(178,258)(179,257)(180,256)(181,262)(182,264)(183,263)(184,270)(185,269)
(186,268)(187,267)(188,266)(189,265)(190,271)(191,273)(192,272)(193,279)
(194,278)(195,277)(196,276)(197,275)(198,274)(199,280)(200,282)(201,281)
(202,288)(203,287)(204,286)(205,285)(206,284)(207,283)(208,289)(209,291)
(210,290)(211,297)(212,296)(213,295)(214,294)(215,293)(216,292)(217,298)
(218,300)(219,299)(220,306)(221,305)(222,304)(223,303)(224,302)(225,301)
(226,307)(227,309)(228,308)(229,315)(230,314)(231,313)(232,312)(233,311)
(234,310)(235,316)(236,318)(237,317)(238,324)(239,323)(240,322)(241,321)
(242,320)(243,319)(325,406)(326,408)(327,407)(328,414)(329,413)(330,412)
(331,411)(332,410)(333,409)(334,415)(335,417)(336,416)(337,423)(338,422)
(339,421)(340,420)(341,419)(342,418)(343,424)(344,426)(345,425)(346,432)
(347,431)(348,430)(349,429)(350,428)(351,427)(352,433)(353,435)(354,434)
(355,441)(356,440)(357,439)(358,438)(359,437)(360,436)(361,442)(362,444)
(363,443)(364,450)(365,449)(366,448)(367,447)(368,446)(369,445)(370,451)
(371,453)(372,452)(373,459)(374,458)(375,457)(376,456)(377,455)(378,454)
(379,460)(380,462)(381,461)(382,468)(383,467)(384,466)(385,465)(386,464)
(387,463)(388,469)(389,471)(390,470)(391,477)(392,476)(393,475)(394,474)
(395,473)(396,472)(397,478)(398,480)(399,479)(400,486)(401,485)(402,484)
(403,483)(404,482)(405,481)(488,489)(490,495)(491,494)(492,493)(497,498)
(499,504)(500,503)(501,502)(506,507)(508,513)(509,512)(510,511)(515,516)
(517,522)(518,521)(519,520)(524,525)(526,531)(527,530)(528,529)(533,534)
(535,540)(536,539)(537,538)(542,543)(544,549)(545,548)(546,547)(551,552)
(553,558)(554,557)(555,556)(560,561)(562,567)(563,566)(564,565)(569,570)
(571,576)(572,575)(573,574)(578,579)(580,585)(581,584)(582,583)(587,588)
(589,594)(590,593)(591,592)(596,597)(598,603)(599,602)(600,601)(605,606)
(607,612)(608,611)(609,610)(614,615)(616,621)(617,620)(618,619)(623,624)
(625,630)(626,629)(627,628)(632,633)(634,639)(635,638)(636,637)(641,642)
(643,648)(644,647)(645,646);
s1 := Sym(648)!( 1,328)( 2,330)( 3,329)( 4,325)( 5,327)( 6,326)( 7,333)
( 8,332)( 9,331)( 10,337)( 11,339)( 12,338)( 13,334)( 14,336)( 15,335)
( 16,342)( 17,341)( 18,340)( 19,346)( 20,348)( 21,347)( 22,343)( 23,345)
( 24,344)( 25,351)( 26,350)( 27,349)( 28,382)( 29,384)( 30,383)( 31,379)
( 32,381)( 33,380)( 34,387)( 35,386)( 36,385)( 37,391)( 38,393)( 39,392)
( 40,388)( 41,390)( 42,389)( 43,396)( 44,395)( 45,394)( 46,400)( 47,402)
( 48,401)( 49,397)( 50,399)( 51,398)( 52,405)( 53,404)( 54,403)( 55,355)
( 56,357)( 57,356)( 58,352)( 59,354)( 60,353)( 61,360)( 62,359)( 63,358)
( 64,364)( 65,366)( 66,365)( 67,361)( 68,363)( 69,362)( 70,369)( 71,368)
( 72,367)( 73,373)( 74,375)( 75,374)( 76,370)( 77,372)( 78,371)( 79,378)
( 80,377)( 81,376)( 82,409)( 83,411)( 84,410)( 85,406)( 86,408)( 87,407)
( 88,414)( 89,413)( 90,412)( 91,418)( 92,420)( 93,419)( 94,415)( 95,417)
( 96,416)( 97,423)( 98,422)( 99,421)(100,427)(101,429)(102,428)(103,424)
(104,426)(105,425)(106,432)(107,431)(108,430)(109,463)(110,465)(111,464)
(112,460)(113,462)(114,461)(115,468)(116,467)(117,466)(118,472)(119,474)
(120,473)(121,469)(122,471)(123,470)(124,477)(125,476)(126,475)(127,481)
(128,483)(129,482)(130,478)(131,480)(132,479)(133,486)(134,485)(135,484)
(136,436)(137,438)(138,437)(139,433)(140,435)(141,434)(142,441)(143,440)
(144,439)(145,445)(146,447)(147,446)(148,442)(149,444)(150,443)(151,450)
(152,449)(153,448)(154,454)(155,456)(156,455)(157,451)(158,453)(159,452)
(160,459)(161,458)(162,457)(163,571)(164,573)(165,572)(166,568)(167,570)
(168,569)(169,576)(170,575)(171,574)(172,580)(173,582)(174,581)(175,577)
(176,579)(177,578)(178,585)(179,584)(180,583)(181,589)(182,591)(183,590)
(184,586)(185,588)(186,587)(187,594)(188,593)(189,592)(190,625)(191,627)
(192,626)(193,622)(194,624)(195,623)(196,630)(197,629)(198,628)(199,634)
(200,636)(201,635)(202,631)(203,633)(204,632)(205,639)(206,638)(207,637)
(208,643)(209,645)(210,644)(211,640)(212,642)(213,641)(214,648)(215,647)
(216,646)(217,598)(218,600)(219,599)(220,595)(221,597)(222,596)(223,603)
(224,602)(225,601)(226,607)(227,609)(228,608)(229,604)(230,606)(231,605)
(232,612)(233,611)(234,610)(235,616)(236,618)(237,617)(238,613)(239,615)
(240,614)(241,621)(242,620)(243,619)(244,490)(245,492)(246,491)(247,487)
(248,489)(249,488)(250,495)(251,494)(252,493)(253,499)(254,501)(255,500)
(256,496)(257,498)(258,497)(259,504)(260,503)(261,502)(262,508)(263,510)
(264,509)(265,505)(266,507)(267,506)(268,513)(269,512)(270,511)(271,544)
(272,546)(273,545)(274,541)(275,543)(276,542)(277,549)(278,548)(279,547)
(280,553)(281,555)(282,554)(283,550)(284,552)(285,551)(286,558)(287,557)
(288,556)(289,562)(290,564)(291,563)(292,559)(293,561)(294,560)(295,567)
(296,566)(297,565)(298,517)(299,519)(300,518)(301,514)(302,516)(303,515)
(304,522)(305,521)(306,520)(307,526)(308,528)(309,527)(310,523)(311,525)
(312,524)(313,531)(314,530)(315,529)(316,535)(317,537)(318,536)(319,532)
(320,534)(321,533)(322,540)(323,539)(324,538);
s2 := Sym(648)!( 1,514)( 2,515)( 3,516)( 4,517)( 5,518)( 6,519)( 7,520)
( 8,521)( 9,522)( 10,532)( 11,533)( 12,534)( 13,535)( 14,536)( 15,537)
( 16,538)( 17,539)( 18,540)( 19,523)( 20,524)( 21,525)( 22,526)( 23,527)
( 24,528)( 25,529)( 26,530)( 27,531)( 28,487)( 29,488)( 30,489)( 31,490)
( 32,491)( 33,492)( 34,493)( 35,494)( 36,495)( 37,505)( 38,506)( 39,507)
( 40,508)( 41,509)( 42,510)( 43,511)( 44,512)( 45,513)( 46,496)( 47,497)
( 48,498)( 49,499)( 50,500)( 51,501)( 52,502)( 53,503)( 54,504)( 55,541)
( 56,542)( 57,543)( 58,544)( 59,545)( 60,546)( 61,547)( 62,548)( 63,549)
( 64,559)( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)
( 72,567)( 73,550)( 74,551)( 75,552)( 76,553)( 77,554)( 78,555)( 79,556)
( 80,557)( 81,558)( 82,595)( 83,596)( 84,597)( 85,598)( 86,599)( 87,600)
( 88,601)( 89,602)( 90,603)( 91,613)( 92,614)( 93,615)( 94,616)( 95,617)
( 96,618)( 97,619)( 98,620)( 99,621)(100,604)(101,605)(102,606)(103,607)
(104,608)(105,609)(106,610)(107,611)(108,612)(109,568)(110,569)(111,570)
(112,571)(113,572)(114,573)(115,574)(116,575)(117,576)(118,586)(119,587)
(120,588)(121,589)(122,590)(123,591)(124,592)(125,593)(126,594)(127,577)
(128,578)(129,579)(130,580)(131,581)(132,582)(133,583)(134,584)(135,585)
(136,622)(137,623)(138,624)(139,625)(140,626)(141,627)(142,628)(143,629)
(144,630)(145,640)(146,641)(147,642)(148,643)(149,644)(150,645)(151,646)
(152,647)(153,648)(154,631)(155,632)(156,633)(157,634)(158,635)(159,636)
(160,637)(161,638)(162,639)(163,433)(164,434)(165,435)(166,436)(167,437)
(168,438)(169,439)(170,440)(171,441)(172,451)(173,452)(174,453)(175,454)
(176,455)(177,456)(178,457)(179,458)(180,459)(181,442)(182,443)(183,444)
(184,445)(185,446)(186,447)(187,448)(188,449)(189,450)(190,406)(191,407)
(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,424)
(200,425)(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)
(208,415)(209,416)(210,417)(211,418)(212,419)(213,420)(214,421)(215,422)
(216,423)(217,460)(218,461)(219,462)(220,463)(221,464)(222,465)(223,466)
(224,467)(225,468)(226,478)(227,479)(228,480)(229,481)(230,482)(231,483)
(232,484)(233,485)(234,486)(235,469)(236,470)(237,471)(238,472)(239,473)
(240,474)(241,475)(242,476)(243,477)(244,352)(245,353)(246,354)(247,355)
(248,356)(249,357)(250,358)(251,359)(252,360)(253,370)(254,371)(255,372)
(256,373)(257,374)(258,375)(259,376)(260,377)(261,378)(262,361)(263,362)
(264,363)(265,364)(266,365)(267,366)(268,367)(269,368)(270,369)(271,325)
(272,326)(273,327)(274,328)(275,329)(276,330)(277,331)(278,332)(279,333)
(280,343)(281,344)(282,345)(283,346)(284,347)(285,348)(286,349)(287,350)
(288,351)(289,334)(290,335)(291,336)(292,337)(293,338)(294,339)(295,340)
(296,341)(297,342)(298,379)(299,380)(300,381)(301,382)(302,383)(303,384)
(304,385)(305,386)(306,387)(307,397)(308,398)(309,399)(310,400)(311,401)
(312,402)(313,403)(314,404)(315,405)(316,388)(317,389)(318,390)(319,391)
(320,392)(321,393)(322,394)(323,395)(324,396);
s3 := Sym(648)!( 1,496)( 2,497)( 3,498)( 4,499)( 5,500)( 6,501)( 7,502)
( 8,503)( 9,504)( 10,487)( 11,488)( 12,489)( 13,490)( 14,491)( 15,492)
( 16,493)( 17,494)( 18,495)( 19,505)( 20,506)( 21,507)( 22,508)( 23,509)
( 24,510)( 25,511)( 26,512)( 27,513)( 28,550)( 29,551)( 30,552)( 31,553)
( 32,554)( 33,555)( 34,556)( 35,557)( 36,558)( 37,541)( 38,542)( 39,543)
( 40,544)( 41,545)( 42,546)( 43,547)( 44,548)( 45,549)( 46,559)( 47,560)
( 48,561)( 49,562)( 50,563)( 51,564)( 52,565)( 53,566)( 54,567)( 55,523)
( 56,524)( 57,525)( 58,526)( 59,527)( 60,528)( 61,529)( 62,530)( 63,531)
( 64,514)( 65,515)( 66,516)( 67,517)( 68,518)( 69,519)( 70,520)( 71,521)
( 72,522)( 73,532)( 74,533)( 75,534)( 76,535)( 77,536)( 78,537)( 79,538)
( 80,539)( 81,540)( 82,577)( 83,578)( 84,579)( 85,580)( 86,581)( 87,582)
( 88,583)( 89,584)( 90,585)( 91,568)( 92,569)( 93,570)( 94,571)( 95,572)
( 96,573)( 97,574)( 98,575)( 99,576)(100,586)(101,587)(102,588)(103,589)
(104,590)(105,591)(106,592)(107,593)(108,594)(109,631)(110,632)(111,633)
(112,634)(113,635)(114,636)(115,637)(116,638)(117,639)(118,622)(119,623)
(120,624)(121,625)(122,626)(123,627)(124,628)(125,629)(126,630)(127,640)
(128,641)(129,642)(130,643)(131,644)(132,645)(133,646)(134,647)(135,648)
(136,604)(137,605)(138,606)(139,607)(140,608)(141,609)(142,610)(143,611)
(144,612)(145,595)(146,596)(147,597)(148,598)(149,599)(150,600)(151,601)
(152,602)(153,603)(154,613)(155,614)(156,615)(157,616)(158,617)(159,618)
(160,619)(161,620)(162,621)(163,415)(164,416)(165,417)(166,418)(167,419)
(168,420)(169,421)(170,422)(171,423)(172,406)(173,407)(174,408)(175,409)
(176,410)(177,411)(178,412)(179,413)(180,414)(181,424)(182,425)(183,426)
(184,427)(185,428)(186,429)(187,430)(188,431)(189,432)(190,469)(191,470)
(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,460)
(200,461)(201,462)(202,463)(203,464)(204,465)(205,466)(206,467)(207,468)
(208,478)(209,479)(210,480)(211,481)(212,482)(213,483)(214,484)(215,485)
(216,486)(217,442)(218,443)(219,444)(220,445)(221,446)(222,447)(223,448)
(224,449)(225,450)(226,433)(227,434)(228,435)(229,436)(230,437)(231,438)
(232,439)(233,440)(234,441)(235,451)(236,452)(237,453)(238,454)(239,455)
(240,456)(241,457)(242,458)(243,459)(244,334)(245,335)(246,336)(247,337)
(248,338)(249,339)(250,340)(251,341)(252,342)(253,325)(254,326)(255,327)
(256,328)(257,329)(258,330)(259,331)(260,332)(261,333)(262,343)(263,344)
(264,345)(265,346)(266,347)(267,348)(268,349)(269,350)(270,351)(271,388)
(272,389)(273,390)(274,391)(275,392)(276,393)(277,394)(278,395)(279,396)
(280,379)(281,380)(282,381)(283,382)(284,383)(285,384)(286,385)(287,386)
(288,387)(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)
(296,404)(297,405)(298,361)(299,362)(300,363)(301,364)(302,365)(303,366)
(304,367)(305,368)(306,369)(307,352)(308,353)(309,354)(310,355)(311,356)
(312,357)(313,358)(314,359)(315,360)(316,370)(317,371)(318,372)(319,373)
(320,374)(321,375)(322,376)(323,377)(324,378);
poly := sub<Sym(648)|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 >;
References : None.
to this polytope