Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*1296g
if this polytope has a name.
Group : SmallGroup(1296,2061)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 108, 324, 54
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 6
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 : {6,6}*648g
   3-fold quotients : {12,6}*432b, {12,6}*432g
   6-fold quotients : {6,6}*216b, {6,6}*216d
   9-fold quotients : {12,6}*144a, {12,6}*144b, {12,6}*144c
   12-fold quotients : {6,6}*108
   18-fold quotients : {6,6}*72a, {6,6}*72b, {6,6}*72c
   27-fold quotients : {12,2}*48, {4,6}*48a
   36-fold quotients : {3,6}*36, {6,3}*36
   54-fold quotients : {2,6}*24, {6,2}*24
   81-fold quotients : {4,2}*16
   108-fold quotients : {2,3}*12, {3,2}*12
   162-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,163)(  2,165)(  3,164)(  4,169)(  5,171)(  6,170)(  7,166)(  8,168)
(  9,167)( 10,181)( 11,183)( 12,182)( 13,187)( 14,189)( 15,188)( 16,184)
( 17,186)( 18,185)( 19,172)( 20,174)( 21,173)( 22,178)( 23,180)( 24,179)
( 25,175)( 26,177)( 27,176)( 28,190)( 29,192)( 30,191)( 31,196)( 32,198)
( 33,197)( 34,193)( 35,195)( 36,194)( 37,208)( 38,210)( 39,209)( 40,214)
( 41,216)( 42,215)( 43,211)( 44,213)( 45,212)( 46,199)( 47,201)( 48,200)
( 49,205)( 50,207)( 51,206)( 52,202)( 53,204)( 54,203)( 55,217)( 56,219)
( 57,218)( 58,223)( 59,225)( 60,224)( 61,220)( 62,222)( 63,221)( 64,235)
( 65,237)( 66,236)( 67,241)( 68,243)( 69,242)( 70,238)( 71,240)( 72,239)
( 73,226)( 74,228)( 75,227)( 76,232)( 77,234)( 78,233)( 79,229)( 80,231)
( 81,230)( 82,244)( 83,246)( 84,245)( 85,250)( 86,252)( 87,251)( 88,247)
( 89,249)( 90,248)( 91,262)( 92,264)( 93,263)( 94,268)( 95,270)( 96,269)
( 97,265)( 98,267)( 99,266)(100,253)(101,255)(102,254)(103,259)(104,261)
(105,260)(106,256)(107,258)(108,257)(109,271)(110,273)(111,272)(112,277)
(113,279)(114,278)(115,274)(116,276)(117,275)(118,289)(119,291)(120,290)
(121,295)(122,297)(123,296)(124,292)(125,294)(126,293)(127,280)(128,282)
(129,281)(130,286)(131,288)(132,287)(133,283)(134,285)(135,284)(136,298)
(137,300)(138,299)(139,304)(140,306)(141,305)(142,301)(143,303)(144,302)
(145,316)(146,318)(147,317)(148,322)(149,324)(150,323)(151,319)(152,321)
(153,320)(154,307)(155,309)(156,308)(157,313)(158,315)(159,314)(160,310)
(161,312)(162,311)(325,568)(326,570)(327,569)(328,574)(329,576)(330,575)
(331,571)(332,573)(333,572)(334,586)(335,588)(336,587)(337,592)(338,594)
(339,593)(340,589)(341,591)(342,590)(343,577)(344,579)(345,578)(346,583)
(347,585)(348,584)(349,580)(350,582)(351,581)(352,595)(353,597)(354,596)
(355,601)(356,603)(357,602)(358,598)(359,600)(360,599)(361,613)(362,615)
(363,614)(364,619)(365,621)(366,620)(367,616)(368,618)(369,617)(370,604)
(371,606)(372,605)(373,610)(374,612)(375,611)(376,607)(377,609)(378,608)
(379,622)(380,624)(381,623)(382,628)(383,630)(384,629)(385,625)(386,627)
(387,626)(388,640)(389,642)(390,641)(391,646)(392,648)(393,647)(394,643)
(395,645)(396,644)(397,631)(398,633)(399,632)(400,637)(401,639)(402,638)
(403,634)(404,636)(405,635)(406,487)(407,489)(408,488)(409,493)(410,495)
(411,494)(412,490)(413,492)(414,491)(415,505)(416,507)(417,506)(418,511)
(419,513)(420,512)(421,508)(422,510)(423,509)(424,496)(425,498)(426,497)
(427,502)(428,504)(429,503)(430,499)(431,501)(432,500)(433,514)(434,516)
(435,515)(436,520)(437,522)(438,521)(439,517)(440,519)(441,518)(442,532)
(443,534)(444,533)(445,538)(446,540)(447,539)(448,535)(449,537)(450,536)
(451,523)(452,525)(453,524)(454,529)(455,531)(456,530)(457,526)(458,528)
(459,527)(460,541)(461,543)(462,542)(463,547)(464,549)(465,548)(466,544)
(467,546)(468,545)(469,559)(470,561)(471,560)(472,565)(473,567)(474,566)
(475,562)(476,564)(477,563)(478,550)(479,552)(480,551)(481,556)(482,558)
(483,557)(484,553)(485,555)(486,554);;
s1 := (  1,499)(  2,500)(  3,501)(  4,496)(  5,497)(  6,498)(  7,502)(  8,503)
(  9,504)( 10,490)( 11,491)( 12,492)( 13,487)( 14,488)( 15,489)( 16,493)
( 17,494)( 18,495)( 19,508)( 20,509)( 21,510)( 22,505)( 23,506)( 24,507)
( 25,511)( 26,512)( 27,513)( 28,553)( 29,554)( 30,555)( 31,550)( 32,551)
( 33,552)( 34,556)( 35,557)( 36,558)( 37,544)( 38,545)( 39,546)( 40,541)
( 41,542)( 42,543)( 43,547)( 44,548)( 45,549)( 46,562)( 47,563)( 48,564)
( 49,559)( 50,560)( 51,561)( 52,565)( 53,566)( 54,567)( 55,526)( 56,527)
( 57,528)( 58,523)( 59,524)( 60,525)( 61,529)( 62,530)( 63,531)( 64,517)
( 65,518)( 66,519)( 67,514)( 68,515)( 69,516)( 70,520)( 71,521)( 72,522)
( 73,535)( 74,536)( 75,537)( 76,532)( 77,533)( 78,534)( 79,538)( 80,539)
( 81,540)( 82,580)( 83,581)( 84,582)( 85,577)( 86,578)( 87,579)( 88,583)
( 89,584)( 90,585)( 91,571)( 92,572)( 93,573)( 94,568)( 95,569)( 96,570)
( 97,574)( 98,575)( 99,576)(100,589)(101,590)(102,591)(103,586)(104,587)
(105,588)(106,592)(107,593)(108,594)(109,634)(110,635)(111,636)(112,631)
(113,632)(114,633)(115,637)(116,638)(117,639)(118,625)(119,626)(120,627)
(121,622)(122,623)(123,624)(124,628)(125,629)(126,630)(127,643)(128,644)
(129,645)(130,640)(131,641)(132,642)(133,646)(134,647)(135,648)(136,607)
(137,608)(138,609)(139,604)(140,605)(141,606)(142,610)(143,611)(144,612)
(145,598)(146,599)(147,600)(148,595)(149,596)(150,597)(151,601)(152,602)
(153,603)(154,616)(155,617)(156,618)(157,613)(158,614)(159,615)(160,619)
(161,620)(162,621)(163,337)(164,338)(165,339)(166,334)(167,335)(168,336)
(169,340)(170,341)(171,342)(172,328)(173,329)(174,330)(175,325)(176,326)
(177,327)(178,331)(179,332)(180,333)(181,346)(182,347)(183,348)(184,343)
(185,344)(186,345)(187,349)(188,350)(189,351)(190,391)(191,392)(192,393)
(193,388)(194,389)(195,390)(196,394)(197,395)(198,396)(199,382)(200,383)
(201,384)(202,379)(203,380)(204,381)(205,385)(206,386)(207,387)(208,400)
(209,401)(210,402)(211,397)(212,398)(213,399)(214,403)(215,404)(216,405)
(217,364)(218,365)(219,366)(220,361)(221,362)(222,363)(223,367)(224,368)
(225,369)(226,355)(227,356)(228,357)(229,352)(230,353)(231,354)(232,358)
(233,359)(234,360)(235,373)(236,374)(237,375)(238,370)(239,371)(240,372)
(241,376)(242,377)(243,378)(244,418)(245,419)(246,420)(247,415)(248,416)
(249,417)(250,421)(251,422)(252,423)(253,409)(254,410)(255,411)(256,406)
(257,407)(258,408)(259,412)(260,413)(261,414)(262,427)(263,428)(264,429)
(265,424)(266,425)(267,426)(268,430)(269,431)(270,432)(271,472)(272,473)
(273,474)(274,469)(275,470)(276,471)(277,475)(278,476)(279,477)(280,463)
(281,464)(282,465)(283,460)(284,461)(285,462)(286,466)(287,467)(288,468)
(289,481)(290,482)(291,483)(292,478)(293,479)(294,480)(295,484)(296,485)
(297,486)(298,445)(299,446)(300,447)(301,442)(302,443)(303,444)(304,448)
(305,449)(306,450)(307,436)(308,437)(309,438)(310,433)(311,434)(312,435)
(313,439)(314,440)(315,441)(316,454)(317,455)(318,456)(319,451)(320,452)
(321,453)(322,457)(323,458)(324,459);;
s2 := (  1,514)(  2,516)(  3,515)(  4,518)(  5,517)(  6,519)(  7,522)(  8,521)
(  9,520)( 10,532)( 11,534)( 12,533)( 13,536)( 14,535)( 15,537)( 16,540)
( 17,539)( 18,538)( 19,523)( 20,525)( 21,524)( 22,527)( 23,526)( 24,528)
( 25,531)( 26,530)( 27,529)( 28,487)( 29,489)( 30,488)( 31,491)( 32,490)
( 33,492)( 34,495)( 35,494)( 36,493)( 37,505)( 38,507)( 39,506)( 40,509)
( 41,508)( 42,510)( 43,513)( 44,512)( 45,511)( 46,496)( 47,498)( 48,497)
( 49,500)( 50,499)( 51,501)( 52,504)( 53,503)( 54,502)( 55,541)( 56,543)
( 57,542)( 58,545)( 59,544)( 60,546)( 61,549)( 62,548)( 63,547)( 64,559)
( 65,561)( 66,560)( 67,563)( 68,562)( 69,564)( 70,567)( 71,566)( 72,565)
( 73,550)( 74,552)( 75,551)( 76,554)( 77,553)( 78,555)( 79,558)( 80,557)
( 81,556)( 82,595)( 83,597)( 84,596)( 85,599)( 86,598)( 87,600)( 88,603)
( 89,602)( 90,601)( 91,613)( 92,615)( 93,614)( 94,617)( 95,616)( 96,618)
( 97,621)( 98,620)( 99,619)(100,604)(101,606)(102,605)(103,608)(104,607)
(105,609)(106,612)(107,611)(108,610)(109,568)(110,570)(111,569)(112,572)
(113,571)(114,573)(115,576)(116,575)(117,574)(118,586)(119,588)(120,587)
(121,590)(122,589)(123,591)(124,594)(125,593)(126,592)(127,577)(128,579)
(129,578)(130,581)(131,580)(132,582)(133,585)(134,584)(135,583)(136,622)
(137,624)(138,623)(139,626)(140,625)(141,627)(142,630)(143,629)(144,628)
(145,640)(146,642)(147,641)(148,644)(149,643)(150,645)(151,648)(152,647)
(153,646)(154,631)(155,633)(156,632)(157,635)(158,634)(159,636)(160,639)
(161,638)(162,637)(163,433)(164,435)(165,434)(166,437)(167,436)(168,438)
(169,441)(170,440)(171,439)(172,451)(173,453)(174,452)(175,455)(176,454)
(177,456)(178,459)(179,458)(180,457)(181,442)(182,444)(183,443)(184,446)
(185,445)(186,447)(187,450)(188,449)(189,448)(190,406)(191,408)(192,407)
(193,410)(194,409)(195,411)(196,414)(197,413)(198,412)(199,424)(200,426)
(201,425)(202,428)(203,427)(204,429)(205,432)(206,431)(207,430)(208,415)
(209,417)(210,416)(211,419)(212,418)(213,420)(214,423)(215,422)(216,421)
(217,460)(218,462)(219,461)(220,464)(221,463)(222,465)(223,468)(224,467)
(225,466)(226,478)(227,480)(228,479)(229,482)(230,481)(231,483)(232,486)
(233,485)(234,484)(235,469)(236,471)(237,470)(238,473)(239,472)(240,474)
(241,477)(242,476)(243,475)(244,352)(245,354)(246,353)(247,356)(248,355)
(249,357)(250,360)(251,359)(252,358)(253,370)(254,372)(255,371)(256,374)
(257,373)(258,375)(259,378)(260,377)(261,376)(262,361)(263,363)(264,362)
(265,365)(266,364)(267,366)(268,369)(269,368)(270,367)(271,325)(272,327)
(273,326)(274,329)(275,328)(276,330)(277,333)(278,332)(279,331)(280,343)
(281,345)(282,344)(283,347)(284,346)(285,348)(286,351)(287,350)(288,349)
(289,334)(290,336)(291,335)(292,338)(293,337)(294,339)(295,342)(296,341)
(297,340)(298,379)(299,381)(300,380)(301,383)(302,382)(303,384)(304,387)
(305,386)(306,385)(307,397)(308,399)(309,398)(310,401)(311,400)(312,402)
(313,405)(314,404)(315,403)(316,388)(317,390)(318,389)(319,392)(320,391)
(321,393)(322,396)(323,395)(324,394);;
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*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(648)!(  1,163)(  2,165)(  3,164)(  4,169)(  5,171)(  6,170)(  7,166)
(  8,168)(  9,167)( 10,181)( 11,183)( 12,182)( 13,187)( 14,189)( 15,188)
( 16,184)( 17,186)( 18,185)( 19,172)( 20,174)( 21,173)( 22,178)( 23,180)
( 24,179)( 25,175)( 26,177)( 27,176)( 28,190)( 29,192)( 30,191)( 31,196)
( 32,198)( 33,197)( 34,193)( 35,195)( 36,194)( 37,208)( 38,210)( 39,209)
( 40,214)( 41,216)( 42,215)( 43,211)( 44,213)( 45,212)( 46,199)( 47,201)
( 48,200)( 49,205)( 50,207)( 51,206)( 52,202)( 53,204)( 54,203)( 55,217)
( 56,219)( 57,218)( 58,223)( 59,225)( 60,224)( 61,220)( 62,222)( 63,221)
( 64,235)( 65,237)( 66,236)( 67,241)( 68,243)( 69,242)( 70,238)( 71,240)
( 72,239)( 73,226)( 74,228)( 75,227)( 76,232)( 77,234)( 78,233)( 79,229)
( 80,231)( 81,230)( 82,244)( 83,246)( 84,245)( 85,250)( 86,252)( 87,251)
( 88,247)( 89,249)( 90,248)( 91,262)( 92,264)( 93,263)( 94,268)( 95,270)
( 96,269)( 97,265)( 98,267)( 99,266)(100,253)(101,255)(102,254)(103,259)
(104,261)(105,260)(106,256)(107,258)(108,257)(109,271)(110,273)(111,272)
(112,277)(113,279)(114,278)(115,274)(116,276)(117,275)(118,289)(119,291)
(120,290)(121,295)(122,297)(123,296)(124,292)(125,294)(126,293)(127,280)
(128,282)(129,281)(130,286)(131,288)(132,287)(133,283)(134,285)(135,284)
(136,298)(137,300)(138,299)(139,304)(140,306)(141,305)(142,301)(143,303)
(144,302)(145,316)(146,318)(147,317)(148,322)(149,324)(150,323)(151,319)
(152,321)(153,320)(154,307)(155,309)(156,308)(157,313)(158,315)(159,314)
(160,310)(161,312)(162,311)(325,568)(326,570)(327,569)(328,574)(329,576)
(330,575)(331,571)(332,573)(333,572)(334,586)(335,588)(336,587)(337,592)
(338,594)(339,593)(340,589)(341,591)(342,590)(343,577)(344,579)(345,578)
(346,583)(347,585)(348,584)(349,580)(350,582)(351,581)(352,595)(353,597)
(354,596)(355,601)(356,603)(357,602)(358,598)(359,600)(360,599)(361,613)
(362,615)(363,614)(364,619)(365,621)(366,620)(367,616)(368,618)(369,617)
(370,604)(371,606)(372,605)(373,610)(374,612)(375,611)(376,607)(377,609)
(378,608)(379,622)(380,624)(381,623)(382,628)(383,630)(384,629)(385,625)
(386,627)(387,626)(388,640)(389,642)(390,641)(391,646)(392,648)(393,647)
(394,643)(395,645)(396,644)(397,631)(398,633)(399,632)(400,637)(401,639)
(402,638)(403,634)(404,636)(405,635)(406,487)(407,489)(408,488)(409,493)
(410,495)(411,494)(412,490)(413,492)(414,491)(415,505)(416,507)(417,506)
(418,511)(419,513)(420,512)(421,508)(422,510)(423,509)(424,496)(425,498)
(426,497)(427,502)(428,504)(429,503)(430,499)(431,501)(432,500)(433,514)
(434,516)(435,515)(436,520)(437,522)(438,521)(439,517)(440,519)(441,518)
(442,532)(443,534)(444,533)(445,538)(446,540)(447,539)(448,535)(449,537)
(450,536)(451,523)(452,525)(453,524)(454,529)(455,531)(456,530)(457,526)
(458,528)(459,527)(460,541)(461,543)(462,542)(463,547)(464,549)(465,548)
(466,544)(467,546)(468,545)(469,559)(470,561)(471,560)(472,565)(473,567)
(474,566)(475,562)(476,564)(477,563)(478,550)(479,552)(480,551)(481,556)
(482,558)(483,557)(484,553)(485,555)(486,554);
s1 := Sym(648)!(  1,499)(  2,500)(  3,501)(  4,496)(  5,497)(  6,498)(  7,502)
(  8,503)(  9,504)( 10,490)( 11,491)( 12,492)( 13,487)( 14,488)( 15,489)
( 16,493)( 17,494)( 18,495)( 19,508)( 20,509)( 21,510)( 22,505)( 23,506)
( 24,507)( 25,511)( 26,512)( 27,513)( 28,553)( 29,554)( 30,555)( 31,550)
( 32,551)( 33,552)( 34,556)( 35,557)( 36,558)( 37,544)( 38,545)( 39,546)
( 40,541)( 41,542)( 42,543)( 43,547)( 44,548)( 45,549)( 46,562)( 47,563)
( 48,564)( 49,559)( 50,560)( 51,561)( 52,565)( 53,566)( 54,567)( 55,526)
( 56,527)( 57,528)( 58,523)( 59,524)( 60,525)( 61,529)( 62,530)( 63,531)
( 64,517)( 65,518)( 66,519)( 67,514)( 68,515)( 69,516)( 70,520)( 71,521)
( 72,522)( 73,535)( 74,536)( 75,537)( 76,532)( 77,533)( 78,534)( 79,538)
( 80,539)( 81,540)( 82,580)( 83,581)( 84,582)( 85,577)( 86,578)( 87,579)
( 88,583)( 89,584)( 90,585)( 91,571)( 92,572)( 93,573)( 94,568)( 95,569)
( 96,570)( 97,574)( 98,575)( 99,576)(100,589)(101,590)(102,591)(103,586)
(104,587)(105,588)(106,592)(107,593)(108,594)(109,634)(110,635)(111,636)
(112,631)(113,632)(114,633)(115,637)(116,638)(117,639)(118,625)(119,626)
(120,627)(121,622)(122,623)(123,624)(124,628)(125,629)(126,630)(127,643)
(128,644)(129,645)(130,640)(131,641)(132,642)(133,646)(134,647)(135,648)
(136,607)(137,608)(138,609)(139,604)(140,605)(141,606)(142,610)(143,611)
(144,612)(145,598)(146,599)(147,600)(148,595)(149,596)(150,597)(151,601)
(152,602)(153,603)(154,616)(155,617)(156,618)(157,613)(158,614)(159,615)
(160,619)(161,620)(162,621)(163,337)(164,338)(165,339)(166,334)(167,335)
(168,336)(169,340)(170,341)(171,342)(172,328)(173,329)(174,330)(175,325)
(176,326)(177,327)(178,331)(179,332)(180,333)(181,346)(182,347)(183,348)
(184,343)(185,344)(186,345)(187,349)(188,350)(189,351)(190,391)(191,392)
(192,393)(193,388)(194,389)(195,390)(196,394)(197,395)(198,396)(199,382)
(200,383)(201,384)(202,379)(203,380)(204,381)(205,385)(206,386)(207,387)
(208,400)(209,401)(210,402)(211,397)(212,398)(213,399)(214,403)(215,404)
(216,405)(217,364)(218,365)(219,366)(220,361)(221,362)(222,363)(223,367)
(224,368)(225,369)(226,355)(227,356)(228,357)(229,352)(230,353)(231,354)
(232,358)(233,359)(234,360)(235,373)(236,374)(237,375)(238,370)(239,371)
(240,372)(241,376)(242,377)(243,378)(244,418)(245,419)(246,420)(247,415)
(248,416)(249,417)(250,421)(251,422)(252,423)(253,409)(254,410)(255,411)
(256,406)(257,407)(258,408)(259,412)(260,413)(261,414)(262,427)(263,428)
(264,429)(265,424)(266,425)(267,426)(268,430)(269,431)(270,432)(271,472)
(272,473)(273,474)(274,469)(275,470)(276,471)(277,475)(278,476)(279,477)
(280,463)(281,464)(282,465)(283,460)(284,461)(285,462)(286,466)(287,467)
(288,468)(289,481)(290,482)(291,483)(292,478)(293,479)(294,480)(295,484)
(296,485)(297,486)(298,445)(299,446)(300,447)(301,442)(302,443)(303,444)
(304,448)(305,449)(306,450)(307,436)(308,437)(309,438)(310,433)(311,434)
(312,435)(313,439)(314,440)(315,441)(316,454)(317,455)(318,456)(319,451)
(320,452)(321,453)(322,457)(323,458)(324,459);
s2 := Sym(648)!(  1,514)(  2,516)(  3,515)(  4,518)(  5,517)(  6,519)(  7,522)
(  8,521)(  9,520)( 10,532)( 11,534)( 12,533)( 13,536)( 14,535)( 15,537)
( 16,540)( 17,539)( 18,538)( 19,523)( 20,525)( 21,524)( 22,527)( 23,526)
( 24,528)( 25,531)( 26,530)( 27,529)( 28,487)( 29,489)( 30,488)( 31,491)
( 32,490)( 33,492)( 34,495)( 35,494)( 36,493)( 37,505)( 38,507)( 39,506)
( 40,509)( 41,508)( 42,510)( 43,513)( 44,512)( 45,511)( 46,496)( 47,498)
( 48,497)( 49,500)( 50,499)( 51,501)( 52,504)( 53,503)( 54,502)( 55,541)
( 56,543)( 57,542)( 58,545)( 59,544)( 60,546)( 61,549)( 62,548)( 63,547)
( 64,559)( 65,561)( 66,560)( 67,563)( 68,562)( 69,564)( 70,567)( 71,566)
( 72,565)( 73,550)( 74,552)( 75,551)( 76,554)( 77,553)( 78,555)( 79,558)
( 80,557)( 81,556)( 82,595)( 83,597)( 84,596)( 85,599)( 86,598)( 87,600)
( 88,603)( 89,602)( 90,601)( 91,613)( 92,615)( 93,614)( 94,617)( 95,616)
( 96,618)( 97,621)( 98,620)( 99,619)(100,604)(101,606)(102,605)(103,608)
(104,607)(105,609)(106,612)(107,611)(108,610)(109,568)(110,570)(111,569)
(112,572)(113,571)(114,573)(115,576)(116,575)(117,574)(118,586)(119,588)
(120,587)(121,590)(122,589)(123,591)(124,594)(125,593)(126,592)(127,577)
(128,579)(129,578)(130,581)(131,580)(132,582)(133,585)(134,584)(135,583)
(136,622)(137,624)(138,623)(139,626)(140,625)(141,627)(142,630)(143,629)
(144,628)(145,640)(146,642)(147,641)(148,644)(149,643)(150,645)(151,648)
(152,647)(153,646)(154,631)(155,633)(156,632)(157,635)(158,634)(159,636)
(160,639)(161,638)(162,637)(163,433)(164,435)(165,434)(166,437)(167,436)
(168,438)(169,441)(170,440)(171,439)(172,451)(173,453)(174,452)(175,455)
(176,454)(177,456)(178,459)(179,458)(180,457)(181,442)(182,444)(183,443)
(184,446)(185,445)(186,447)(187,450)(188,449)(189,448)(190,406)(191,408)
(192,407)(193,410)(194,409)(195,411)(196,414)(197,413)(198,412)(199,424)
(200,426)(201,425)(202,428)(203,427)(204,429)(205,432)(206,431)(207,430)
(208,415)(209,417)(210,416)(211,419)(212,418)(213,420)(214,423)(215,422)
(216,421)(217,460)(218,462)(219,461)(220,464)(221,463)(222,465)(223,468)
(224,467)(225,466)(226,478)(227,480)(228,479)(229,482)(230,481)(231,483)
(232,486)(233,485)(234,484)(235,469)(236,471)(237,470)(238,473)(239,472)
(240,474)(241,477)(242,476)(243,475)(244,352)(245,354)(246,353)(247,356)
(248,355)(249,357)(250,360)(251,359)(252,358)(253,370)(254,372)(255,371)
(256,374)(257,373)(258,375)(259,378)(260,377)(261,376)(262,361)(263,363)
(264,362)(265,365)(266,364)(267,366)(268,369)(269,368)(270,367)(271,325)
(272,327)(273,326)(274,329)(275,328)(276,330)(277,333)(278,332)(279,331)
(280,343)(281,345)(282,344)(283,347)(284,346)(285,348)(286,351)(287,350)
(288,349)(289,334)(290,336)(291,335)(292,338)(293,337)(294,339)(295,342)
(296,341)(297,340)(298,379)(299,381)(300,380)(301,383)(302,382)(303,384)
(304,387)(305,386)(306,385)(307,397)(308,399)(309,398)(310,401)(311,400)
(312,402)(313,405)(314,404)(315,403)(316,388)(317,390)(318,389)(319,392)
(320,391)(321,393)(322,396)(323,395)(324,394);
poly := sub<Sym(648)|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*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*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 >;

References : None.
to this polytope