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Polytope of Type {9,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,6,6}*1944b
if this polytope has a name.
Group : SmallGroup(1944,952)
Rank : 4
Schlafli Type : {9,6,6}
Number of vertices, edges, etc : 9, 81, 54, 18
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 6
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 : {9,6,3}*972b
   3-fold quotients : {9,6,6}*648a, {3,6,6}*648b
   6-fold quotients : {9,6,3}*324, {3,6,3}*324a
   9-fold quotients : {9,2,6}*216, {3,6,6}*216a
   18-fold quotients : {9,2,3}*108, {3,6,3}*108
   27-fold quotients : {9,2,2}*72, {3,2,6}*72
   54-fold quotients : {3,2,3}*36
   81-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 10, 19)( 11, 21)( 12, 20)( 13, 25)
( 14, 27)( 15, 26)( 16, 22)( 17, 24)( 18, 23)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)
( 44, 51)( 45, 50)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 73)( 65, 75)
( 66, 74)( 67, 79)( 68, 81)( 69, 80)( 70, 76)( 71, 78)( 72, 77)( 82,172)
( 83,174)( 84,173)( 85,178)( 86,180)( 87,179)( 88,175)( 89,177)( 90,176)
( 91,163)( 92,165)( 93,164)( 94,169)( 95,171)( 96,170)( 97,166)( 98,168)
( 99,167)(100,181)(101,183)(102,182)(103,187)(104,189)(105,188)(106,184)
(107,186)(108,185)(109,199)(110,201)(111,200)(112,205)(113,207)(114,206)
(115,202)(116,204)(117,203)(118,190)(119,192)(120,191)(121,196)(122,198)
(123,197)(124,193)(125,195)(126,194)(127,208)(128,210)(129,209)(130,214)
(131,216)(132,215)(133,211)(134,213)(135,212)(136,226)(137,228)(138,227)
(139,232)(140,234)(141,233)(142,229)(143,231)(144,230)(145,217)(146,219)
(147,218)(148,223)(149,225)(150,224)(151,220)(152,222)(153,221)(154,235)
(155,237)(156,236)(157,241)(158,243)(159,242)(160,238)(161,240)(162,239)
(245,246)(247,250)(248,252)(249,251)(253,262)(254,264)(255,263)(256,268)
(257,270)(258,269)(259,265)(260,267)(261,266)(272,273)(274,277)(275,279)
(276,278)(280,289)(281,291)(282,290)(283,295)(284,297)(285,296)(286,292)
(287,294)(288,293)(299,300)(301,304)(302,306)(303,305)(307,316)(308,318)
(309,317)(310,322)(311,324)(312,323)(313,319)(314,321)(315,320)(325,415)
(326,417)(327,416)(328,421)(329,423)(330,422)(331,418)(332,420)(333,419)
(334,406)(335,408)(336,407)(337,412)(338,414)(339,413)(340,409)(341,411)
(342,410)(343,424)(344,426)(345,425)(346,430)(347,432)(348,431)(349,427)
(350,429)(351,428)(352,442)(353,444)(354,443)(355,448)(356,450)(357,449)
(358,445)(359,447)(360,446)(361,433)(362,435)(363,434)(364,439)(365,441)
(366,440)(367,436)(368,438)(369,437)(370,451)(371,453)(372,452)(373,457)
(374,459)(375,458)(376,454)(377,456)(378,455)(379,469)(380,471)(381,470)
(382,475)(383,477)(384,476)(385,472)(386,474)(387,473)(388,460)(389,462)
(390,461)(391,466)(392,468)(393,467)(394,463)(395,465)(396,464)(397,478)
(398,480)(399,479)(400,484)(401,486)(402,485)(403,481)(404,483)(405,482);;
s1 := (  1, 82)(  2, 84)(  3, 83)(  4, 88)(  5, 90)(  6, 89)(  7, 85)(  8, 87)
(  9, 86)( 10,100)( 11,102)( 12,101)( 13,106)( 14,108)( 15,107)( 16,103)
( 17,105)( 18,104)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)( 24, 98)
( 25, 94)( 26, 96)( 27, 95)( 28,113)( 29,112)( 30,114)( 31,110)( 32,109)
( 33,111)( 34,116)( 35,115)( 36,117)( 37,131)( 38,130)( 39,132)( 40,128)
( 41,127)( 42,129)( 43,134)( 44,133)( 45,135)( 46,122)( 47,121)( 48,123)
( 49,119)( 50,118)( 51,120)( 52,125)( 53,124)( 54,126)( 55,143)( 56,142)
( 57,144)( 58,140)( 59,139)( 60,141)( 61,137)( 62,136)( 63,138)( 64,161)
( 65,160)( 66,162)( 67,158)( 68,157)( 69,159)( 70,155)( 71,154)( 72,156)
( 73,152)( 74,151)( 75,153)( 76,149)( 77,148)( 78,150)( 79,146)( 80,145)
( 81,147)(163,172)(164,174)(165,173)(166,178)(167,180)(168,179)(169,175)
(170,177)(171,176)(182,183)(184,187)(185,189)(186,188)(190,203)(191,202)
(192,204)(193,200)(194,199)(195,201)(196,206)(197,205)(198,207)(208,212)
(209,211)(210,213)(214,215)(217,233)(218,232)(219,234)(220,230)(221,229)
(222,231)(223,227)(224,226)(225,228)(235,242)(236,241)(237,243)(238,239)
(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)(251,330)
(252,329)(253,343)(254,345)(255,344)(256,349)(257,351)(258,350)(259,346)
(260,348)(261,347)(262,334)(263,336)(264,335)(265,340)(266,342)(267,341)
(268,337)(269,339)(270,338)(271,356)(272,355)(273,357)(274,353)(275,352)
(276,354)(277,359)(278,358)(279,360)(280,374)(281,373)(282,375)(283,371)
(284,370)(285,372)(286,377)(287,376)(288,378)(289,365)(290,364)(291,366)
(292,362)(293,361)(294,363)(295,368)(296,367)(297,369)(298,386)(299,385)
(300,387)(301,383)(302,382)(303,384)(304,380)(305,379)(306,381)(307,404)
(308,403)(309,405)(310,401)(311,400)(312,402)(313,398)(314,397)(315,399)
(316,395)(317,394)(318,396)(319,392)(320,391)(321,393)(322,389)(323,388)
(324,390)(406,415)(407,417)(408,416)(409,421)(410,423)(411,422)(412,418)
(413,420)(414,419)(425,426)(427,430)(428,432)(429,431)(433,446)(434,445)
(435,447)(436,443)(437,442)(438,444)(439,449)(440,448)(441,450)(451,455)
(452,454)(453,456)(457,458)(460,476)(461,475)(462,477)(463,473)(464,472)
(465,474)(466,470)(467,469)(468,471)(478,485)(479,484)(480,486)(481,482);;
s2 := (  1, 28)(  2, 29)(  3, 30)(  4, 35)(  5, 36)(  6, 34)(  7, 33)(  8, 31)
(  9, 32)( 10, 37)( 11, 38)( 12, 39)( 13, 44)( 14, 45)( 15, 43)( 16, 42)
( 17, 40)( 18, 41)( 19, 46)( 20, 47)( 21, 48)( 22, 53)( 23, 54)( 24, 52)
( 25, 51)( 26, 49)( 27, 50)( 58, 62)( 59, 63)( 60, 61)( 67, 71)( 68, 72)
( 69, 70)( 76, 80)( 77, 81)( 78, 79)( 82,109)( 83,110)( 84,111)( 85,116)
( 86,117)( 87,115)( 88,114)( 89,112)( 90,113)( 91,118)( 92,119)( 93,120)
( 94,125)( 95,126)( 96,124)( 97,123)( 98,121)( 99,122)(100,127)(101,128)
(102,129)(103,134)(104,135)(105,133)(106,132)(107,130)(108,131)(139,143)
(140,144)(141,142)(148,152)(149,153)(150,151)(157,161)(158,162)(159,160)
(163,190)(164,191)(165,192)(166,197)(167,198)(168,196)(169,195)(170,193)
(171,194)(172,199)(173,200)(174,201)(175,206)(176,207)(177,205)(178,204)
(179,202)(180,203)(181,208)(182,209)(183,210)(184,215)(185,216)(186,214)
(187,213)(188,211)(189,212)(220,224)(221,225)(222,223)(229,233)(230,234)
(231,232)(238,242)(239,243)(240,241)(244,271)(245,272)(246,273)(247,278)
(248,279)(249,277)(250,276)(251,274)(252,275)(253,280)(254,281)(255,282)
(256,287)(257,288)(258,286)(259,285)(260,283)(261,284)(262,289)(263,290)
(264,291)(265,296)(266,297)(267,295)(268,294)(269,292)(270,293)(301,305)
(302,306)(303,304)(310,314)(311,315)(312,313)(319,323)(320,324)(321,322)
(325,352)(326,353)(327,354)(328,359)(329,360)(330,358)(331,357)(332,355)
(333,356)(334,361)(335,362)(336,363)(337,368)(338,369)(339,367)(340,366)
(341,364)(342,365)(343,370)(344,371)(345,372)(346,377)(347,378)(348,376)
(349,375)(350,373)(351,374)(382,386)(383,387)(384,385)(391,395)(392,396)
(393,394)(400,404)(401,405)(402,403)(406,433)(407,434)(408,435)(409,440)
(410,441)(411,439)(412,438)(413,436)(414,437)(415,442)(416,443)(417,444)
(418,449)(419,450)(420,448)(421,447)(422,445)(423,446)(424,451)(425,452)
(426,453)(427,458)(428,459)(429,457)(430,456)(431,454)(432,455)(463,467)
(464,468)(465,466)(472,476)(473,477)(474,475)(481,485)(482,486)(483,484);;
s3 := (  1,244)(  2,245)(  3,246)(  4,250)(  5,251)(  6,252)(  7,247)(  8,248)
(  9,249)( 10,253)( 11,254)( 12,255)( 13,259)( 14,260)( 15,261)( 16,256)
( 17,257)( 18,258)( 19,262)( 20,263)( 21,264)( 22,268)( 23,269)( 24,270)
( 25,265)( 26,266)( 27,267)( 28,298)( 29,299)( 30,300)( 31,304)( 32,305)
( 33,306)( 34,301)( 35,302)( 36,303)( 37,307)( 38,308)( 39,309)( 40,313)
( 41,314)( 42,315)( 43,310)( 44,311)( 45,312)( 46,316)( 47,317)( 48,318)
( 49,322)( 50,323)( 51,324)( 52,319)( 53,320)( 54,321)( 55,271)( 56,272)
( 57,273)( 58,277)( 59,278)( 60,279)( 61,274)( 62,275)( 63,276)( 64,280)
( 65,281)( 66,282)( 67,286)( 68,287)( 69,288)( 70,283)( 71,284)( 72,285)
( 73,289)( 74,290)( 75,291)( 76,295)( 77,296)( 78,297)( 79,292)( 80,293)
( 81,294)( 82,325)( 83,326)( 84,327)( 85,331)( 86,332)( 87,333)( 88,328)
( 89,329)( 90,330)( 91,334)( 92,335)( 93,336)( 94,340)( 95,341)( 96,342)
( 97,337)( 98,338)( 99,339)(100,343)(101,344)(102,345)(103,349)(104,350)
(105,351)(106,346)(107,347)(108,348)(109,379)(110,380)(111,381)(112,385)
(113,386)(114,387)(115,382)(116,383)(117,384)(118,388)(119,389)(120,390)
(121,394)(122,395)(123,396)(124,391)(125,392)(126,393)(127,397)(128,398)
(129,399)(130,403)(131,404)(132,405)(133,400)(134,401)(135,402)(136,352)
(137,353)(138,354)(139,358)(140,359)(141,360)(142,355)(143,356)(144,357)
(145,361)(146,362)(147,363)(148,367)(149,368)(150,369)(151,364)(152,365)
(153,366)(154,370)(155,371)(156,372)(157,376)(158,377)(159,378)(160,373)
(161,374)(162,375)(163,406)(164,407)(165,408)(166,412)(167,413)(168,414)
(169,409)(170,410)(171,411)(172,415)(173,416)(174,417)(175,421)(176,422)
(177,423)(178,418)(179,419)(180,420)(181,424)(182,425)(183,426)(184,430)
(185,431)(186,432)(187,427)(188,428)(189,429)(190,460)(191,461)(192,462)
(193,466)(194,467)(195,468)(196,463)(197,464)(198,465)(199,469)(200,470)
(201,471)(202,475)(203,476)(204,477)(205,472)(206,473)(207,474)(208,478)
(209,479)(210,480)(211,484)(212,485)(213,486)(214,481)(215,482)(216,483)
(217,433)(218,434)(219,435)(220,439)(221,440)(222,441)(223,436)(224,437)
(225,438)(226,442)(227,443)(228,444)(229,448)(230,449)(231,450)(232,445)
(233,446)(234,447)(235,451)(236,452)(237,453)(238,457)(239,458)(240,459)
(241,454)(242,455)(243,456);;
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*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(486)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 10, 19)( 11, 21)( 12, 20)
( 13, 25)( 14, 27)( 15, 26)( 16, 22)( 17, 24)( 18, 23)( 29, 30)( 31, 34)
( 32, 36)( 33, 35)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)
( 43, 49)( 44, 51)( 45, 50)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 73)
( 65, 75)( 66, 74)( 67, 79)( 68, 81)( 69, 80)( 70, 76)( 71, 78)( 72, 77)
( 82,172)( 83,174)( 84,173)( 85,178)( 86,180)( 87,179)( 88,175)( 89,177)
( 90,176)( 91,163)( 92,165)( 93,164)( 94,169)( 95,171)( 96,170)( 97,166)
( 98,168)( 99,167)(100,181)(101,183)(102,182)(103,187)(104,189)(105,188)
(106,184)(107,186)(108,185)(109,199)(110,201)(111,200)(112,205)(113,207)
(114,206)(115,202)(116,204)(117,203)(118,190)(119,192)(120,191)(121,196)
(122,198)(123,197)(124,193)(125,195)(126,194)(127,208)(128,210)(129,209)
(130,214)(131,216)(132,215)(133,211)(134,213)(135,212)(136,226)(137,228)
(138,227)(139,232)(140,234)(141,233)(142,229)(143,231)(144,230)(145,217)
(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)(152,222)(153,221)
(154,235)(155,237)(156,236)(157,241)(158,243)(159,242)(160,238)(161,240)
(162,239)(245,246)(247,250)(248,252)(249,251)(253,262)(254,264)(255,263)
(256,268)(257,270)(258,269)(259,265)(260,267)(261,266)(272,273)(274,277)
(275,279)(276,278)(280,289)(281,291)(282,290)(283,295)(284,297)(285,296)
(286,292)(287,294)(288,293)(299,300)(301,304)(302,306)(303,305)(307,316)
(308,318)(309,317)(310,322)(311,324)(312,323)(313,319)(314,321)(315,320)
(325,415)(326,417)(327,416)(328,421)(329,423)(330,422)(331,418)(332,420)
(333,419)(334,406)(335,408)(336,407)(337,412)(338,414)(339,413)(340,409)
(341,411)(342,410)(343,424)(344,426)(345,425)(346,430)(347,432)(348,431)
(349,427)(350,429)(351,428)(352,442)(353,444)(354,443)(355,448)(356,450)
(357,449)(358,445)(359,447)(360,446)(361,433)(362,435)(363,434)(364,439)
(365,441)(366,440)(367,436)(368,438)(369,437)(370,451)(371,453)(372,452)
(373,457)(374,459)(375,458)(376,454)(377,456)(378,455)(379,469)(380,471)
(381,470)(382,475)(383,477)(384,476)(385,472)(386,474)(387,473)(388,460)
(389,462)(390,461)(391,466)(392,468)(393,467)(394,463)(395,465)(396,464)
(397,478)(398,480)(399,479)(400,484)(401,486)(402,485)(403,481)(404,483)
(405,482);
s1 := Sym(486)!(  1, 82)(  2, 84)(  3, 83)(  4, 88)(  5, 90)(  6, 89)(  7, 85)
(  8, 87)(  9, 86)( 10,100)( 11,102)( 12,101)( 13,106)( 14,108)( 15,107)
( 16,103)( 17,105)( 18,104)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)
( 24, 98)( 25, 94)( 26, 96)( 27, 95)( 28,113)( 29,112)( 30,114)( 31,110)
( 32,109)( 33,111)( 34,116)( 35,115)( 36,117)( 37,131)( 38,130)( 39,132)
( 40,128)( 41,127)( 42,129)( 43,134)( 44,133)( 45,135)( 46,122)( 47,121)
( 48,123)( 49,119)( 50,118)( 51,120)( 52,125)( 53,124)( 54,126)( 55,143)
( 56,142)( 57,144)( 58,140)( 59,139)( 60,141)( 61,137)( 62,136)( 63,138)
( 64,161)( 65,160)( 66,162)( 67,158)( 68,157)( 69,159)( 70,155)( 71,154)
( 72,156)( 73,152)( 74,151)( 75,153)( 76,149)( 77,148)( 78,150)( 79,146)
( 80,145)( 81,147)(163,172)(164,174)(165,173)(166,178)(167,180)(168,179)
(169,175)(170,177)(171,176)(182,183)(184,187)(185,189)(186,188)(190,203)
(191,202)(192,204)(193,200)(194,199)(195,201)(196,206)(197,205)(198,207)
(208,212)(209,211)(210,213)(214,215)(217,233)(218,232)(219,234)(220,230)
(221,229)(222,231)(223,227)(224,226)(225,228)(235,242)(236,241)(237,243)
(238,239)(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)
(251,330)(252,329)(253,343)(254,345)(255,344)(256,349)(257,351)(258,350)
(259,346)(260,348)(261,347)(262,334)(263,336)(264,335)(265,340)(266,342)
(267,341)(268,337)(269,339)(270,338)(271,356)(272,355)(273,357)(274,353)
(275,352)(276,354)(277,359)(278,358)(279,360)(280,374)(281,373)(282,375)
(283,371)(284,370)(285,372)(286,377)(287,376)(288,378)(289,365)(290,364)
(291,366)(292,362)(293,361)(294,363)(295,368)(296,367)(297,369)(298,386)
(299,385)(300,387)(301,383)(302,382)(303,384)(304,380)(305,379)(306,381)
(307,404)(308,403)(309,405)(310,401)(311,400)(312,402)(313,398)(314,397)
(315,399)(316,395)(317,394)(318,396)(319,392)(320,391)(321,393)(322,389)
(323,388)(324,390)(406,415)(407,417)(408,416)(409,421)(410,423)(411,422)
(412,418)(413,420)(414,419)(425,426)(427,430)(428,432)(429,431)(433,446)
(434,445)(435,447)(436,443)(437,442)(438,444)(439,449)(440,448)(441,450)
(451,455)(452,454)(453,456)(457,458)(460,476)(461,475)(462,477)(463,473)
(464,472)(465,474)(466,470)(467,469)(468,471)(478,485)(479,484)(480,486)
(481,482);
s2 := Sym(486)!(  1, 28)(  2, 29)(  3, 30)(  4, 35)(  5, 36)(  6, 34)(  7, 33)
(  8, 31)(  9, 32)( 10, 37)( 11, 38)( 12, 39)( 13, 44)( 14, 45)( 15, 43)
( 16, 42)( 17, 40)( 18, 41)( 19, 46)( 20, 47)( 21, 48)( 22, 53)( 23, 54)
( 24, 52)( 25, 51)( 26, 49)( 27, 50)( 58, 62)( 59, 63)( 60, 61)( 67, 71)
( 68, 72)( 69, 70)( 76, 80)( 77, 81)( 78, 79)( 82,109)( 83,110)( 84,111)
( 85,116)( 86,117)( 87,115)( 88,114)( 89,112)( 90,113)( 91,118)( 92,119)
( 93,120)( 94,125)( 95,126)( 96,124)( 97,123)( 98,121)( 99,122)(100,127)
(101,128)(102,129)(103,134)(104,135)(105,133)(106,132)(107,130)(108,131)
(139,143)(140,144)(141,142)(148,152)(149,153)(150,151)(157,161)(158,162)
(159,160)(163,190)(164,191)(165,192)(166,197)(167,198)(168,196)(169,195)
(170,193)(171,194)(172,199)(173,200)(174,201)(175,206)(176,207)(177,205)
(178,204)(179,202)(180,203)(181,208)(182,209)(183,210)(184,215)(185,216)
(186,214)(187,213)(188,211)(189,212)(220,224)(221,225)(222,223)(229,233)
(230,234)(231,232)(238,242)(239,243)(240,241)(244,271)(245,272)(246,273)
(247,278)(248,279)(249,277)(250,276)(251,274)(252,275)(253,280)(254,281)
(255,282)(256,287)(257,288)(258,286)(259,285)(260,283)(261,284)(262,289)
(263,290)(264,291)(265,296)(266,297)(267,295)(268,294)(269,292)(270,293)
(301,305)(302,306)(303,304)(310,314)(311,315)(312,313)(319,323)(320,324)
(321,322)(325,352)(326,353)(327,354)(328,359)(329,360)(330,358)(331,357)
(332,355)(333,356)(334,361)(335,362)(336,363)(337,368)(338,369)(339,367)
(340,366)(341,364)(342,365)(343,370)(344,371)(345,372)(346,377)(347,378)
(348,376)(349,375)(350,373)(351,374)(382,386)(383,387)(384,385)(391,395)
(392,396)(393,394)(400,404)(401,405)(402,403)(406,433)(407,434)(408,435)
(409,440)(410,441)(411,439)(412,438)(413,436)(414,437)(415,442)(416,443)
(417,444)(418,449)(419,450)(420,448)(421,447)(422,445)(423,446)(424,451)
(425,452)(426,453)(427,458)(428,459)(429,457)(430,456)(431,454)(432,455)
(463,467)(464,468)(465,466)(472,476)(473,477)(474,475)(481,485)(482,486)
(483,484);
s3 := Sym(486)!(  1,244)(  2,245)(  3,246)(  4,250)(  5,251)(  6,252)(  7,247)
(  8,248)(  9,249)( 10,253)( 11,254)( 12,255)( 13,259)( 14,260)( 15,261)
( 16,256)( 17,257)( 18,258)( 19,262)( 20,263)( 21,264)( 22,268)( 23,269)
( 24,270)( 25,265)( 26,266)( 27,267)( 28,298)( 29,299)( 30,300)( 31,304)
( 32,305)( 33,306)( 34,301)( 35,302)( 36,303)( 37,307)( 38,308)( 39,309)
( 40,313)( 41,314)( 42,315)( 43,310)( 44,311)( 45,312)( 46,316)( 47,317)
( 48,318)( 49,322)( 50,323)( 51,324)( 52,319)( 53,320)( 54,321)( 55,271)
( 56,272)( 57,273)( 58,277)( 59,278)( 60,279)( 61,274)( 62,275)( 63,276)
( 64,280)( 65,281)( 66,282)( 67,286)( 68,287)( 69,288)( 70,283)( 71,284)
( 72,285)( 73,289)( 74,290)( 75,291)( 76,295)( 77,296)( 78,297)( 79,292)
( 80,293)( 81,294)( 82,325)( 83,326)( 84,327)( 85,331)( 86,332)( 87,333)
( 88,328)( 89,329)( 90,330)( 91,334)( 92,335)( 93,336)( 94,340)( 95,341)
( 96,342)( 97,337)( 98,338)( 99,339)(100,343)(101,344)(102,345)(103,349)
(104,350)(105,351)(106,346)(107,347)(108,348)(109,379)(110,380)(111,381)
(112,385)(113,386)(114,387)(115,382)(116,383)(117,384)(118,388)(119,389)
(120,390)(121,394)(122,395)(123,396)(124,391)(125,392)(126,393)(127,397)
(128,398)(129,399)(130,403)(131,404)(132,405)(133,400)(134,401)(135,402)
(136,352)(137,353)(138,354)(139,358)(140,359)(141,360)(142,355)(143,356)
(144,357)(145,361)(146,362)(147,363)(148,367)(149,368)(150,369)(151,364)
(152,365)(153,366)(154,370)(155,371)(156,372)(157,376)(158,377)(159,378)
(160,373)(161,374)(162,375)(163,406)(164,407)(165,408)(166,412)(167,413)
(168,414)(169,409)(170,410)(171,411)(172,415)(173,416)(174,417)(175,421)
(176,422)(177,423)(178,418)(179,419)(180,420)(181,424)(182,425)(183,426)
(184,430)(185,431)(186,432)(187,427)(188,428)(189,429)(190,460)(191,461)
(192,462)(193,466)(194,467)(195,468)(196,463)(197,464)(198,465)(199,469)
(200,470)(201,471)(202,475)(203,476)(204,477)(205,472)(206,473)(207,474)
(208,478)(209,479)(210,480)(211,484)(212,485)(213,486)(214,481)(215,482)
(216,483)(217,433)(218,434)(219,435)(220,439)(221,440)(222,441)(223,436)
(224,437)(225,438)(226,442)(227,443)(228,444)(229,448)(230,449)(231,450)
(232,445)(233,446)(234,447)(235,451)(236,452)(237,453)(238,457)(239,458)
(240,459)(241,454)(242,455)(243,456);
poly := sub<Sym(486)|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*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope