Questions?
See the FAQ
or other info.

Polytope of Type {3,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,6}*1944a
if this polytope has a name.
Group : SmallGroup(1944,941)
Rank : 4
Schlafli Type : {3,6,6}
Number of vertices, edges, etc : 9, 81, 162, 18
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 6
Special Properties :
   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 : {3,6,3}*972
   3-fold quotients : {3,6,6}*648a, {3,6,6}*648b
   6-fold quotients : {3,6,3}*324a, {3,6,3}*324b
   9-fold quotients : {3,6,6}*216a
   18-fold quotients : {3,6,3}*108
   27-fold quotients : {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 := (  4,  8)(  5,  9)(  6,  7)( 10, 19)( 11, 20)( 12, 21)( 13, 26)( 14, 27)
( 15, 25)( 16, 24)( 17, 22)( 18, 23)( 31, 35)( 32, 36)( 33, 34)( 37, 46)
( 38, 47)( 39, 48)( 40, 53)( 41, 54)( 42, 52)( 43, 51)( 44, 49)( 45, 50)
( 58, 62)( 59, 63)( 60, 61)( 64, 73)( 65, 74)( 66, 75)( 67, 80)( 68, 81)
( 69, 79)( 70, 78)( 71, 76)( 72, 77)( 82,163)( 83,164)( 84,165)( 85,170)
( 86,171)( 87,169)( 88,168)( 89,166)( 90,167)( 91,181)( 92,182)( 93,183)
( 94,188)( 95,189)( 96,187)( 97,186)( 98,184)( 99,185)(100,172)(101,173)
(102,174)(103,179)(104,180)(105,178)(106,177)(107,175)(108,176)(109,190)
(110,191)(111,192)(112,197)(113,198)(114,196)(115,195)(116,193)(117,194)
(118,208)(119,209)(120,210)(121,215)(122,216)(123,214)(124,213)(125,211)
(126,212)(127,199)(128,200)(129,201)(130,206)(131,207)(132,205)(133,204)
(134,202)(135,203)(136,217)(137,218)(138,219)(139,224)(140,225)(141,223)
(142,222)(143,220)(144,221)(145,235)(146,236)(147,237)(148,242)(149,243)
(150,241)(151,240)(152,238)(153,239)(154,226)(155,227)(156,228)(157,233)
(158,234)(159,232)(160,231)(161,229)(162,230)(247,251)(248,252)(249,250)
(253,262)(254,263)(255,264)(256,269)(257,270)(258,268)(259,267)(260,265)
(261,266)(274,278)(275,279)(276,277)(280,289)(281,290)(282,291)(283,296)
(284,297)(285,295)(286,294)(287,292)(288,293)(301,305)(302,306)(303,304)
(307,316)(308,317)(309,318)(310,323)(311,324)(312,322)(313,321)(314,319)
(315,320)(325,406)(326,407)(327,408)(328,413)(329,414)(330,412)(331,411)
(332,409)(333,410)(334,424)(335,425)(336,426)(337,431)(338,432)(339,430)
(340,429)(341,427)(342,428)(343,415)(344,416)(345,417)(346,422)(347,423)
(348,421)(349,420)(350,418)(351,419)(352,433)(353,434)(354,435)(355,440)
(356,441)(357,439)(358,438)(359,436)(360,437)(361,451)(362,452)(363,453)
(364,458)(365,459)(366,457)(367,456)(368,454)(369,455)(370,442)(371,443)
(372,444)(373,449)(374,450)(375,448)(376,447)(377,445)(378,446)(379,460)
(380,461)(381,462)(382,467)(383,468)(384,466)(385,465)(386,463)(387,464)
(388,478)(389,479)(390,480)(391,485)(392,486)(393,484)(394,483)(395,481)
(396,482)(397,469)(398,470)(399,471)(400,476)(401,477)(402,475)(403,474)
(404,472)(405,473);;
s1 := (  1, 82)(  2, 83)(  3, 84)(  4, 89)(  5, 90)(  6, 88)(  7, 87)(  8, 85)
(  9, 86)( 10,102)( 11,100)( 12,101)( 13,106)( 14,107)( 15,108)( 16,104)
( 17,105)( 18,103)( 19, 92)( 20, 93)( 21, 91)( 22, 99)( 23, 97)( 24, 98)
( 25, 94)( 26, 95)( 27, 96)( 28,121)( 29,122)( 30,123)( 31,119)( 32,120)
( 33,118)( 34,126)( 35,124)( 36,125)( 37,114)( 38,112)( 39,113)( 40,109)
( 41,110)( 42,111)( 43,116)( 44,117)( 45,115)( 46,131)( 47,132)( 48,130)
( 49,129)( 50,127)( 51,128)( 52,133)( 53,134)( 54,135)( 55,159)( 56,157)
( 57,158)( 58,154)( 59,155)( 60,156)( 61,161)( 62,162)( 63,160)( 64,149)
( 65,150)( 66,148)( 67,147)( 68,145)( 69,146)( 70,151)( 71,152)( 72,153)
( 73,139)( 74,140)( 75,141)( 76,137)( 77,138)( 78,136)( 79,144)( 80,142)
( 81,143)(166,170)(167,171)(168,169)(172,183)(173,181)(174,182)(175,187)
(176,188)(177,189)(178,185)(179,186)(180,184)(190,202)(191,203)(192,204)
(193,200)(194,201)(195,199)(196,207)(197,205)(198,206)(208,212)(209,213)
(210,211)(217,240)(218,238)(219,239)(220,235)(221,236)(222,237)(223,242)
(224,243)(225,241)(226,230)(227,231)(228,229)(244,325)(245,326)(246,327)
(247,332)(248,333)(249,331)(250,330)(251,328)(252,329)(253,345)(254,343)
(255,344)(256,349)(257,350)(258,351)(259,347)(260,348)(261,346)(262,335)
(263,336)(264,334)(265,342)(266,340)(267,341)(268,337)(269,338)(270,339)
(271,364)(272,365)(273,366)(274,362)(275,363)(276,361)(277,369)(278,367)
(279,368)(280,357)(281,355)(282,356)(283,352)(284,353)(285,354)(286,359)
(287,360)(288,358)(289,374)(290,375)(291,373)(292,372)(293,370)(294,371)
(295,376)(296,377)(297,378)(298,402)(299,400)(300,401)(301,397)(302,398)
(303,399)(304,404)(305,405)(306,403)(307,392)(308,393)(309,391)(310,390)
(311,388)(312,389)(313,394)(314,395)(315,396)(316,382)(317,383)(318,384)
(319,380)(320,381)(321,379)(322,387)(323,385)(324,386)(409,413)(410,414)
(411,412)(415,426)(416,424)(417,425)(418,430)(419,431)(420,432)(421,428)
(422,429)(423,427)(433,445)(434,446)(435,447)(436,443)(437,444)(438,442)
(439,450)(440,448)(441,449)(451,455)(452,456)(453,454)(460,483)(461,481)
(462,482)(463,478)(464,479)(465,480)(466,485)(467,486)(468,484)(469,473)
(470,474)(471,472);;
s2 := (  1, 28)(  2, 30)(  3, 29)(  4, 33)(  5, 32)(  6, 31)(  7, 35)(  8, 34)
(  9, 36)( 10, 50)( 11, 49)( 12, 51)( 13, 52)( 14, 54)( 15, 53)( 16, 48)
( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 38)( 23, 37)( 24, 39)
( 25, 40)( 26, 42)( 27, 41)( 56, 57)( 58, 60)( 61, 62)( 64, 77)( 65, 76)
( 66, 78)( 67, 79)( 68, 81)( 69, 80)( 70, 75)( 71, 74)( 72, 73)( 82,109)
( 83,111)( 84,110)( 85,114)( 86,113)( 87,112)( 88,116)( 89,115)( 90,117)
( 91,131)( 92,130)( 93,132)( 94,133)( 95,135)( 96,134)( 97,129)( 98,128)
( 99,127)(100,126)(101,125)(102,124)(103,119)(104,118)(105,120)(106,121)
(107,123)(108,122)(137,138)(139,141)(142,143)(145,158)(146,157)(147,159)
(148,160)(149,162)(150,161)(151,156)(152,155)(153,154)(163,190)(164,192)
(165,191)(166,195)(167,194)(168,193)(169,197)(170,196)(171,198)(172,212)
(173,211)(174,213)(175,214)(176,216)(177,215)(178,210)(179,209)(180,208)
(181,207)(182,206)(183,205)(184,200)(185,199)(186,201)(187,202)(188,204)
(189,203)(218,219)(220,222)(223,224)(226,239)(227,238)(228,240)(229,241)
(230,243)(231,242)(232,237)(233,236)(234,235)(244,271)(245,273)(246,272)
(247,276)(248,275)(249,274)(250,278)(251,277)(252,279)(253,293)(254,292)
(255,294)(256,295)(257,297)(258,296)(259,291)(260,290)(261,289)(262,288)
(263,287)(264,286)(265,281)(266,280)(267,282)(268,283)(269,285)(270,284)
(299,300)(301,303)(304,305)(307,320)(308,319)(309,321)(310,322)(311,324)
(312,323)(313,318)(314,317)(315,316)(325,352)(326,354)(327,353)(328,357)
(329,356)(330,355)(331,359)(332,358)(333,360)(334,374)(335,373)(336,375)
(337,376)(338,378)(339,377)(340,372)(341,371)(342,370)(343,369)(344,368)
(345,367)(346,362)(347,361)(348,363)(349,364)(350,366)(351,365)(380,381)
(382,384)(385,386)(388,401)(389,400)(390,402)(391,403)(392,405)(393,404)
(394,399)(395,398)(396,397)(406,433)(407,435)(408,434)(409,438)(410,437)
(411,436)(412,440)(413,439)(414,441)(415,455)(416,454)(417,456)(418,457)
(419,459)(420,458)(421,453)(422,452)(423,451)(424,450)(425,449)(426,448)
(427,443)(428,442)(429,444)(430,445)(431,447)(432,446)(461,462)(463,465)
(466,467)(469,482)(470,481)(471,483)(472,484)(473,486)(474,485)(475,480)
(476,479)(477,478);;
s3 := (  1,244)(  2,246)(  3,245)(  4,249)(  5,248)(  6,247)(  7,251)(  8,250)
(  9,252)( 10,262)( 11,264)( 12,263)( 13,267)( 14,266)( 15,265)( 16,269)
( 17,268)( 18,270)( 19,253)( 20,255)( 21,254)( 22,258)( 23,257)( 24,256)
( 25,260)( 26,259)( 27,261)( 28,298)( 29,300)( 30,299)( 31,303)( 32,302)
( 33,301)( 34,305)( 35,304)( 36,306)( 37,316)( 38,318)( 39,317)( 40,321)
( 41,320)( 42,319)( 43,323)( 44,322)( 45,324)( 46,307)( 47,309)( 48,308)
( 49,312)( 50,311)( 51,310)( 52,314)( 53,313)( 54,315)( 55,271)( 56,273)
( 57,272)( 58,276)( 59,275)( 60,274)( 61,278)( 62,277)( 63,279)( 64,289)
( 65,291)( 66,290)( 67,294)( 68,293)( 69,292)( 70,296)( 71,295)( 72,297)
( 73,280)( 74,282)( 75,281)( 76,285)( 77,284)( 78,283)( 79,287)( 80,286)
( 81,288)( 82,325)( 83,327)( 84,326)( 85,330)( 86,329)( 87,328)( 88,332)
( 89,331)( 90,333)( 91,343)( 92,345)( 93,344)( 94,348)( 95,347)( 96,346)
( 97,350)( 98,349)( 99,351)(100,334)(101,336)(102,335)(103,339)(104,338)
(105,337)(106,341)(107,340)(108,342)(109,379)(110,381)(111,380)(112,384)
(113,383)(114,382)(115,386)(116,385)(117,387)(118,397)(119,399)(120,398)
(121,402)(122,401)(123,400)(124,404)(125,403)(126,405)(127,388)(128,390)
(129,389)(130,393)(131,392)(132,391)(133,395)(134,394)(135,396)(136,352)
(137,354)(138,353)(139,357)(140,356)(141,355)(142,359)(143,358)(144,360)
(145,370)(146,372)(147,371)(148,375)(149,374)(150,373)(151,377)(152,376)
(153,378)(154,361)(155,363)(156,362)(157,366)(158,365)(159,364)(160,368)
(161,367)(162,369)(163,406)(164,408)(165,407)(166,411)(167,410)(168,409)
(169,413)(170,412)(171,414)(172,424)(173,426)(174,425)(175,429)(176,428)
(177,427)(178,431)(179,430)(180,432)(181,415)(182,417)(183,416)(184,420)
(185,419)(186,418)(187,422)(188,421)(189,423)(190,460)(191,462)(192,461)
(193,465)(194,464)(195,463)(196,467)(197,466)(198,468)(199,478)(200,480)
(201,479)(202,483)(203,482)(204,481)(205,485)(206,484)(207,486)(208,469)
(209,471)(210,470)(211,474)(212,473)(213,472)(214,476)(215,475)(216,477)
(217,433)(218,435)(219,434)(220,438)(221,437)(222,436)(223,440)(224,439)
(225,441)(226,451)(227,453)(228,452)(229,456)(230,455)(231,454)(232,458)
(233,457)(234,459)(235,442)(236,444)(237,443)(238,447)(239,446)(240,445)
(241,449)(242,448)(243,450);;
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, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2, 
s2*s0*s3*s2*s1*s2*s1*s2*s0*s1*s2*s3*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(486)!(  4,  8)(  5,  9)(  6,  7)( 10, 19)( 11, 20)( 12, 21)( 13, 26)
( 14, 27)( 15, 25)( 16, 24)( 17, 22)( 18, 23)( 31, 35)( 32, 36)( 33, 34)
( 37, 46)( 38, 47)( 39, 48)( 40, 53)( 41, 54)( 42, 52)( 43, 51)( 44, 49)
( 45, 50)( 58, 62)( 59, 63)( 60, 61)( 64, 73)( 65, 74)( 66, 75)( 67, 80)
( 68, 81)( 69, 79)( 70, 78)( 71, 76)( 72, 77)( 82,163)( 83,164)( 84,165)
( 85,170)( 86,171)( 87,169)( 88,168)( 89,166)( 90,167)( 91,181)( 92,182)
( 93,183)( 94,188)( 95,189)( 96,187)( 97,186)( 98,184)( 99,185)(100,172)
(101,173)(102,174)(103,179)(104,180)(105,178)(106,177)(107,175)(108,176)
(109,190)(110,191)(111,192)(112,197)(113,198)(114,196)(115,195)(116,193)
(117,194)(118,208)(119,209)(120,210)(121,215)(122,216)(123,214)(124,213)
(125,211)(126,212)(127,199)(128,200)(129,201)(130,206)(131,207)(132,205)
(133,204)(134,202)(135,203)(136,217)(137,218)(138,219)(139,224)(140,225)
(141,223)(142,222)(143,220)(144,221)(145,235)(146,236)(147,237)(148,242)
(149,243)(150,241)(151,240)(152,238)(153,239)(154,226)(155,227)(156,228)
(157,233)(158,234)(159,232)(160,231)(161,229)(162,230)(247,251)(248,252)
(249,250)(253,262)(254,263)(255,264)(256,269)(257,270)(258,268)(259,267)
(260,265)(261,266)(274,278)(275,279)(276,277)(280,289)(281,290)(282,291)
(283,296)(284,297)(285,295)(286,294)(287,292)(288,293)(301,305)(302,306)
(303,304)(307,316)(308,317)(309,318)(310,323)(311,324)(312,322)(313,321)
(314,319)(315,320)(325,406)(326,407)(327,408)(328,413)(329,414)(330,412)
(331,411)(332,409)(333,410)(334,424)(335,425)(336,426)(337,431)(338,432)
(339,430)(340,429)(341,427)(342,428)(343,415)(344,416)(345,417)(346,422)
(347,423)(348,421)(349,420)(350,418)(351,419)(352,433)(353,434)(354,435)
(355,440)(356,441)(357,439)(358,438)(359,436)(360,437)(361,451)(362,452)
(363,453)(364,458)(365,459)(366,457)(367,456)(368,454)(369,455)(370,442)
(371,443)(372,444)(373,449)(374,450)(375,448)(376,447)(377,445)(378,446)
(379,460)(380,461)(381,462)(382,467)(383,468)(384,466)(385,465)(386,463)
(387,464)(388,478)(389,479)(390,480)(391,485)(392,486)(393,484)(394,483)
(395,481)(396,482)(397,469)(398,470)(399,471)(400,476)(401,477)(402,475)
(403,474)(404,472)(405,473);
s1 := Sym(486)!(  1, 82)(  2, 83)(  3, 84)(  4, 89)(  5, 90)(  6, 88)(  7, 87)
(  8, 85)(  9, 86)( 10,102)( 11,100)( 12,101)( 13,106)( 14,107)( 15,108)
( 16,104)( 17,105)( 18,103)( 19, 92)( 20, 93)( 21, 91)( 22, 99)( 23, 97)
( 24, 98)( 25, 94)( 26, 95)( 27, 96)( 28,121)( 29,122)( 30,123)( 31,119)
( 32,120)( 33,118)( 34,126)( 35,124)( 36,125)( 37,114)( 38,112)( 39,113)
( 40,109)( 41,110)( 42,111)( 43,116)( 44,117)( 45,115)( 46,131)( 47,132)
( 48,130)( 49,129)( 50,127)( 51,128)( 52,133)( 53,134)( 54,135)( 55,159)
( 56,157)( 57,158)( 58,154)( 59,155)( 60,156)( 61,161)( 62,162)( 63,160)
( 64,149)( 65,150)( 66,148)( 67,147)( 68,145)( 69,146)( 70,151)( 71,152)
( 72,153)( 73,139)( 74,140)( 75,141)( 76,137)( 77,138)( 78,136)( 79,144)
( 80,142)( 81,143)(166,170)(167,171)(168,169)(172,183)(173,181)(174,182)
(175,187)(176,188)(177,189)(178,185)(179,186)(180,184)(190,202)(191,203)
(192,204)(193,200)(194,201)(195,199)(196,207)(197,205)(198,206)(208,212)
(209,213)(210,211)(217,240)(218,238)(219,239)(220,235)(221,236)(222,237)
(223,242)(224,243)(225,241)(226,230)(227,231)(228,229)(244,325)(245,326)
(246,327)(247,332)(248,333)(249,331)(250,330)(251,328)(252,329)(253,345)
(254,343)(255,344)(256,349)(257,350)(258,351)(259,347)(260,348)(261,346)
(262,335)(263,336)(264,334)(265,342)(266,340)(267,341)(268,337)(269,338)
(270,339)(271,364)(272,365)(273,366)(274,362)(275,363)(276,361)(277,369)
(278,367)(279,368)(280,357)(281,355)(282,356)(283,352)(284,353)(285,354)
(286,359)(287,360)(288,358)(289,374)(290,375)(291,373)(292,372)(293,370)
(294,371)(295,376)(296,377)(297,378)(298,402)(299,400)(300,401)(301,397)
(302,398)(303,399)(304,404)(305,405)(306,403)(307,392)(308,393)(309,391)
(310,390)(311,388)(312,389)(313,394)(314,395)(315,396)(316,382)(317,383)
(318,384)(319,380)(320,381)(321,379)(322,387)(323,385)(324,386)(409,413)
(410,414)(411,412)(415,426)(416,424)(417,425)(418,430)(419,431)(420,432)
(421,428)(422,429)(423,427)(433,445)(434,446)(435,447)(436,443)(437,444)
(438,442)(439,450)(440,448)(441,449)(451,455)(452,456)(453,454)(460,483)
(461,481)(462,482)(463,478)(464,479)(465,480)(466,485)(467,486)(468,484)
(469,473)(470,474)(471,472);
s2 := Sym(486)!(  1, 28)(  2, 30)(  3, 29)(  4, 33)(  5, 32)(  6, 31)(  7, 35)
(  8, 34)(  9, 36)( 10, 50)( 11, 49)( 12, 51)( 13, 52)( 14, 54)( 15, 53)
( 16, 48)( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 38)( 23, 37)
( 24, 39)( 25, 40)( 26, 42)( 27, 41)( 56, 57)( 58, 60)( 61, 62)( 64, 77)
( 65, 76)( 66, 78)( 67, 79)( 68, 81)( 69, 80)( 70, 75)( 71, 74)( 72, 73)
( 82,109)( 83,111)( 84,110)( 85,114)( 86,113)( 87,112)( 88,116)( 89,115)
( 90,117)( 91,131)( 92,130)( 93,132)( 94,133)( 95,135)( 96,134)( 97,129)
( 98,128)( 99,127)(100,126)(101,125)(102,124)(103,119)(104,118)(105,120)
(106,121)(107,123)(108,122)(137,138)(139,141)(142,143)(145,158)(146,157)
(147,159)(148,160)(149,162)(150,161)(151,156)(152,155)(153,154)(163,190)
(164,192)(165,191)(166,195)(167,194)(168,193)(169,197)(170,196)(171,198)
(172,212)(173,211)(174,213)(175,214)(176,216)(177,215)(178,210)(179,209)
(180,208)(181,207)(182,206)(183,205)(184,200)(185,199)(186,201)(187,202)
(188,204)(189,203)(218,219)(220,222)(223,224)(226,239)(227,238)(228,240)
(229,241)(230,243)(231,242)(232,237)(233,236)(234,235)(244,271)(245,273)
(246,272)(247,276)(248,275)(249,274)(250,278)(251,277)(252,279)(253,293)
(254,292)(255,294)(256,295)(257,297)(258,296)(259,291)(260,290)(261,289)
(262,288)(263,287)(264,286)(265,281)(266,280)(267,282)(268,283)(269,285)
(270,284)(299,300)(301,303)(304,305)(307,320)(308,319)(309,321)(310,322)
(311,324)(312,323)(313,318)(314,317)(315,316)(325,352)(326,354)(327,353)
(328,357)(329,356)(330,355)(331,359)(332,358)(333,360)(334,374)(335,373)
(336,375)(337,376)(338,378)(339,377)(340,372)(341,371)(342,370)(343,369)
(344,368)(345,367)(346,362)(347,361)(348,363)(349,364)(350,366)(351,365)
(380,381)(382,384)(385,386)(388,401)(389,400)(390,402)(391,403)(392,405)
(393,404)(394,399)(395,398)(396,397)(406,433)(407,435)(408,434)(409,438)
(410,437)(411,436)(412,440)(413,439)(414,441)(415,455)(416,454)(417,456)
(418,457)(419,459)(420,458)(421,453)(422,452)(423,451)(424,450)(425,449)
(426,448)(427,443)(428,442)(429,444)(430,445)(431,447)(432,446)(461,462)
(463,465)(466,467)(469,482)(470,481)(471,483)(472,484)(473,486)(474,485)
(475,480)(476,479)(477,478);
s3 := Sym(486)!(  1,244)(  2,246)(  3,245)(  4,249)(  5,248)(  6,247)(  7,251)
(  8,250)(  9,252)( 10,262)( 11,264)( 12,263)( 13,267)( 14,266)( 15,265)
( 16,269)( 17,268)( 18,270)( 19,253)( 20,255)( 21,254)( 22,258)( 23,257)
( 24,256)( 25,260)( 26,259)( 27,261)( 28,298)( 29,300)( 30,299)( 31,303)
( 32,302)( 33,301)( 34,305)( 35,304)( 36,306)( 37,316)( 38,318)( 39,317)
( 40,321)( 41,320)( 42,319)( 43,323)( 44,322)( 45,324)( 46,307)( 47,309)
( 48,308)( 49,312)( 50,311)( 51,310)( 52,314)( 53,313)( 54,315)( 55,271)
( 56,273)( 57,272)( 58,276)( 59,275)( 60,274)( 61,278)( 62,277)( 63,279)
( 64,289)( 65,291)( 66,290)( 67,294)( 68,293)( 69,292)( 70,296)( 71,295)
( 72,297)( 73,280)( 74,282)( 75,281)( 76,285)( 77,284)( 78,283)( 79,287)
( 80,286)( 81,288)( 82,325)( 83,327)( 84,326)( 85,330)( 86,329)( 87,328)
( 88,332)( 89,331)( 90,333)( 91,343)( 92,345)( 93,344)( 94,348)( 95,347)
( 96,346)( 97,350)( 98,349)( 99,351)(100,334)(101,336)(102,335)(103,339)
(104,338)(105,337)(106,341)(107,340)(108,342)(109,379)(110,381)(111,380)
(112,384)(113,383)(114,382)(115,386)(116,385)(117,387)(118,397)(119,399)
(120,398)(121,402)(122,401)(123,400)(124,404)(125,403)(126,405)(127,388)
(128,390)(129,389)(130,393)(131,392)(132,391)(133,395)(134,394)(135,396)
(136,352)(137,354)(138,353)(139,357)(140,356)(141,355)(142,359)(143,358)
(144,360)(145,370)(146,372)(147,371)(148,375)(149,374)(150,373)(151,377)
(152,376)(153,378)(154,361)(155,363)(156,362)(157,366)(158,365)(159,364)
(160,368)(161,367)(162,369)(163,406)(164,408)(165,407)(166,411)(167,410)
(168,409)(169,413)(170,412)(171,414)(172,424)(173,426)(174,425)(175,429)
(176,428)(177,427)(178,431)(179,430)(180,432)(181,415)(182,417)(183,416)
(184,420)(185,419)(186,418)(187,422)(188,421)(189,423)(190,460)(191,462)
(192,461)(193,465)(194,464)(195,463)(196,467)(197,466)(198,468)(199,478)
(200,480)(201,479)(202,483)(203,482)(204,481)(205,485)(206,484)(207,486)
(208,469)(209,471)(210,470)(211,474)(212,473)(213,472)(214,476)(215,475)
(216,477)(217,433)(218,435)(219,434)(220,438)(221,437)(222,436)(223,440)
(224,439)(225,441)(226,451)(227,453)(228,452)(229,456)(230,455)(231,454)
(232,458)(233,457)(234,459)(235,442)(236,444)(237,443)(238,447)(239,446)
(240,445)(241,449)(242,448)(243,450);
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, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2, 
s2*s0*s3*s2*s1*s2*s1*s2*s0*s1*s2*s3*s2*s0*s1*s2*s1*s2*s0*s1 >; 
 
References : None.
to this polytope