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