Polytope of Type {6,6,9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,9}*1944a
if this polytope has a name.
Group : SmallGroup(1944,949)
Rank : 4
Schlafli Type : {6,6,9}
Number of vertices, edges, etc : 6, 54, 81, 27
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 : {3,6,9}*972a
3-fold quotients : {6,6,9}*648a, {6,6,3}*648b
6-fold quotients : {3,6,9}*324, {3,6,3}*324a
9-fold quotients : {6,2,9}*216, {6,6,3}*216a
18-fold quotients : {3,2,9}*108, {3,6,3}*108
27-fold quotients : {2,2,9}*72, {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 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 61)
( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)( 39, 65)
( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)( 47, 75)
( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)( 83, 84)
( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)
(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)
(114,143)(115,139)(116,141)(117,140)(118,145)(119,147)(120,146)(121,151)
(122,153)(123,152)(124,148)(125,150)(126,149)(127,154)(128,156)(129,155)
(130,160)(131,162)(132,161)(133,157)(134,159)(135,158)(164,165)(166,169)
(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)(184,187)
(185,189)(186,188)(190,217)(191,219)(192,218)(193,223)(194,225)(195,224)
(196,220)(197,222)(198,221)(199,226)(200,228)(201,227)(202,232)(203,234)
(204,233)(205,229)(206,231)(207,230)(208,235)(209,237)(210,236)(211,241)
(212,243)(213,242)(214,238)(215,240)(216,239)(245,246)(247,250)(248,252)
(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)(266,270)
(267,269)(271,298)(272,300)(273,299)(274,304)(275,306)(276,305)(277,301)
(278,303)(279,302)(280,307)(281,309)(282,308)(283,313)(284,315)(285,314)
(286,310)(287,312)(288,311)(289,316)(290,318)(291,317)(292,322)(293,324)
(294,323)(295,319)(296,321)(297,320)(326,327)(328,331)(329,333)(330,332)
(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)(348,350)
(352,379)(353,381)(354,380)(355,385)(356,387)(357,386)(358,382)(359,384)
(360,383)(361,388)(362,390)(363,389)(364,394)(365,396)(366,395)(367,391)
(368,393)(369,392)(370,397)(371,399)(372,398)(373,403)(374,405)(375,404)
(376,400)(377,402)(378,401)(407,408)(409,412)(410,414)(411,413)(416,417)
(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)(433,460)
(434,462)(435,461)(436,466)(437,468)(438,467)(439,463)(440,465)(441,464)
(442,469)(443,471)(444,470)(445,475)(446,477)(447,476)(448,472)(449,474)
(450,473)(451,478)(452,480)(453,479)(454,484)(455,486)(456,485)(457,481)
(458,483)(459,482);;
s1 := ( 1,271)( 2,273)( 3,272)( 4,277)( 5,279)( 6,278)( 7,274)( 8,276)
( 9,275)( 10,280)( 11,282)( 12,281)( 13,286)( 14,288)( 15,287)( 16,283)
( 17,285)( 18,284)( 19,289)( 20,291)( 21,290)( 22,295)( 23,297)( 24,296)
( 25,292)( 26,294)( 27,293)( 28,244)( 29,246)( 30,245)( 31,250)( 32,252)
( 33,251)( 34,247)( 35,249)( 36,248)( 37,253)( 38,255)( 39,254)( 40,259)
( 41,261)( 42,260)( 43,256)( 44,258)( 45,257)( 46,262)( 47,264)( 48,263)
( 49,268)( 50,270)( 51,269)( 52,265)( 53,267)( 54,266)( 55,298)( 56,300)
( 57,299)( 58,304)( 59,306)( 60,305)( 61,301)( 62,303)( 63,302)( 64,307)
( 65,309)( 66,308)( 67,313)( 68,315)( 69,314)( 70,310)( 71,312)( 72,311)
( 73,316)( 74,318)( 75,317)( 76,322)( 77,324)( 78,323)( 79,319)( 80,321)
( 81,320)( 82,352)( 83,354)( 84,353)( 85,358)( 86,360)( 87,359)( 88,355)
( 89,357)( 90,356)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)( 96,368)
( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)(104,378)
(105,377)(106,373)(107,375)(108,374)(109,325)(110,327)(111,326)(112,331)
(113,333)(114,332)(115,328)(116,330)(117,329)(118,334)(119,336)(120,335)
(121,340)(122,342)(123,341)(124,337)(125,339)(126,338)(127,343)(128,345)
(129,344)(130,349)(131,351)(132,350)(133,346)(134,348)(135,347)(136,379)
(137,381)(138,380)(139,385)(140,387)(141,386)(142,382)(143,384)(144,383)
(145,388)(146,390)(147,389)(148,394)(149,396)(150,395)(151,391)(152,393)
(153,392)(154,397)(155,399)(156,398)(157,403)(158,405)(159,404)(160,400)
(161,402)(162,401)(163,433)(164,435)(165,434)(166,439)(167,441)(168,440)
(169,436)(170,438)(171,437)(172,442)(173,444)(174,443)(175,448)(176,450)
(177,449)(178,445)(179,447)(180,446)(181,451)(182,453)(183,452)(184,457)
(185,459)(186,458)(187,454)(188,456)(189,455)(190,406)(191,408)(192,407)
(193,412)(194,414)(195,413)(196,409)(197,411)(198,410)(199,415)(200,417)
(201,416)(202,421)(203,423)(204,422)(205,418)(206,420)(207,419)(208,424)
(209,426)(210,425)(211,430)(212,432)(213,431)(214,427)(215,429)(216,428)
(217,460)(218,462)(219,461)(220,466)(221,468)(222,467)(223,463)(224,465)
(225,464)(226,469)(227,471)(228,470)(229,475)(230,477)(231,476)(232,472)
(233,474)(234,473)(235,478)(236,480)(237,479)(238,484)(239,486)(240,485)
(241,481)(242,483)(243,482);;
s2 := ( 1, 82)( 2, 83)( 3, 84)( 4, 89)( 5, 90)( 6, 88)( 7, 87)( 8, 85)
( 9, 86)( 10,100)( 11,101)( 12,102)( 13,107)( 14,108)( 15,106)( 16,105)
( 17,103)( 18,104)( 19, 91)( 20, 92)( 21, 93)( 22, 98)( 23, 99)( 24, 97)
( 25, 96)( 26, 94)( 27, 95)( 28,113)( 29,114)( 30,112)( 31,111)( 32,109)
( 33,110)( 34,115)( 35,116)( 36,117)( 37,131)( 38,132)( 39,130)( 40,129)
( 41,127)( 42,128)( 43,133)( 44,134)( 45,135)( 46,122)( 47,123)( 48,121)
( 49,120)( 50,118)( 51,119)( 52,124)( 53,125)( 54,126)( 55,144)( 56,142)
( 57,143)( 58,139)( 59,140)( 60,141)( 61,137)( 62,138)( 63,136)( 64,162)
( 65,160)( 66,161)( 67,157)( 68,158)( 69,159)( 70,155)( 71,156)( 72,154)
( 73,153)( 74,151)( 75,152)( 76,148)( 77,149)( 78,150)( 79,146)( 80,147)
( 81,145)(163,172)(164,173)(165,174)(166,179)(167,180)(168,178)(169,177)
(170,175)(171,176)(184,188)(185,189)(186,187)(190,203)(191,204)(192,202)
(193,201)(194,199)(195,200)(196,205)(197,206)(198,207)(208,212)(209,213)
(210,211)(217,234)(218,232)(219,233)(220,229)(221,230)(222,231)(223,227)
(224,228)(225,226)(235,243)(236,241)(237,242)(244,325)(245,326)(246,327)
(247,332)(248,333)(249,331)(250,330)(251,328)(252,329)(253,343)(254,344)
(255,345)(256,350)(257,351)(258,349)(259,348)(260,346)(261,347)(262,334)
(263,335)(264,336)(265,341)(266,342)(267,340)(268,339)(269,337)(270,338)
(271,356)(272,357)(273,355)(274,354)(275,352)(276,353)(277,358)(278,359)
(279,360)(280,374)(281,375)(282,373)(283,372)(284,370)(285,371)(286,376)
(287,377)(288,378)(289,365)(290,366)(291,364)(292,363)(293,361)(294,362)
(295,367)(296,368)(297,369)(298,387)(299,385)(300,386)(301,382)(302,383)
(303,384)(304,380)(305,381)(306,379)(307,405)(308,403)(309,404)(310,400)
(311,401)(312,402)(313,398)(314,399)(315,397)(316,396)(317,394)(318,395)
(319,391)(320,392)(321,393)(322,389)(323,390)(324,388)(406,415)(407,416)
(408,417)(409,422)(410,423)(411,421)(412,420)(413,418)(414,419)(427,431)
(428,432)(429,430)(433,446)(434,447)(435,445)(436,444)(437,442)(438,443)
(439,448)(440,449)(441,450)(451,455)(452,456)(453,454)(460,477)(461,475)
(462,476)(463,472)(464,473)(465,474)(466,470)(467,471)(468,469)(478,486)
(479,484)(480,485);;
s3 := ( 4, 7)( 5, 8)( 6, 9)( 10, 19)( 11, 20)( 12, 21)( 13, 25)( 14, 26)
( 15, 27)( 16, 22)( 17, 23)( 18, 24)( 31, 34)( 32, 35)( 33, 36)( 37, 46)
( 38, 47)( 39, 48)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)( 45, 51)
( 58, 61)( 59, 62)( 60, 63)( 64, 73)( 65, 74)( 66, 75)( 67, 79)( 68, 80)
( 69, 81)( 70, 76)( 71, 77)( 72, 78)( 82,172)( 83,173)( 84,174)( 85,178)
( 86,179)( 87,180)( 88,175)( 89,176)( 90,177)( 91,163)( 92,164)( 93,165)
( 94,169)( 95,170)( 96,171)( 97,166)( 98,167)( 99,168)(100,181)(101,182)
(102,183)(103,187)(104,188)(105,189)(106,184)(107,185)(108,186)(109,199)
(110,200)(111,201)(112,205)(113,206)(114,207)(115,202)(116,203)(117,204)
(118,190)(119,191)(120,192)(121,196)(122,197)(123,198)(124,193)(125,194)
(126,195)(127,208)(128,209)(129,210)(130,214)(131,215)(132,216)(133,211)
(134,212)(135,213)(136,226)(137,227)(138,228)(139,232)(140,233)(141,234)
(142,229)(143,230)(144,231)(145,217)(146,218)(147,219)(148,223)(149,224)
(150,225)(151,220)(152,221)(153,222)(154,235)(155,236)(156,237)(157,241)
(158,242)(159,243)(160,238)(161,239)(162,240)(247,250)(248,251)(249,252)
(253,262)(254,263)(255,264)(256,268)(257,269)(258,270)(259,265)(260,266)
(261,267)(274,277)(275,278)(276,279)(280,289)(281,290)(282,291)(283,295)
(284,296)(285,297)(286,292)(287,293)(288,294)(301,304)(302,305)(303,306)
(307,316)(308,317)(309,318)(310,322)(311,323)(312,324)(313,319)(314,320)
(315,321)(325,415)(326,416)(327,417)(328,421)(329,422)(330,423)(331,418)
(332,419)(333,420)(334,406)(335,407)(336,408)(337,412)(338,413)(339,414)
(340,409)(341,410)(342,411)(343,424)(344,425)(345,426)(346,430)(347,431)
(348,432)(349,427)(350,428)(351,429)(352,442)(353,443)(354,444)(355,448)
(356,449)(357,450)(358,445)(359,446)(360,447)(361,433)(362,434)(363,435)
(364,439)(365,440)(366,441)(367,436)(368,437)(369,438)(370,451)(371,452)
(372,453)(373,457)(374,458)(375,459)(376,454)(377,455)(378,456)(379,469)
(380,470)(381,471)(382,475)(383,476)(384,477)(385,472)(386,473)(387,474)
(388,460)(389,461)(390,462)(391,466)(392,467)(393,468)(394,463)(395,464)
(396,465)(397,478)(398,479)(399,480)(400,484)(401,485)(402,486)(403,481)
(404,482)(405,483);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(486)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 55)( 29, 57)( 30, 56)
( 31, 61)( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)
( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)
( 47, 75)( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)
( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)
(101,102)(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)
(113,144)(114,143)(115,139)(116,141)(117,140)(118,145)(119,147)(120,146)
(121,151)(122,153)(123,152)(124,148)(125,150)(126,149)(127,154)(128,156)
(129,155)(130,160)(131,162)(132,161)(133,157)(134,159)(135,158)(164,165)
(166,169)(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)
(184,187)(185,189)(186,188)(190,217)(191,219)(192,218)(193,223)(194,225)
(195,224)(196,220)(197,222)(198,221)(199,226)(200,228)(201,227)(202,232)
(203,234)(204,233)(205,229)(206,231)(207,230)(208,235)(209,237)(210,236)
(211,241)(212,243)(213,242)(214,238)(215,240)(216,239)(245,246)(247,250)
(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)
(266,270)(267,269)(271,298)(272,300)(273,299)(274,304)(275,306)(276,305)
(277,301)(278,303)(279,302)(280,307)(281,309)(282,308)(283,313)(284,315)
(285,314)(286,310)(287,312)(288,311)(289,316)(290,318)(291,317)(292,322)
(293,324)(294,323)(295,319)(296,321)(297,320)(326,327)(328,331)(329,333)
(330,332)(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)
(348,350)(352,379)(353,381)(354,380)(355,385)(356,387)(357,386)(358,382)
(359,384)(360,383)(361,388)(362,390)(363,389)(364,394)(365,396)(366,395)
(367,391)(368,393)(369,392)(370,397)(371,399)(372,398)(373,403)(374,405)
(375,404)(376,400)(377,402)(378,401)(407,408)(409,412)(410,414)(411,413)
(416,417)(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)
(433,460)(434,462)(435,461)(436,466)(437,468)(438,467)(439,463)(440,465)
(441,464)(442,469)(443,471)(444,470)(445,475)(446,477)(447,476)(448,472)
(449,474)(450,473)(451,478)(452,480)(453,479)(454,484)(455,486)(456,485)
(457,481)(458,483)(459,482);
s1 := Sym(486)!( 1,271)( 2,273)( 3,272)( 4,277)( 5,279)( 6,278)( 7,274)
( 8,276)( 9,275)( 10,280)( 11,282)( 12,281)( 13,286)( 14,288)( 15,287)
( 16,283)( 17,285)( 18,284)( 19,289)( 20,291)( 21,290)( 22,295)( 23,297)
( 24,296)( 25,292)( 26,294)( 27,293)( 28,244)( 29,246)( 30,245)( 31,250)
( 32,252)( 33,251)( 34,247)( 35,249)( 36,248)( 37,253)( 38,255)( 39,254)
( 40,259)( 41,261)( 42,260)( 43,256)( 44,258)( 45,257)( 46,262)( 47,264)
( 48,263)( 49,268)( 50,270)( 51,269)( 52,265)( 53,267)( 54,266)( 55,298)
( 56,300)( 57,299)( 58,304)( 59,306)( 60,305)( 61,301)( 62,303)( 63,302)
( 64,307)( 65,309)( 66,308)( 67,313)( 68,315)( 69,314)( 70,310)( 71,312)
( 72,311)( 73,316)( 74,318)( 75,317)( 76,322)( 77,324)( 78,323)( 79,319)
( 80,321)( 81,320)( 82,352)( 83,354)( 84,353)( 85,358)( 86,360)( 87,359)
( 88,355)( 89,357)( 90,356)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)
( 96,368)( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)
(104,378)(105,377)(106,373)(107,375)(108,374)(109,325)(110,327)(111,326)
(112,331)(113,333)(114,332)(115,328)(116,330)(117,329)(118,334)(119,336)
(120,335)(121,340)(122,342)(123,341)(124,337)(125,339)(126,338)(127,343)
(128,345)(129,344)(130,349)(131,351)(132,350)(133,346)(134,348)(135,347)
(136,379)(137,381)(138,380)(139,385)(140,387)(141,386)(142,382)(143,384)
(144,383)(145,388)(146,390)(147,389)(148,394)(149,396)(150,395)(151,391)
(152,393)(153,392)(154,397)(155,399)(156,398)(157,403)(158,405)(159,404)
(160,400)(161,402)(162,401)(163,433)(164,435)(165,434)(166,439)(167,441)
(168,440)(169,436)(170,438)(171,437)(172,442)(173,444)(174,443)(175,448)
(176,450)(177,449)(178,445)(179,447)(180,446)(181,451)(182,453)(183,452)
(184,457)(185,459)(186,458)(187,454)(188,456)(189,455)(190,406)(191,408)
(192,407)(193,412)(194,414)(195,413)(196,409)(197,411)(198,410)(199,415)
(200,417)(201,416)(202,421)(203,423)(204,422)(205,418)(206,420)(207,419)
(208,424)(209,426)(210,425)(211,430)(212,432)(213,431)(214,427)(215,429)
(216,428)(217,460)(218,462)(219,461)(220,466)(221,468)(222,467)(223,463)
(224,465)(225,464)(226,469)(227,471)(228,470)(229,475)(230,477)(231,476)
(232,472)(233,474)(234,473)(235,478)(236,480)(237,479)(238,484)(239,486)
(240,485)(241,481)(242,483)(243,482);
s2 := Sym(486)!( 1, 82)( 2, 83)( 3, 84)( 4, 89)( 5, 90)( 6, 88)( 7, 87)
( 8, 85)( 9, 86)( 10,100)( 11,101)( 12,102)( 13,107)( 14,108)( 15,106)
( 16,105)( 17,103)( 18,104)( 19, 91)( 20, 92)( 21, 93)( 22, 98)( 23, 99)
( 24, 97)( 25, 96)( 26, 94)( 27, 95)( 28,113)( 29,114)( 30,112)( 31,111)
( 32,109)( 33,110)( 34,115)( 35,116)( 36,117)( 37,131)( 38,132)( 39,130)
( 40,129)( 41,127)( 42,128)( 43,133)( 44,134)( 45,135)( 46,122)( 47,123)
( 48,121)( 49,120)( 50,118)( 51,119)( 52,124)( 53,125)( 54,126)( 55,144)
( 56,142)( 57,143)( 58,139)( 59,140)( 60,141)( 61,137)( 62,138)( 63,136)
( 64,162)( 65,160)( 66,161)( 67,157)( 68,158)( 69,159)( 70,155)( 71,156)
( 72,154)( 73,153)( 74,151)( 75,152)( 76,148)( 77,149)( 78,150)( 79,146)
( 80,147)( 81,145)(163,172)(164,173)(165,174)(166,179)(167,180)(168,178)
(169,177)(170,175)(171,176)(184,188)(185,189)(186,187)(190,203)(191,204)
(192,202)(193,201)(194,199)(195,200)(196,205)(197,206)(198,207)(208,212)
(209,213)(210,211)(217,234)(218,232)(219,233)(220,229)(221,230)(222,231)
(223,227)(224,228)(225,226)(235,243)(236,241)(237,242)(244,325)(245,326)
(246,327)(247,332)(248,333)(249,331)(250,330)(251,328)(252,329)(253,343)
(254,344)(255,345)(256,350)(257,351)(258,349)(259,348)(260,346)(261,347)
(262,334)(263,335)(264,336)(265,341)(266,342)(267,340)(268,339)(269,337)
(270,338)(271,356)(272,357)(273,355)(274,354)(275,352)(276,353)(277,358)
(278,359)(279,360)(280,374)(281,375)(282,373)(283,372)(284,370)(285,371)
(286,376)(287,377)(288,378)(289,365)(290,366)(291,364)(292,363)(293,361)
(294,362)(295,367)(296,368)(297,369)(298,387)(299,385)(300,386)(301,382)
(302,383)(303,384)(304,380)(305,381)(306,379)(307,405)(308,403)(309,404)
(310,400)(311,401)(312,402)(313,398)(314,399)(315,397)(316,396)(317,394)
(318,395)(319,391)(320,392)(321,393)(322,389)(323,390)(324,388)(406,415)
(407,416)(408,417)(409,422)(410,423)(411,421)(412,420)(413,418)(414,419)
(427,431)(428,432)(429,430)(433,446)(434,447)(435,445)(436,444)(437,442)
(438,443)(439,448)(440,449)(441,450)(451,455)(452,456)(453,454)(460,477)
(461,475)(462,476)(463,472)(464,473)(465,474)(466,470)(467,471)(468,469)
(478,486)(479,484)(480,485);
s3 := Sym(486)!( 4, 7)( 5, 8)( 6, 9)( 10, 19)( 11, 20)( 12, 21)( 13, 25)
( 14, 26)( 15, 27)( 16, 22)( 17, 23)( 18, 24)( 31, 34)( 32, 35)( 33, 36)
( 37, 46)( 38, 47)( 39, 48)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)
( 45, 51)( 58, 61)( 59, 62)( 60, 63)( 64, 73)( 65, 74)( 66, 75)( 67, 79)
( 68, 80)( 69, 81)( 70, 76)( 71, 77)( 72, 78)( 82,172)( 83,173)( 84,174)
( 85,178)( 86,179)( 87,180)( 88,175)( 89,176)( 90,177)( 91,163)( 92,164)
( 93,165)( 94,169)( 95,170)( 96,171)( 97,166)( 98,167)( 99,168)(100,181)
(101,182)(102,183)(103,187)(104,188)(105,189)(106,184)(107,185)(108,186)
(109,199)(110,200)(111,201)(112,205)(113,206)(114,207)(115,202)(116,203)
(117,204)(118,190)(119,191)(120,192)(121,196)(122,197)(123,198)(124,193)
(125,194)(126,195)(127,208)(128,209)(129,210)(130,214)(131,215)(132,216)
(133,211)(134,212)(135,213)(136,226)(137,227)(138,228)(139,232)(140,233)
(141,234)(142,229)(143,230)(144,231)(145,217)(146,218)(147,219)(148,223)
(149,224)(150,225)(151,220)(152,221)(153,222)(154,235)(155,236)(156,237)
(157,241)(158,242)(159,243)(160,238)(161,239)(162,240)(247,250)(248,251)
(249,252)(253,262)(254,263)(255,264)(256,268)(257,269)(258,270)(259,265)
(260,266)(261,267)(274,277)(275,278)(276,279)(280,289)(281,290)(282,291)
(283,295)(284,296)(285,297)(286,292)(287,293)(288,294)(301,304)(302,305)
(303,306)(307,316)(308,317)(309,318)(310,322)(311,323)(312,324)(313,319)
(314,320)(315,321)(325,415)(326,416)(327,417)(328,421)(329,422)(330,423)
(331,418)(332,419)(333,420)(334,406)(335,407)(336,408)(337,412)(338,413)
(339,414)(340,409)(341,410)(342,411)(343,424)(344,425)(345,426)(346,430)
(347,431)(348,432)(349,427)(350,428)(351,429)(352,442)(353,443)(354,444)
(355,448)(356,449)(357,450)(358,445)(359,446)(360,447)(361,433)(362,434)
(363,435)(364,439)(365,440)(366,441)(367,436)(368,437)(369,438)(370,451)
(371,452)(372,453)(373,457)(374,458)(375,459)(376,454)(377,455)(378,456)
(379,469)(380,470)(381,471)(382,475)(383,476)(384,477)(385,472)(386,473)
(387,474)(388,460)(389,461)(390,462)(391,466)(392,467)(393,468)(394,463)
(395,464)(396,465)(397,478)(398,479)(399,480)(400,484)(401,485)(402,486)
(403,481)(404,482)(405,483);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope