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Polytope of Type {6,6,9}

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