Questions?
See the FAQ
or other info.

Polytope of Type {6,6,27}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,27}*1944a
if this polytope has a name.
Group : SmallGroup(1944,948)
Rank : 4
Schlafli Type : {6,6,27}
Number of vertices, edges, etc : 6, 18, 81, 27
Order of s0s1s2s3 : 54
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 : {3,6,27}*972
   3-fold quotients : {6,6,9}*648a, {6,2,27}*648
   6-fold quotients : {3,6,9}*324, {3,2,27}*324
   9-fold quotients : {2,2,27}*216, {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)(  4,277)(  5,278)(  6,279)(  7,274)(  8,275)
(  9,276)( 10,280)( 11,281)( 12,282)( 13,286)( 14,287)( 15,288)( 16,283)
( 17,284)( 18,285)( 19,289)( 20,290)( 21,291)( 22,295)( 23,296)( 24,297)
( 25,292)( 26,293)( 27,294)( 28,244)( 29,245)( 30,246)( 31,250)( 32,251)
( 33,252)( 34,247)( 35,248)( 36,249)( 37,253)( 38,254)( 39,255)( 40,259)
( 41,260)( 42,261)( 43,256)( 44,257)( 45,258)( 46,262)( 47,263)( 48,264)
( 49,268)( 50,269)( 51,270)( 52,265)( 53,266)( 54,267)( 55,298)( 56,299)
( 57,300)( 58,304)( 59,305)( 60,306)( 61,301)( 62,302)( 63,303)( 64,307)
( 65,308)( 66,309)( 67,313)( 68,314)( 69,315)( 70,310)( 71,311)( 72,312)
( 73,316)( 74,317)( 75,318)( 76,322)( 77,323)( 78,324)( 79,319)( 80,320)
( 81,321)( 82,352)( 83,353)( 84,354)( 85,358)( 86,359)( 87,360)( 88,355)
( 89,356)( 90,357)( 91,361)( 92,362)( 93,363)( 94,367)( 95,368)( 96,369)
( 97,364)( 98,365)( 99,366)(100,370)(101,371)(102,372)(103,376)(104,377)
(105,378)(106,373)(107,374)(108,375)(109,325)(110,326)(111,327)(112,331)
(113,332)(114,333)(115,328)(116,329)(117,330)(118,334)(119,335)(120,336)
(121,340)(122,341)(123,342)(124,337)(125,338)(126,339)(127,343)(128,344)
(129,345)(130,349)(131,350)(132,351)(133,346)(134,347)(135,348)(136,379)
(137,380)(138,381)(139,385)(140,386)(141,387)(142,382)(143,383)(144,384)
(145,388)(146,389)(147,390)(148,394)(149,395)(150,396)(151,391)(152,392)
(153,393)(154,397)(155,398)(156,399)(157,403)(158,404)(159,405)(160,400)
(161,401)(162,402)(163,433)(164,434)(165,435)(166,439)(167,440)(168,441)
(169,436)(170,437)(171,438)(172,442)(173,443)(174,444)(175,448)(176,449)
(177,450)(178,445)(179,446)(180,447)(181,451)(182,452)(183,453)(184,457)
(185,458)(186,459)(187,454)(188,455)(189,456)(190,406)(191,407)(192,408)
(193,412)(194,413)(195,414)(196,409)(197,410)(198,411)(199,415)(200,416)
(201,417)(202,421)(203,422)(204,423)(205,418)(206,419)(207,420)(208,424)
(209,425)(210,426)(211,430)(212,431)(213,432)(214,427)(215,428)(216,429)
(217,460)(218,461)(219,462)(220,466)(221,467)(222,468)(223,463)(224,464)
(225,465)(226,469)(227,470)(228,471)(229,475)(230,476)(231,477)(232,472)
(233,473)(234,474)(235,478)(236,479)(237,480)(238,484)(239,485)(240,486)
(241,481)(242,482)(243,483);;
s2 := (  1, 82)(  2, 84)(  3, 83)(  4, 88)(  5, 90)(  6, 89)(  7, 85)(  8, 87)
(  9, 86)( 10,102)( 11,101)( 12,100)( 13,108)( 14,107)( 15,106)( 16,105)
( 17,104)( 18,103)( 19, 93)( 20, 92)( 21, 91)( 22, 99)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28,112)( 29,114)( 30,113)( 31,109)( 32,111)
( 33,110)( 34,115)( 35,117)( 36,116)( 37,132)( 38,131)( 39,130)( 40,129)
( 41,128)( 42,127)( 43,135)( 44,134)( 45,133)( 46,123)( 47,122)( 48,121)
( 49,120)( 50,119)( 51,118)( 52,126)( 53,125)( 54,124)( 55,142)( 56,144)
( 57,143)( 58,139)( 59,141)( 60,140)( 61,136)( 62,138)( 63,137)( 64,162)
( 65,161)( 66,160)( 67,159)( 68,158)( 69,157)( 70,156)( 71,155)( 72,154)
( 73,153)( 74,152)( 75,151)( 76,150)( 77,149)( 78,148)( 79,147)( 80,146)
( 81,145)(163,183)(164,182)(165,181)(166,189)(167,188)(168,187)(169,186)
(170,185)(171,184)(172,174)(175,180)(176,179)(177,178)(190,213)(191,212)
(192,211)(193,210)(194,209)(195,208)(196,216)(197,215)(198,214)(199,204)
(200,203)(201,202)(205,207)(217,243)(218,242)(219,241)(220,240)(221,239)
(222,238)(223,237)(224,236)(225,235)(226,234)(227,233)(228,232)(229,231)
(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)(251,330)
(252,329)(253,345)(254,344)(255,343)(256,351)(257,350)(258,349)(259,348)
(260,347)(261,346)(262,336)(263,335)(264,334)(265,342)(266,341)(267,340)
(268,339)(269,338)(270,337)(271,355)(272,357)(273,356)(274,352)(275,354)
(276,353)(277,358)(278,360)(279,359)(280,375)(281,374)(282,373)(283,372)
(284,371)(285,370)(286,378)(287,377)(288,376)(289,366)(290,365)(291,364)
(292,363)(293,362)(294,361)(295,369)(296,368)(297,367)(298,385)(299,387)
(300,386)(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)(307,405)
(308,404)(309,403)(310,402)(311,401)(312,400)(313,399)(314,398)(315,397)
(316,396)(317,395)(318,394)(319,393)(320,392)(321,391)(322,390)(323,389)
(324,388)(406,426)(407,425)(408,424)(409,432)(410,431)(411,430)(412,429)
(413,428)(414,427)(415,417)(418,423)(419,422)(420,421)(433,456)(434,455)
(435,454)(436,453)(437,452)(438,451)(439,459)(440,458)(441,457)(442,447)
(443,446)(444,445)(448,450)(460,486)(461,485)(462,484)(463,483)(464,482)
(465,481)(466,480)(467,479)(468,478)(469,477)(470,476)(471,475)(472,474);;
s3 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 10, 21)( 11, 20)( 12, 19)( 13, 27)
( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)( 43, 51)
( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)( 65, 74)
( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 82,183)
( 83,182)( 84,181)( 85,189)( 86,188)( 87,187)( 88,186)( 89,185)( 90,184)
( 91,174)( 92,173)( 93,172)( 94,180)( 95,179)( 96,178)( 97,177)( 98,176)
( 99,175)(100,165)(101,164)(102,163)(103,171)(104,170)(105,169)(106,168)
(107,167)(108,166)(109,210)(110,209)(111,208)(112,216)(113,215)(114,214)
(115,213)(116,212)(117,211)(118,201)(119,200)(120,199)(121,207)(122,206)
(123,205)(124,204)(125,203)(126,202)(127,192)(128,191)(129,190)(130,198)
(131,197)(132,196)(133,195)(134,194)(135,193)(136,237)(137,236)(138,235)
(139,243)(140,242)(141,241)(142,240)(143,239)(144,238)(145,228)(146,227)
(147,226)(148,234)(149,233)(150,232)(151,231)(152,230)(153,229)(154,219)
(155,218)(156,217)(157,225)(158,224)(159,223)(160,222)(161,221)(162,220)
(245,246)(247,250)(248,252)(249,251)(253,264)(254,263)(255,262)(256,270)
(257,269)(258,268)(259,267)(260,266)(261,265)(272,273)(274,277)(275,279)
(276,278)(280,291)(281,290)(282,289)(283,297)(284,296)(285,295)(286,294)
(287,293)(288,292)(299,300)(301,304)(302,306)(303,305)(307,318)(308,317)
(309,316)(310,324)(311,323)(312,322)(313,321)(314,320)(315,319)(325,426)
(326,425)(327,424)(328,432)(329,431)(330,430)(331,429)(332,428)(333,427)
(334,417)(335,416)(336,415)(337,423)(338,422)(339,421)(340,420)(341,419)
(342,418)(343,408)(344,407)(345,406)(346,414)(347,413)(348,412)(349,411)
(350,410)(351,409)(352,453)(353,452)(354,451)(355,459)(356,458)(357,457)
(358,456)(359,455)(360,454)(361,444)(362,443)(363,442)(364,450)(365,449)
(366,448)(367,447)(368,446)(369,445)(370,435)(371,434)(372,433)(373,441)
(374,440)(375,439)(376,438)(377,437)(378,436)(379,480)(380,479)(381,478)
(382,486)(383,485)(384,484)(385,483)(386,482)(387,481)(388,471)(389,470)
(390,469)(391,477)(392,476)(393,475)(394,474)(395,473)(396,472)(397,462)
(398,461)(399,460)(400,468)(401,467)(402,466)(403,465)(404,464)(405,463);;
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, 
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)(  4,277)(  5,278)(  6,279)(  7,274)
(  8,275)(  9,276)( 10,280)( 11,281)( 12,282)( 13,286)( 14,287)( 15,288)
( 16,283)( 17,284)( 18,285)( 19,289)( 20,290)( 21,291)( 22,295)( 23,296)
( 24,297)( 25,292)( 26,293)( 27,294)( 28,244)( 29,245)( 30,246)( 31,250)
( 32,251)( 33,252)( 34,247)( 35,248)( 36,249)( 37,253)( 38,254)( 39,255)
( 40,259)( 41,260)( 42,261)( 43,256)( 44,257)( 45,258)( 46,262)( 47,263)
( 48,264)( 49,268)( 50,269)( 51,270)( 52,265)( 53,266)( 54,267)( 55,298)
( 56,299)( 57,300)( 58,304)( 59,305)( 60,306)( 61,301)( 62,302)( 63,303)
( 64,307)( 65,308)( 66,309)( 67,313)( 68,314)( 69,315)( 70,310)( 71,311)
( 72,312)( 73,316)( 74,317)( 75,318)( 76,322)( 77,323)( 78,324)( 79,319)
( 80,320)( 81,321)( 82,352)( 83,353)( 84,354)( 85,358)( 86,359)( 87,360)
( 88,355)( 89,356)( 90,357)( 91,361)( 92,362)( 93,363)( 94,367)( 95,368)
( 96,369)( 97,364)( 98,365)( 99,366)(100,370)(101,371)(102,372)(103,376)
(104,377)(105,378)(106,373)(107,374)(108,375)(109,325)(110,326)(111,327)
(112,331)(113,332)(114,333)(115,328)(116,329)(117,330)(118,334)(119,335)
(120,336)(121,340)(122,341)(123,342)(124,337)(125,338)(126,339)(127,343)
(128,344)(129,345)(130,349)(131,350)(132,351)(133,346)(134,347)(135,348)
(136,379)(137,380)(138,381)(139,385)(140,386)(141,387)(142,382)(143,383)
(144,384)(145,388)(146,389)(147,390)(148,394)(149,395)(150,396)(151,391)
(152,392)(153,393)(154,397)(155,398)(156,399)(157,403)(158,404)(159,405)
(160,400)(161,401)(162,402)(163,433)(164,434)(165,435)(166,439)(167,440)
(168,441)(169,436)(170,437)(171,438)(172,442)(173,443)(174,444)(175,448)
(176,449)(177,450)(178,445)(179,446)(180,447)(181,451)(182,452)(183,453)
(184,457)(185,458)(186,459)(187,454)(188,455)(189,456)(190,406)(191,407)
(192,408)(193,412)(194,413)(195,414)(196,409)(197,410)(198,411)(199,415)
(200,416)(201,417)(202,421)(203,422)(204,423)(205,418)(206,419)(207,420)
(208,424)(209,425)(210,426)(211,430)(212,431)(213,432)(214,427)(215,428)
(216,429)(217,460)(218,461)(219,462)(220,466)(221,467)(222,468)(223,463)
(224,464)(225,465)(226,469)(227,470)(228,471)(229,475)(230,476)(231,477)
(232,472)(233,473)(234,474)(235,478)(236,479)(237,480)(238,484)(239,485)
(240,486)(241,481)(242,482)(243,483);
s2 := Sym(486)!(  1, 82)(  2, 84)(  3, 83)(  4, 88)(  5, 90)(  6, 89)(  7, 85)
(  8, 87)(  9, 86)( 10,102)( 11,101)( 12,100)( 13,108)( 14,107)( 15,106)
( 16,105)( 17,104)( 18,103)( 19, 93)( 20, 92)( 21, 91)( 22, 99)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28,112)( 29,114)( 30,113)( 31,109)
( 32,111)( 33,110)( 34,115)( 35,117)( 36,116)( 37,132)( 38,131)( 39,130)
( 40,129)( 41,128)( 42,127)( 43,135)( 44,134)( 45,133)( 46,123)( 47,122)
( 48,121)( 49,120)( 50,119)( 51,118)( 52,126)( 53,125)( 54,124)( 55,142)
( 56,144)( 57,143)( 58,139)( 59,141)( 60,140)( 61,136)( 62,138)( 63,137)
( 64,162)( 65,161)( 66,160)( 67,159)( 68,158)( 69,157)( 70,156)( 71,155)
( 72,154)( 73,153)( 74,152)( 75,151)( 76,150)( 77,149)( 78,148)( 79,147)
( 80,146)( 81,145)(163,183)(164,182)(165,181)(166,189)(167,188)(168,187)
(169,186)(170,185)(171,184)(172,174)(175,180)(176,179)(177,178)(190,213)
(191,212)(192,211)(193,210)(194,209)(195,208)(196,216)(197,215)(198,214)
(199,204)(200,203)(201,202)(205,207)(217,243)(218,242)(219,241)(220,240)
(221,239)(222,238)(223,237)(224,236)(225,235)(226,234)(227,233)(228,232)
(229,231)(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)
(251,330)(252,329)(253,345)(254,344)(255,343)(256,351)(257,350)(258,349)
(259,348)(260,347)(261,346)(262,336)(263,335)(264,334)(265,342)(266,341)
(267,340)(268,339)(269,338)(270,337)(271,355)(272,357)(273,356)(274,352)
(275,354)(276,353)(277,358)(278,360)(279,359)(280,375)(281,374)(282,373)
(283,372)(284,371)(285,370)(286,378)(287,377)(288,376)(289,366)(290,365)
(291,364)(292,363)(293,362)(294,361)(295,369)(296,368)(297,367)(298,385)
(299,387)(300,386)(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)
(307,405)(308,404)(309,403)(310,402)(311,401)(312,400)(313,399)(314,398)
(315,397)(316,396)(317,395)(318,394)(319,393)(320,392)(321,391)(322,390)
(323,389)(324,388)(406,426)(407,425)(408,424)(409,432)(410,431)(411,430)
(412,429)(413,428)(414,427)(415,417)(418,423)(419,422)(420,421)(433,456)
(434,455)(435,454)(436,453)(437,452)(438,451)(439,459)(440,458)(441,457)
(442,447)(443,446)(444,445)(448,450)(460,486)(461,485)(462,484)(463,483)
(464,482)(465,481)(466,480)(467,479)(468,478)(469,477)(470,476)(471,475)
(472,474);
s3 := Sym(486)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 10, 21)( 11, 20)( 12, 19)
( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)
( 32, 36)( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)
( 43, 51)( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)
( 65, 74)( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)
( 82,183)( 83,182)( 84,181)( 85,189)( 86,188)( 87,187)( 88,186)( 89,185)
( 90,184)( 91,174)( 92,173)( 93,172)( 94,180)( 95,179)( 96,178)( 97,177)
( 98,176)( 99,175)(100,165)(101,164)(102,163)(103,171)(104,170)(105,169)
(106,168)(107,167)(108,166)(109,210)(110,209)(111,208)(112,216)(113,215)
(114,214)(115,213)(116,212)(117,211)(118,201)(119,200)(120,199)(121,207)
(122,206)(123,205)(124,204)(125,203)(126,202)(127,192)(128,191)(129,190)
(130,198)(131,197)(132,196)(133,195)(134,194)(135,193)(136,237)(137,236)
(138,235)(139,243)(140,242)(141,241)(142,240)(143,239)(144,238)(145,228)
(146,227)(147,226)(148,234)(149,233)(150,232)(151,231)(152,230)(153,229)
(154,219)(155,218)(156,217)(157,225)(158,224)(159,223)(160,222)(161,221)
(162,220)(245,246)(247,250)(248,252)(249,251)(253,264)(254,263)(255,262)
(256,270)(257,269)(258,268)(259,267)(260,266)(261,265)(272,273)(274,277)
(275,279)(276,278)(280,291)(281,290)(282,289)(283,297)(284,296)(285,295)
(286,294)(287,293)(288,292)(299,300)(301,304)(302,306)(303,305)(307,318)
(308,317)(309,316)(310,324)(311,323)(312,322)(313,321)(314,320)(315,319)
(325,426)(326,425)(327,424)(328,432)(329,431)(330,430)(331,429)(332,428)
(333,427)(334,417)(335,416)(336,415)(337,423)(338,422)(339,421)(340,420)
(341,419)(342,418)(343,408)(344,407)(345,406)(346,414)(347,413)(348,412)
(349,411)(350,410)(351,409)(352,453)(353,452)(354,451)(355,459)(356,458)
(357,457)(358,456)(359,455)(360,454)(361,444)(362,443)(363,442)(364,450)
(365,449)(366,448)(367,447)(368,446)(369,445)(370,435)(371,434)(372,433)
(373,441)(374,440)(375,439)(376,438)(377,437)(378,436)(379,480)(380,479)
(381,478)(382,486)(383,485)(384,484)(385,483)(386,482)(387,481)(388,471)
(389,470)(390,469)(391,477)(392,476)(393,475)(394,474)(395,473)(396,472)
(397,462)(398,461)(399,460)(400,468)(401,467)(402,466)(403,465)(404,464)
(405,463);
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, 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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope