Polytope of Type {54,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {54,6,3}*1944a
if this polytope has a name.
Group : SmallGroup(1944,948)
Rank : 4
Schlafli Type : {54,6,3}
Number of vertices, edges, etc : 54, 162, 9, 3
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 : {27,6,3}*972
3-fold quotients : {18,6,3}*648a, {54,2,3}*648
6-fold quotients : {9,6,3}*324, {27,2,3}*324
9-fold quotients : {18,2,3}*216, {6,6,3}*216a
18-fold quotients : {9,2,3}*108, {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 := ( 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);;
s1 := ( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)
( 9,329)( 10,345)( 11,344)( 12,343)( 13,351)( 14,350)( 15,349)( 16,348)
( 17,347)( 18,346)( 19,336)( 20,335)( 21,334)( 22,342)( 23,341)( 24,340)
( 25,339)( 26,338)( 27,337)( 28,355)( 29,357)( 30,356)( 31,352)( 32,354)
( 33,353)( 34,358)( 35,360)( 36,359)( 37,375)( 38,374)( 39,373)( 40,372)
( 41,371)( 42,370)( 43,378)( 44,377)( 45,376)( 46,366)( 47,365)( 48,364)
( 49,363)( 50,362)( 51,361)( 52,369)( 53,368)( 54,367)( 55,385)( 56,387)
( 57,386)( 58,382)( 59,384)( 60,383)( 61,379)( 62,381)( 63,380)( 64,405)
( 65,404)( 66,403)( 67,402)( 68,401)( 69,400)( 70,399)( 71,398)( 72,397)
( 73,396)( 74,395)( 75,394)( 76,393)( 77,392)( 78,391)( 79,390)( 80,389)
( 81,388)( 82,244)( 83,246)( 84,245)( 85,250)( 86,252)( 87,251)( 88,247)
( 89,249)( 90,248)( 91,264)( 92,263)( 93,262)( 94,270)( 95,269)( 96,268)
( 97,267)( 98,266)( 99,265)(100,255)(101,254)(102,253)(103,261)(104,260)
(105,259)(106,258)(107,257)(108,256)(109,274)(110,276)(111,275)(112,271)
(113,273)(114,272)(115,277)(116,279)(117,278)(118,294)(119,293)(120,292)
(121,291)(122,290)(123,289)(124,297)(125,296)(126,295)(127,285)(128,284)
(129,283)(130,282)(131,281)(132,280)(133,288)(134,287)(135,286)(136,304)
(137,306)(138,305)(139,301)(140,303)(141,302)(142,298)(143,300)(144,299)
(145,324)(146,323)(147,322)(148,321)(149,320)(150,319)(151,318)(152,317)
(153,316)(154,315)(155,314)(156,313)(157,312)(158,311)(159,310)(160,309)
(161,308)(162,307)(163,426)(164,425)(165,424)(166,432)(167,431)(168,430)
(169,429)(170,428)(171,427)(172,417)(173,416)(174,415)(175,423)(176,422)
(177,421)(178,420)(179,419)(180,418)(181,408)(182,407)(183,406)(184,414)
(185,413)(186,412)(187,411)(188,410)(189,409)(190,456)(191,455)(192,454)
(193,453)(194,452)(195,451)(196,459)(197,458)(198,457)(199,447)(200,446)
(201,445)(202,444)(203,443)(204,442)(205,450)(206,449)(207,448)(208,438)
(209,437)(210,436)(211,435)(212,434)(213,433)(214,441)(215,440)(216,439)
(217,486)(218,485)(219,484)(220,483)(221,482)(222,481)(223,480)(224,479)
(225,478)(226,477)(227,476)(228,475)(229,474)(230,473)(231,472)(232,471)
(233,470)(234,469)(235,468)(236,467)(237,466)(238,465)(239,464)(240,463)
(241,462)(242,461)(243,460);;
s2 := ( 1, 28)( 2, 29)( 3, 30)( 4, 34)( 5, 35)( 6, 36)( 7, 31)( 8, 32)
( 9, 33)( 10, 37)( 11, 38)( 12, 39)( 13, 43)( 14, 44)( 15, 45)( 16, 40)
( 17, 41)( 18, 42)( 19, 46)( 20, 47)( 21, 48)( 22, 52)( 23, 53)( 24, 54)
( 25, 49)( 26, 50)( 27, 51)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)
( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 82,109)( 83,110)( 84,111)( 85,115)
( 86,116)( 87,117)( 88,112)( 89,113)( 90,114)( 91,118)( 92,119)( 93,120)
( 94,124)( 95,125)( 96,126)( 97,121)( 98,122)( 99,123)(100,127)(101,128)
(102,129)(103,133)(104,134)(105,135)(106,130)(107,131)(108,132)(139,142)
(140,143)(141,144)(148,151)(149,152)(150,153)(157,160)(158,161)(159,162)
(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)
(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)
(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)
(187,211)(188,212)(189,213)(220,223)(221,224)(222,225)(229,232)(230,233)
(231,234)(238,241)(239,242)(240,243)(244,271)(245,272)(246,273)(247,277)
(248,278)(249,279)(250,274)(251,275)(252,276)(253,280)(254,281)(255,282)
(256,286)(257,287)(258,288)(259,283)(260,284)(261,285)(262,289)(263,290)
(264,291)(265,295)(266,296)(267,297)(268,292)(269,293)(270,294)(301,304)
(302,305)(303,306)(310,313)(311,314)(312,315)(319,322)(320,323)(321,324)
(325,352)(326,353)(327,354)(328,358)(329,359)(330,360)(331,355)(332,356)
(333,357)(334,361)(335,362)(336,363)(337,367)(338,368)(339,369)(340,364)
(341,365)(342,366)(343,370)(344,371)(345,372)(346,376)(347,377)(348,378)
(349,373)(350,374)(351,375)(382,385)(383,386)(384,387)(391,394)(392,395)
(393,396)(400,403)(401,404)(402,405)(406,433)(407,434)(408,435)(409,439)
(410,440)(411,441)(412,436)(413,437)(414,438)(415,442)(416,443)(417,444)
(418,448)(419,449)(420,450)(421,445)(422,446)(423,447)(424,451)(425,452)
(426,453)(427,457)(428,458)(429,459)(430,454)(431,455)(432,456)(463,466)
(464,467)(465,468)(472,475)(473,476)(474,477)(481,484)(482,485)(483,486);;
s3 := ( 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);;
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,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(486)!( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)
( 8,330)( 9,329)( 10,345)( 11,344)( 12,343)( 13,351)( 14,350)( 15,349)
( 16,348)( 17,347)( 18,346)( 19,336)( 20,335)( 21,334)( 22,342)( 23,341)
( 24,340)( 25,339)( 26,338)( 27,337)( 28,355)( 29,357)( 30,356)( 31,352)
( 32,354)( 33,353)( 34,358)( 35,360)( 36,359)( 37,375)( 38,374)( 39,373)
( 40,372)( 41,371)( 42,370)( 43,378)( 44,377)( 45,376)( 46,366)( 47,365)
( 48,364)( 49,363)( 50,362)( 51,361)( 52,369)( 53,368)( 54,367)( 55,385)
( 56,387)( 57,386)( 58,382)( 59,384)( 60,383)( 61,379)( 62,381)( 63,380)
( 64,405)( 65,404)( 66,403)( 67,402)( 68,401)( 69,400)( 70,399)( 71,398)
( 72,397)( 73,396)( 74,395)( 75,394)( 76,393)( 77,392)( 78,391)( 79,390)
( 80,389)( 81,388)( 82,244)( 83,246)( 84,245)( 85,250)( 86,252)( 87,251)
( 88,247)( 89,249)( 90,248)( 91,264)( 92,263)( 93,262)( 94,270)( 95,269)
( 96,268)( 97,267)( 98,266)( 99,265)(100,255)(101,254)(102,253)(103,261)
(104,260)(105,259)(106,258)(107,257)(108,256)(109,274)(110,276)(111,275)
(112,271)(113,273)(114,272)(115,277)(116,279)(117,278)(118,294)(119,293)
(120,292)(121,291)(122,290)(123,289)(124,297)(125,296)(126,295)(127,285)
(128,284)(129,283)(130,282)(131,281)(132,280)(133,288)(134,287)(135,286)
(136,304)(137,306)(138,305)(139,301)(140,303)(141,302)(142,298)(143,300)
(144,299)(145,324)(146,323)(147,322)(148,321)(149,320)(150,319)(151,318)
(152,317)(153,316)(154,315)(155,314)(156,313)(157,312)(158,311)(159,310)
(160,309)(161,308)(162,307)(163,426)(164,425)(165,424)(166,432)(167,431)
(168,430)(169,429)(170,428)(171,427)(172,417)(173,416)(174,415)(175,423)
(176,422)(177,421)(178,420)(179,419)(180,418)(181,408)(182,407)(183,406)
(184,414)(185,413)(186,412)(187,411)(188,410)(189,409)(190,456)(191,455)
(192,454)(193,453)(194,452)(195,451)(196,459)(197,458)(198,457)(199,447)
(200,446)(201,445)(202,444)(203,443)(204,442)(205,450)(206,449)(207,448)
(208,438)(209,437)(210,436)(211,435)(212,434)(213,433)(214,441)(215,440)
(216,439)(217,486)(218,485)(219,484)(220,483)(221,482)(222,481)(223,480)
(224,479)(225,478)(226,477)(227,476)(228,475)(229,474)(230,473)(231,472)
(232,471)(233,470)(234,469)(235,468)(236,467)(237,466)(238,465)(239,464)
(240,463)(241,462)(242,461)(243,460);
s2 := Sym(486)!( 1, 28)( 2, 29)( 3, 30)( 4, 34)( 5, 35)( 6, 36)( 7, 31)
( 8, 32)( 9, 33)( 10, 37)( 11, 38)( 12, 39)( 13, 43)( 14, 44)( 15, 45)
( 16, 40)( 17, 41)( 18, 42)( 19, 46)( 20, 47)( 21, 48)( 22, 52)( 23, 53)
( 24, 54)( 25, 49)( 26, 50)( 27, 51)( 58, 61)( 59, 62)( 60, 63)( 67, 70)
( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 82,109)( 83,110)( 84,111)
( 85,115)( 86,116)( 87,117)( 88,112)( 89,113)( 90,114)( 91,118)( 92,119)
( 93,120)( 94,124)( 95,125)( 96,126)( 97,121)( 98,122)( 99,123)(100,127)
(101,128)(102,129)(103,133)(104,134)(105,135)(106,130)(107,131)(108,132)
(139,142)(140,143)(141,144)(148,151)(149,152)(150,153)(157,160)(158,161)
(159,162)(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)
(170,194)(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)
(178,202)(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)
(186,216)(187,211)(188,212)(189,213)(220,223)(221,224)(222,225)(229,232)
(230,233)(231,234)(238,241)(239,242)(240,243)(244,271)(245,272)(246,273)
(247,277)(248,278)(249,279)(250,274)(251,275)(252,276)(253,280)(254,281)
(255,282)(256,286)(257,287)(258,288)(259,283)(260,284)(261,285)(262,289)
(263,290)(264,291)(265,295)(266,296)(267,297)(268,292)(269,293)(270,294)
(301,304)(302,305)(303,306)(310,313)(311,314)(312,315)(319,322)(320,323)
(321,324)(325,352)(326,353)(327,354)(328,358)(329,359)(330,360)(331,355)
(332,356)(333,357)(334,361)(335,362)(336,363)(337,367)(338,368)(339,369)
(340,364)(341,365)(342,366)(343,370)(344,371)(345,372)(346,376)(347,377)
(348,378)(349,373)(350,374)(351,375)(382,385)(383,386)(384,387)(391,394)
(392,395)(393,396)(400,403)(401,404)(402,405)(406,433)(407,434)(408,435)
(409,439)(410,440)(411,441)(412,436)(413,437)(414,438)(415,442)(416,443)
(417,444)(418,448)(419,449)(420,450)(421,445)(422,446)(423,447)(424,451)
(425,452)(426,453)(427,457)(428,458)(429,459)(430,454)(431,455)(432,456)
(463,466)(464,467)(465,468)(472,475)(473,476)(474,477)(481,484)(482,485)
(483,486);
s3 := 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);
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, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope