Polytope of Type {18,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6,3}*1944b
if this polytope has a name.
Group : SmallGroup(1944,952)
Rank : 4
Schlafli Type : {18,6,3}
Number of vertices, edges, etc : 18, 162, 27, 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 : {9,6,3}*972b
3-fold quotients : {18,6,3}*648a, {6,6,3}*648b
6-fold quotients : {9,6,3}*324, {3,6,3}*324a
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, 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);;
s1 := ( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)
( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)( 16,346)
( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)( 24,341)
( 25,337)( 26,339)( 27,338)( 28,356)( 29,355)( 30,357)( 31,353)( 32,352)
( 33,354)( 34,359)( 35,358)( 36,360)( 37,374)( 38,373)( 39,375)( 40,371)
( 41,370)( 42,372)( 43,377)( 44,376)( 45,378)( 46,365)( 47,364)( 48,366)
( 49,362)( 50,361)( 51,363)( 52,368)( 53,367)( 54,369)( 55,386)( 56,385)
( 57,387)( 58,383)( 59,382)( 60,384)( 61,380)( 62,379)( 63,381)( 64,404)
( 65,403)( 66,405)( 67,401)( 68,400)( 69,402)( 70,398)( 71,397)( 72,399)
( 73,395)( 74,394)( 75,396)( 76,392)( 77,391)( 78,393)( 79,389)( 80,388)
( 81,390)( 82,244)( 83,246)( 84,245)( 85,250)( 86,252)( 87,251)( 88,247)
( 89,249)( 90,248)( 91,262)( 92,264)( 93,263)( 94,268)( 95,270)( 96,269)
( 97,265)( 98,267)( 99,266)(100,253)(101,255)(102,254)(103,259)(104,261)
(105,260)(106,256)(107,258)(108,257)(109,275)(110,274)(111,276)(112,272)
(113,271)(114,273)(115,278)(116,277)(117,279)(118,293)(119,292)(120,294)
(121,290)(122,289)(123,291)(124,296)(125,295)(126,297)(127,284)(128,283)
(129,285)(130,281)(131,280)(132,282)(133,287)(134,286)(135,288)(136,305)
(137,304)(138,306)(139,302)(140,301)(141,303)(142,299)(143,298)(144,300)
(145,323)(146,322)(147,324)(148,320)(149,319)(150,321)(151,317)(152,316)
(153,318)(154,314)(155,313)(156,315)(157,311)(158,310)(159,312)(160,308)
(161,307)(162,309)(163,415)(164,417)(165,416)(166,421)(167,423)(168,422)
(169,418)(170,420)(171,419)(172,406)(173,408)(174,407)(175,412)(176,414)
(177,413)(178,409)(179,411)(180,410)(181,424)(182,426)(183,425)(184,430)
(185,432)(186,431)(187,427)(188,429)(189,428)(190,446)(191,445)(192,447)
(193,443)(194,442)(195,444)(196,449)(197,448)(198,450)(199,437)(200,436)
(201,438)(202,434)(203,433)(204,435)(205,440)(206,439)(207,441)(208,455)
(209,454)(210,456)(211,452)(212,451)(213,453)(214,458)(215,457)(216,459)
(217,476)(218,475)(219,477)(220,473)(221,472)(222,474)(223,470)(224,469)
(225,471)(226,467)(227,466)(228,468)(229,464)(230,463)(231,465)(232,461)
(233,460)(234,462)(235,485)(236,484)(237,486)(238,482)(239,481)(240,483)
(241,479)(242,478)(243,480);;
s2 := ( 1, 28)( 2, 29)( 3, 30)( 4, 35)( 5, 36)( 6, 34)( 7, 33)( 8, 31)
( 9, 32)( 10, 37)( 11, 38)( 12, 39)( 13, 44)( 14, 45)( 15, 43)( 16, 42)
( 17, 40)( 18, 41)( 19, 46)( 20, 47)( 21, 48)( 22, 53)( 23, 54)( 24, 52)
( 25, 51)( 26, 49)( 27, 50)( 58, 62)( 59, 63)( 60, 61)( 67, 71)( 68, 72)
( 69, 70)( 76, 80)( 77, 81)( 78, 79)( 82,109)( 83,110)( 84,111)( 85,116)
( 86,117)( 87,115)( 88,114)( 89,112)( 90,113)( 91,118)( 92,119)( 93,120)
( 94,125)( 95,126)( 96,124)( 97,123)( 98,121)( 99,122)(100,127)(101,128)
(102,129)(103,134)(104,135)(105,133)(106,132)(107,130)(108,131)(139,143)
(140,144)(141,142)(148,152)(149,153)(150,151)(157,161)(158,162)(159,160)
(163,190)(164,191)(165,192)(166,197)(167,198)(168,196)(169,195)(170,193)
(171,194)(172,199)(173,200)(174,201)(175,206)(176,207)(177,205)(178,204)
(179,202)(180,203)(181,208)(182,209)(183,210)(184,215)(185,216)(186,214)
(187,213)(188,211)(189,212)(220,224)(221,225)(222,223)(229,233)(230,234)
(231,232)(238,242)(239,243)(240,241)(244,271)(245,272)(246,273)(247,278)
(248,279)(249,277)(250,276)(251,274)(252,275)(253,280)(254,281)(255,282)
(256,287)(257,288)(258,286)(259,285)(260,283)(261,284)(262,289)(263,290)
(264,291)(265,296)(266,297)(267,295)(268,294)(269,292)(270,293)(301,305)
(302,306)(303,304)(310,314)(311,315)(312,313)(319,323)(320,324)(321,322)
(325,352)(326,353)(327,354)(328,359)(329,360)(330,358)(331,357)(332,355)
(333,356)(334,361)(335,362)(336,363)(337,368)(338,369)(339,367)(340,366)
(341,364)(342,365)(343,370)(344,371)(345,372)(346,377)(347,378)(348,376)
(349,375)(350,373)(351,374)(382,386)(383,387)(384,385)(391,395)(392,396)
(393,394)(400,404)(401,405)(402,403)(406,433)(407,434)(408,435)(409,440)
(410,441)(411,439)(412,438)(413,436)(414,437)(415,442)(416,443)(417,444)
(418,449)(419,450)(420,448)(421,447)(422,445)(423,446)(424,451)(425,452)
(426,453)(427,458)(428,459)(429,457)(430,456)(431,454)(432,455)(463,467)
(464,468)(465,466)(472,476)(473,477)(474,475)(481,485)(482,486)(483,484);;
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, s0*s1*s2*s1*s0*s1*s0*s1*s2*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, 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);
s1 := Sym(486)!( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)
( 8,330)( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)
( 16,346)( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)
( 24,341)( 25,337)( 26,339)( 27,338)( 28,356)( 29,355)( 30,357)( 31,353)
( 32,352)( 33,354)( 34,359)( 35,358)( 36,360)( 37,374)( 38,373)( 39,375)
( 40,371)( 41,370)( 42,372)( 43,377)( 44,376)( 45,378)( 46,365)( 47,364)
( 48,366)( 49,362)( 50,361)( 51,363)( 52,368)( 53,367)( 54,369)( 55,386)
( 56,385)( 57,387)( 58,383)( 59,382)( 60,384)( 61,380)( 62,379)( 63,381)
( 64,404)( 65,403)( 66,405)( 67,401)( 68,400)( 69,402)( 70,398)( 71,397)
( 72,399)( 73,395)( 74,394)( 75,396)( 76,392)( 77,391)( 78,393)( 79,389)
( 80,388)( 81,390)( 82,244)( 83,246)( 84,245)( 85,250)( 86,252)( 87,251)
( 88,247)( 89,249)( 90,248)( 91,262)( 92,264)( 93,263)( 94,268)( 95,270)
( 96,269)( 97,265)( 98,267)( 99,266)(100,253)(101,255)(102,254)(103,259)
(104,261)(105,260)(106,256)(107,258)(108,257)(109,275)(110,274)(111,276)
(112,272)(113,271)(114,273)(115,278)(116,277)(117,279)(118,293)(119,292)
(120,294)(121,290)(122,289)(123,291)(124,296)(125,295)(126,297)(127,284)
(128,283)(129,285)(130,281)(131,280)(132,282)(133,287)(134,286)(135,288)
(136,305)(137,304)(138,306)(139,302)(140,301)(141,303)(142,299)(143,298)
(144,300)(145,323)(146,322)(147,324)(148,320)(149,319)(150,321)(151,317)
(152,316)(153,318)(154,314)(155,313)(156,315)(157,311)(158,310)(159,312)
(160,308)(161,307)(162,309)(163,415)(164,417)(165,416)(166,421)(167,423)
(168,422)(169,418)(170,420)(171,419)(172,406)(173,408)(174,407)(175,412)
(176,414)(177,413)(178,409)(179,411)(180,410)(181,424)(182,426)(183,425)
(184,430)(185,432)(186,431)(187,427)(188,429)(189,428)(190,446)(191,445)
(192,447)(193,443)(194,442)(195,444)(196,449)(197,448)(198,450)(199,437)
(200,436)(201,438)(202,434)(203,433)(204,435)(205,440)(206,439)(207,441)
(208,455)(209,454)(210,456)(211,452)(212,451)(213,453)(214,458)(215,457)
(216,459)(217,476)(218,475)(219,477)(220,473)(221,472)(222,474)(223,470)
(224,469)(225,471)(226,467)(227,466)(228,468)(229,464)(230,463)(231,465)
(232,461)(233,460)(234,462)(235,485)(236,484)(237,486)(238,482)(239,481)
(240,483)(241,479)(242,478)(243,480);
s2 := Sym(486)!( 1, 28)( 2, 29)( 3, 30)( 4, 35)( 5, 36)( 6, 34)( 7, 33)
( 8, 31)( 9, 32)( 10, 37)( 11, 38)( 12, 39)( 13, 44)( 14, 45)( 15, 43)
( 16, 42)( 17, 40)( 18, 41)( 19, 46)( 20, 47)( 21, 48)( 22, 53)( 23, 54)
( 24, 52)( 25, 51)( 26, 49)( 27, 50)( 58, 62)( 59, 63)( 60, 61)( 67, 71)
( 68, 72)( 69, 70)( 76, 80)( 77, 81)( 78, 79)( 82,109)( 83,110)( 84,111)
( 85,116)( 86,117)( 87,115)( 88,114)( 89,112)( 90,113)( 91,118)( 92,119)
( 93,120)( 94,125)( 95,126)( 96,124)( 97,123)( 98,121)( 99,122)(100,127)
(101,128)(102,129)(103,134)(104,135)(105,133)(106,132)(107,130)(108,131)
(139,143)(140,144)(141,142)(148,152)(149,153)(150,151)(157,161)(158,162)
(159,160)(163,190)(164,191)(165,192)(166,197)(167,198)(168,196)(169,195)
(170,193)(171,194)(172,199)(173,200)(174,201)(175,206)(176,207)(177,205)
(178,204)(179,202)(180,203)(181,208)(182,209)(183,210)(184,215)(185,216)
(186,214)(187,213)(188,211)(189,212)(220,224)(221,225)(222,223)(229,233)
(230,234)(231,232)(238,242)(239,243)(240,241)(244,271)(245,272)(246,273)
(247,278)(248,279)(249,277)(250,276)(251,274)(252,275)(253,280)(254,281)
(255,282)(256,287)(257,288)(258,286)(259,285)(260,283)(261,284)(262,289)
(263,290)(264,291)(265,296)(266,297)(267,295)(268,294)(269,292)(270,293)
(301,305)(302,306)(303,304)(310,314)(311,315)(312,313)(319,323)(320,324)
(321,322)(325,352)(326,353)(327,354)(328,359)(329,360)(330,358)(331,357)
(332,355)(333,356)(334,361)(335,362)(336,363)(337,368)(338,369)(339,367)
(340,366)(341,364)(342,365)(343,370)(344,371)(345,372)(346,377)(347,378)
(348,376)(349,375)(350,373)(351,374)(382,386)(383,387)(384,385)(391,395)
(392,396)(393,394)(400,404)(401,405)(402,403)(406,433)(407,434)(408,435)
(409,440)(410,441)(411,439)(412,438)(413,436)(414,437)(415,442)(416,443)
(417,444)(418,449)(419,450)(420,448)(421,447)(422,445)(423,446)(424,451)
(425,452)(426,453)(427,458)(428,459)(429,457)(430,456)(431,454)(432,455)
(463,467)(464,468)(465,466)(472,476)(473,477)(474,475)(481,485)(482,486)
(483,484);
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,
s0*s1*s2*s1*s0*s1*s0*s1*s2*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