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Polytope of Type {4,6,39}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,39}*1872
if this polytope has a name.
Group : SmallGroup(1872,922)
Rank : 4
Schlafli Type : {4,6,39}
Number of vertices, edges, etc : 4, 12, 117, 39
Order of s0s1s2s3 : 156
Order of s0s1s2s3s2s1 : 2
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 : {2,6,39}*936
   3-fold quotients : {4,2,39}*624
   6-fold quotients : {2,2,39}*312
   9-fold quotients : {4,2,13}*208
   13-fold quotients : {4,6,3}*144
   18-fold quotients : {2,2,13}*104
   26-fold quotients : {2,6,3}*72
   39-fold quotients : {4,2,3}*48
   78-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,235)(  2,236)(  3,237)(  4,238)(  5,239)(  6,240)(  7,241)(  8,242)
(  9,243)( 10,244)( 11,245)( 12,246)( 13,247)( 14,248)( 15,249)( 16,250)
( 17,251)( 18,252)( 19,253)( 20,254)( 21,255)( 22,256)( 23,257)( 24,258)
( 25,259)( 26,260)( 27,261)( 28,262)( 29,263)( 30,264)( 31,265)( 32,266)
( 33,267)( 34,268)( 35,269)( 36,270)( 37,271)( 38,272)( 39,273)( 40,274)
( 41,275)( 42,276)( 43,277)( 44,278)( 45,279)( 46,280)( 47,281)( 48,282)
( 49,283)( 50,284)( 51,285)( 52,286)( 53,287)( 54,288)( 55,289)( 56,290)
( 57,291)( 58,292)( 59,293)( 60,294)( 61,295)( 62,296)( 63,297)( 64,298)
( 65,299)( 66,300)( 67,301)( 68,302)( 69,303)( 70,304)( 71,305)( 72,306)
( 73,307)( 74,308)( 75,309)( 76,310)( 77,311)( 78,312)( 79,313)( 80,314)
( 81,315)( 82,316)( 83,317)( 84,318)( 85,319)( 86,320)( 87,321)( 88,322)
( 89,323)( 90,324)( 91,325)( 92,326)( 93,327)( 94,328)( 95,329)( 96,330)
( 97,331)( 98,332)( 99,333)(100,334)(101,335)(102,336)(103,337)(104,338)
(105,339)(106,340)(107,341)(108,342)(109,343)(110,344)(111,345)(112,346)
(113,347)(114,348)(115,349)(116,350)(117,351)(118,352)(119,353)(120,354)
(121,355)(122,356)(123,357)(124,358)(125,359)(126,360)(127,361)(128,362)
(129,363)(130,364)(131,365)(132,366)(133,367)(134,368)(135,369)(136,370)
(137,371)(138,372)(139,373)(140,374)(141,375)(142,376)(143,377)(144,378)
(145,379)(146,380)(147,381)(148,382)(149,383)(150,384)(151,385)(152,386)
(153,387)(154,388)(155,389)(156,390)(157,391)(158,392)(159,393)(160,394)
(161,395)(162,396)(163,397)(164,398)(165,399)(166,400)(167,401)(168,402)
(169,403)(170,404)(171,405)(172,406)(173,407)(174,408)(175,409)(176,410)
(177,411)(178,412)(179,413)(180,414)(181,415)(182,416)(183,417)(184,418)
(185,419)(186,420)(187,421)(188,422)(189,423)(190,424)(191,425)(192,426)
(193,427)(194,428)(195,429)(196,430)(197,431)(198,432)(199,433)(200,434)
(201,435)(202,436)(203,437)(204,438)(205,439)(206,440)(207,441)(208,442)
(209,443)(210,444)(211,445)(212,446)(213,447)(214,448)(215,449)(216,450)
(217,451)(218,452)(219,453)(220,454)(221,455)(222,456)(223,457)(224,458)
(225,459)(226,460)(227,461)(228,462)(229,463)(230,464)(231,465)(232,466)
(233,467)(234,468);;
s1 := ( 40, 79)( 41, 80)( 42, 81)( 43, 82)( 44, 83)( 45, 84)( 46, 85)( 47, 86)
( 48, 87)( 49, 88)( 50, 89)( 51, 90)( 52, 91)( 53, 92)( 54, 93)( 55, 94)
( 56, 95)( 57, 96)( 58, 97)( 59, 98)( 60, 99)( 61,100)( 62,101)( 63,102)
( 64,103)( 65,104)( 66,105)( 67,106)( 68,107)( 69,108)( 70,109)( 71,110)
( 72,111)( 73,112)( 74,113)( 75,114)( 76,115)( 77,116)( 78,117)(157,196)
(158,197)(159,198)(160,199)(161,200)(162,201)(163,202)(164,203)(165,204)
(166,205)(167,206)(168,207)(169,208)(170,209)(171,210)(172,211)(173,212)
(174,213)(175,214)(176,215)(177,216)(178,217)(179,218)(180,219)(181,220)
(182,221)(183,222)(184,223)(185,224)(186,225)(187,226)(188,227)(189,228)
(190,229)(191,230)(192,231)(193,232)(194,233)(195,234)(235,352)(236,353)
(237,354)(238,355)(239,356)(240,357)(241,358)(242,359)(243,360)(244,361)
(245,362)(246,363)(247,364)(248,365)(249,366)(250,367)(251,368)(252,369)
(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,376)(260,377)
(261,378)(262,379)(263,380)(264,381)(265,382)(266,383)(267,384)(268,385)
(269,386)(270,387)(271,388)(272,389)(273,390)(274,430)(275,431)(276,432)
(277,433)(278,434)(279,435)(280,436)(281,437)(282,438)(283,439)(284,440)
(285,441)(286,442)(287,443)(288,444)(289,445)(290,446)(291,447)(292,448)
(293,449)(294,450)(295,451)(296,452)(297,453)(298,454)(299,455)(300,456)
(301,457)(302,458)(303,459)(304,460)(305,461)(306,462)(307,463)(308,464)
(309,465)(310,466)(311,467)(312,468)(313,391)(314,392)(315,393)(316,394)
(317,395)(318,396)(319,397)(320,398)(321,399)(322,400)(323,401)(324,402)
(325,403)(326,404)(327,405)(328,406)(329,407)(330,408)(331,409)(332,410)
(333,411)(334,412)(335,413)(336,414)(337,415)(338,416)(339,417)(340,418)
(341,419)(342,420)(343,421)(344,422)(345,423)(346,424)(347,425)(348,426)
(349,427)(350,428)(351,429);;
s2 := (  1, 40)(  2, 52)(  3, 51)(  4, 50)(  5, 49)(  6, 48)(  7, 47)(  8, 46)
(  9, 45)( 10, 44)( 11, 43)( 12, 42)( 13, 41)( 14, 66)( 15, 78)( 16, 77)
( 17, 76)( 18, 75)( 19, 74)( 20, 73)( 21, 72)( 22, 71)( 23, 70)( 24, 69)
( 25, 68)( 26, 67)( 27, 53)( 28, 65)( 29, 64)( 30, 63)( 31, 62)( 32, 61)
( 33, 60)( 34, 59)( 35, 58)( 36, 57)( 37, 56)( 38, 55)( 39, 54)( 80, 91)
( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 92,105)( 93,117)( 94,116)
( 95,115)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)
(103,107)(104,106)(118,157)(119,169)(120,168)(121,167)(122,166)(123,165)
(124,164)(125,163)(126,162)(127,161)(128,160)(129,159)(130,158)(131,183)
(132,195)(133,194)(134,193)(135,192)(136,191)(137,190)(138,189)(139,188)
(140,187)(141,186)(142,185)(143,184)(144,170)(145,182)(146,181)(147,180)
(148,179)(149,178)(150,177)(151,176)(152,175)(153,174)(154,173)(155,172)
(156,171)(197,208)(198,207)(199,206)(200,205)(201,204)(202,203)(209,222)
(210,234)(211,233)(212,232)(213,231)(214,230)(215,229)(216,228)(217,227)
(218,226)(219,225)(220,224)(221,223)(235,274)(236,286)(237,285)(238,284)
(239,283)(240,282)(241,281)(242,280)(243,279)(244,278)(245,277)(246,276)
(247,275)(248,300)(249,312)(250,311)(251,310)(252,309)(253,308)(254,307)
(255,306)(256,305)(257,304)(258,303)(259,302)(260,301)(261,287)(262,299)
(263,298)(264,297)(265,296)(266,295)(267,294)(268,293)(269,292)(270,291)
(271,290)(272,289)(273,288)(314,325)(315,324)(316,323)(317,322)(318,321)
(319,320)(326,339)(327,351)(328,350)(329,349)(330,348)(331,347)(332,346)
(333,345)(334,344)(335,343)(336,342)(337,341)(338,340)(352,391)(353,403)
(354,402)(355,401)(356,400)(357,399)(358,398)(359,397)(360,396)(361,395)
(362,394)(363,393)(364,392)(365,417)(366,429)(367,428)(368,427)(369,426)
(370,425)(371,424)(372,423)(373,422)(374,421)(375,420)(376,419)(377,418)
(378,404)(379,416)(380,415)(381,414)(382,413)(383,412)(384,411)(385,410)
(386,409)(387,408)(388,407)(389,406)(390,405)(431,442)(432,441)(433,440)
(434,439)(435,438)(436,437)(443,456)(444,468)(445,467)(446,466)(447,465)
(448,464)(449,463)(450,462)(451,461)(452,460)(453,459)(454,458)(455,457);;
s3 := (  1, 15)(  2, 14)(  3, 26)(  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)
(  9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 27, 28)( 29, 39)( 30, 38)
( 31, 37)( 32, 36)( 33, 35)( 40, 93)( 41, 92)( 42,104)( 43,103)( 44,102)
( 45,101)( 46,100)( 47, 99)( 48, 98)( 49, 97)( 50, 96)( 51, 95)( 52, 94)
( 53, 80)( 54, 79)( 55, 91)( 56, 90)( 57, 89)( 58, 88)( 59, 87)( 60, 86)
( 61, 85)( 62, 84)( 63, 83)( 64, 82)( 65, 81)( 66,106)( 67,105)( 68,117)
( 69,116)( 70,115)( 71,114)( 72,113)( 73,112)( 74,111)( 75,110)( 76,109)
( 77,108)( 78,107)(118,132)(119,131)(120,143)(121,142)(122,141)(123,140)
(124,139)(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)(144,145)
(146,156)(147,155)(148,154)(149,153)(150,152)(157,210)(158,209)(159,221)
(160,220)(161,219)(162,218)(163,217)(164,216)(165,215)(166,214)(167,213)
(168,212)(169,211)(170,197)(171,196)(172,208)(173,207)(174,206)(175,205)
(176,204)(177,203)(178,202)(179,201)(180,200)(181,199)(182,198)(183,223)
(184,222)(185,234)(186,233)(187,232)(188,231)(189,230)(190,229)(191,228)
(192,227)(193,226)(194,225)(195,224)(235,249)(236,248)(237,260)(238,259)
(239,258)(240,257)(241,256)(242,255)(243,254)(244,253)(245,252)(246,251)
(247,250)(261,262)(263,273)(264,272)(265,271)(266,270)(267,269)(274,327)
(275,326)(276,338)(277,337)(278,336)(279,335)(280,334)(281,333)(282,332)
(283,331)(284,330)(285,329)(286,328)(287,314)(288,313)(289,325)(290,324)
(291,323)(292,322)(293,321)(294,320)(295,319)(296,318)(297,317)(298,316)
(299,315)(300,340)(301,339)(302,351)(303,350)(304,349)(305,348)(306,347)
(307,346)(308,345)(309,344)(310,343)(311,342)(312,341)(352,366)(353,365)
(354,377)(355,376)(356,375)(357,374)(358,373)(359,372)(360,371)(361,370)
(362,369)(363,368)(364,367)(378,379)(380,390)(381,389)(382,388)(383,387)
(384,386)(391,444)(392,443)(393,455)(394,454)(395,453)(396,452)(397,451)
(398,450)(399,449)(400,448)(401,447)(402,446)(403,445)(404,431)(405,430)
(406,442)(407,441)(408,440)(409,439)(410,438)(411,437)(412,436)(413,435)
(414,434)(415,433)(416,432)(417,457)(418,456)(419,468)(420,467)(421,466)
(422,465)(423,464)(424,463)(425,462)(426,461)(427,460)(428,459)(429,458);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
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*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*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(468)!(  1,235)(  2,236)(  3,237)(  4,238)(  5,239)(  6,240)(  7,241)
(  8,242)(  9,243)( 10,244)( 11,245)( 12,246)( 13,247)( 14,248)( 15,249)
( 16,250)( 17,251)( 18,252)( 19,253)( 20,254)( 21,255)( 22,256)( 23,257)
( 24,258)( 25,259)( 26,260)( 27,261)( 28,262)( 29,263)( 30,264)( 31,265)
( 32,266)( 33,267)( 34,268)( 35,269)( 36,270)( 37,271)( 38,272)( 39,273)
( 40,274)( 41,275)( 42,276)( 43,277)( 44,278)( 45,279)( 46,280)( 47,281)
( 48,282)( 49,283)( 50,284)( 51,285)( 52,286)( 53,287)( 54,288)( 55,289)
( 56,290)( 57,291)( 58,292)( 59,293)( 60,294)( 61,295)( 62,296)( 63,297)
( 64,298)( 65,299)( 66,300)( 67,301)( 68,302)( 69,303)( 70,304)( 71,305)
( 72,306)( 73,307)( 74,308)( 75,309)( 76,310)( 77,311)( 78,312)( 79,313)
( 80,314)( 81,315)( 82,316)( 83,317)( 84,318)( 85,319)( 86,320)( 87,321)
( 88,322)( 89,323)( 90,324)( 91,325)( 92,326)( 93,327)( 94,328)( 95,329)
( 96,330)( 97,331)( 98,332)( 99,333)(100,334)(101,335)(102,336)(103,337)
(104,338)(105,339)(106,340)(107,341)(108,342)(109,343)(110,344)(111,345)
(112,346)(113,347)(114,348)(115,349)(116,350)(117,351)(118,352)(119,353)
(120,354)(121,355)(122,356)(123,357)(124,358)(125,359)(126,360)(127,361)
(128,362)(129,363)(130,364)(131,365)(132,366)(133,367)(134,368)(135,369)
(136,370)(137,371)(138,372)(139,373)(140,374)(141,375)(142,376)(143,377)
(144,378)(145,379)(146,380)(147,381)(148,382)(149,383)(150,384)(151,385)
(152,386)(153,387)(154,388)(155,389)(156,390)(157,391)(158,392)(159,393)
(160,394)(161,395)(162,396)(163,397)(164,398)(165,399)(166,400)(167,401)
(168,402)(169,403)(170,404)(171,405)(172,406)(173,407)(174,408)(175,409)
(176,410)(177,411)(178,412)(179,413)(180,414)(181,415)(182,416)(183,417)
(184,418)(185,419)(186,420)(187,421)(188,422)(189,423)(190,424)(191,425)
(192,426)(193,427)(194,428)(195,429)(196,430)(197,431)(198,432)(199,433)
(200,434)(201,435)(202,436)(203,437)(204,438)(205,439)(206,440)(207,441)
(208,442)(209,443)(210,444)(211,445)(212,446)(213,447)(214,448)(215,449)
(216,450)(217,451)(218,452)(219,453)(220,454)(221,455)(222,456)(223,457)
(224,458)(225,459)(226,460)(227,461)(228,462)(229,463)(230,464)(231,465)
(232,466)(233,467)(234,468);
s1 := Sym(468)!( 40, 79)( 41, 80)( 42, 81)( 43, 82)( 44, 83)( 45, 84)( 46, 85)
( 47, 86)( 48, 87)( 49, 88)( 50, 89)( 51, 90)( 52, 91)( 53, 92)( 54, 93)
( 55, 94)( 56, 95)( 57, 96)( 58, 97)( 59, 98)( 60, 99)( 61,100)( 62,101)
( 63,102)( 64,103)( 65,104)( 66,105)( 67,106)( 68,107)( 69,108)( 70,109)
( 71,110)( 72,111)( 73,112)( 74,113)( 75,114)( 76,115)( 77,116)( 78,117)
(157,196)(158,197)(159,198)(160,199)(161,200)(162,201)(163,202)(164,203)
(165,204)(166,205)(167,206)(168,207)(169,208)(170,209)(171,210)(172,211)
(173,212)(174,213)(175,214)(176,215)(177,216)(178,217)(179,218)(180,219)
(181,220)(182,221)(183,222)(184,223)(185,224)(186,225)(187,226)(188,227)
(189,228)(190,229)(191,230)(192,231)(193,232)(194,233)(195,234)(235,352)
(236,353)(237,354)(238,355)(239,356)(240,357)(241,358)(242,359)(243,360)
(244,361)(245,362)(246,363)(247,364)(248,365)(249,366)(250,367)(251,368)
(252,369)(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,376)
(260,377)(261,378)(262,379)(263,380)(264,381)(265,382)(266,383)(267,384)
(268,385)(269,386)(270,387)(271,388)(272,389)(273,390)(274,430)(275,431)
(276,432)(277,433)(278,434)(279,435)(280,436)(281,437)(282,438)(283,439)
(284,440)(285,441)(286,442)(287,443)(288,444)(289,445)(290,446)(291,447)
(292,448)(293,449)(294,450)(295,451)(296,452)(297,453)(298,454)(299,455)
(300,456)(301,457)(302,458)(303,459)(304,460)(305,461)(306,462)(307,463)
(308,464)(309,465)(310,466)(311,467)(312,468)(313,391)(314,392)(315,393)
(316,394)(317,395)(318,396)(319,397)(320,398)(321,399)(322,400)(323,401)
(324,402)(325,403)(326,404)(327,405)(328,406)(329,407)(330,408)(331,409)
(332,410)(333,411)(334,412)(335,413)(336,414)(337,415)(338,416)(339,417)
(340,418)(341,419)(342,420)(343,421)(344,422)(345,423)(346,424)(347,425)
(348,426)(349,427)(350,428)(351,429);
s2 := Sym(468)!(  1, 40)(  2, 52)(  3, 51)(  4, 50)(  5, 49)(  6, 48)(  7, 47)
(  8, 46)(  9, 45)( 10, 44)( 11, 43)( 12, 42)( 13, 41)( 14, 66)( 15, 78)
( 16, 77)( 17, 76)( 18, 75)( 19, 74)( 20, 73)( 21, 72)( 22, 71)( 23, 70)
( 24, 69)( 25, 68)( 26, 67)( 27, 53)( 28, 65)( 29, 64)( 30, 63)( 31, 62)
( 32, 61)( 33, 60)( 34, 59)( 35, 58)( 36, 57)( 37, 56)( 38, 55)( 39, 54)
( 80, 91)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 92,105)( 93,117)
( 94,116)( 95,115)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(101,109)
(102,108)(103,107)(104,106)(118,157)(119,169)(120,168)(121,167)(122,166)
(123,165)(124,164)(125,163)(126,162)(127,161)(128,160)(129,159)(130,158)
(131,183)(132,195)(133,194)(134,193)(135,192)(136,191)(137,190)(138,189)
(139,188)(140,187)(141,186)(142,185)(143,184)(144,170)(145,182)(146,181)
(147,180)(148,179)(149,178)(150,177)(151,176)(152,175)(153,174)(154,173)
(155,172)(156,171)(197,208)(198,207)(199,206)(200,205)(201,204)(202,203)
(209,222)(210,234)(211,233)(212,232)(213,231)(214,230)(215,229)(216,228)
(217,227)(218,226)(219,225)(220,224)(221,223)(235,274)(236,286)(237,285)
(238,284)(239,283)(240,282)(241,281)(242,280)(243,279)(244,278)(245,277)
(246,276)(247,275)(248,300)(249,312)(250,311)(251,310)(252,309)(253,308)
(254,307)(255,306)(256,305)(257,304)(258,303)(259,302)(260,301)(261,287)
(262,299)(263,298)(264,297)(265,296)(266,295)(267,294)(268,293)(269,292)
(270,291)(271,290)(272,289)(273,288)(314,325)(315,324)(316,323)(317,322)
(318,321)(319,320)(326,339)(327,351)(328,350)(329,349)(330,348)(331,347)
(332,346)(333,345)(334,344)(335,343)(336,342)(337,341)(338,340)(352,391)
(353,403)(354,402)(355,401)(356,400)(357,399)(358,398)(359,397)(360,396)
(361,395)(362,394)(363,393)(364,392)(365,417)(366,429)(367,428)(368,427)
(369,426)(370,425)(371,424)(372,423)(373,422)(374,421)(375,420)(376,419)
(377,418)(378,404)(379,416)(380,415)(381,414)(382,413)(383,412)(384,411)
(385,410)(386,409)(387,408)(388,407)(389,406)(390,405)(431,442)(432,441)
(433,440)(434,439)(435,438)(436,437)(443,456)(444,468)(445,467)(446,466)
(447,465)(448,464)(449,463)(450,462)(451,461)(452,460)(453,459)(454,458)
(455,457);
s3 := Sym(468)!(  1, 15)(  2, 14)(  3, 26)(  4, 25)(  5, 24)(  6, 23)(  7, 22)
(  8, 21)(  9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 27, 28)( 29, 39)
( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 40, 93)( 41, 92)( 42,104)( 43,103)
( 44,102)( 45,101)( 46,100)( 47, 99)( 48, 98)( 49, 97)( 50, 96)( 51, 95)
( 52, 94)( 53, 80)( 54, 79)( 55, 91)( 56, 90)( 57, 89)( 58, 88)( 59, 87)
( 60, 86)( 61, 85)( 62, 84)( 63, 83)( 64, 82)( 65, 81)( 66,106)( 67,105)
( 68,117)( 69,116)( 70,115)( 71,114)( 72,113)( 73,112)( 74,111)( 75,110)
( 76,109)( 77,108)( 78,107)(118,132)(119,131)(120,143)(121,142)(122,141)
(123,140)(124,139)(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)
(144,145)(146,156)(147,155)(148,154)(149,153)(150,152)(157,210)(158,209)
(159,221)(160,220)(161,219)(162,218)(163,217)(164,216)(165,215)(166,214)
(167,213)(168,212)(169,211)(170,197)(171,196)(172,208)(173,207)(174,206)
(175,205)(176,204)(177,203)(178,202)(179,201)(180,200)(181,199)(182,198)
(183,223)(184,222)(185,234)(186,233)(187,232)(188,231)(189,230)(190,229)
(191,228)(192,227)(193,226)(194,225)(195,224)(235,249)(236,248)(237,260)
(238,259)(239,258)(240,257)(241,256)(242,255)(243,254)(244,253)(245,252)
(246,251)(247,250)(261,262)(263,273)(264,272)(265,271)(266,270)(267,269)
(274,327)(275,326)(276,338)(277,337)(278,336)(279,335)(280,334)(281,333)
(282,332)(283,331)(284,330)(285,329)(286,328)(287,314)(288,313)(289,325)
(290,324)(291,323)(292,322)(293,321)(294,320)(295,319)(296,318)(297,317)
(298,316)(299,315)(300,340)(301,339)(302,351)(303,350)(304,349)(305,348)
(306,347)(307,346)(308,345)(309,344)(310,343)(311,342)(312,341)(352,366)
(353,365)(354,377)(355,376)(356,375)(357,374)(358,373)(359,372)(360,371)
(361,370)(362,369)(363,368)(364,367)(378,379)(380,390)(381,389)(382,388)
(383,387)(384,386)(391,444)(392,443)(393,455)(394,454)(395,453)(396,452)
(397,451)(398,450)(399,449)(400,448)(401,447)(402,446)(403,445)(404,431)
(405,430)(406,442)(407,441)(408,440)(409,439)(410,438)(411,437)(412,436)
(413,435)(414,434)(415,433)(416,432)(417,457)(418,456)(419,468)(420,467)
(421,466)(422,465)(423,464)(424,463)(425,462)(426,461)(427,460)(428,459)
(429,458);
poly := sub<Sym(468)|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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 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*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*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope