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Polytope of Type {39,6,4}

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