Polytope of Type {2,4,27,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,27,4}*1728
if this polytope has a name.
Group : SmallGroup(1728,20783)
Rank : 5
Schlafli Type : {2,4,27,4}
Number of vertices, edges, etc : 2, 4, 54, 54, 4
Order of s0s1s2s3s4 : 54
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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) :
3-fold quotients : {2,4,9,4}*576
9-fold quotients : {2,4,3,4}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)
( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)
( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)
( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)
( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)( 74, 82)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)
( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)
(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)(122,130)
(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)
(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(153,161)(154,162)
(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)(170,178)
(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)
(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(201,209)(202,210)
(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(217,225)(218,226)
(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(233,241)(234,242)
(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(249,257)(250,258)
(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(265,273)(266,274)
(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(281,289)(282,290)
(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(297,305)(298,306)
(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(313,321)(314,322)
(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)(329,337)(330,338)
(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)(345,353)(346,354)
(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)(361,369)(362,370)
(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)(377,385)(378,386)
(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)(393,401)(394,402)
(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)(409,417)(410,418)
(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)(425,433)(426,434);;
s2 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 35)( 20, 37)
( 21, 36)( 22, 38)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 39)( 28, 41)
( 29, 40)( 30, 42)( 31, 47)( 32, 49)( 33, 48)( 34, 50)( 51,115)( 52,117)
( 53,116)( 54,118)( 55,123)( 56,125)( 57,124)( 58,126)( 59,119)( 60,121)
( 61,120)( 62,122)( 63,127)( 64,129)( 65,128)( 66,130)( 67, 99)( 68,101)
( 69,100)( 70,102)( 71,107)( 72,109)( 73,108)( 74,110)( 75,103)( 76,105)
( 77,104)( 78,106)( 79,111)( 80,113)( 81,112)( 82,114)( 83,131)( 84,133)
( 85,132)( 86,134)( 87,139)( 88,141)( 89,140)( 90,142)( 91,135)( 92,137)
( 93,136)( 94,138)( 95,143)( 96,145)( 97,144)( 98,146)(147,387)(148,389)
(149,388)(150,390)(151,395)(152,397)(153,396)(154,398)(155,391)(156,393)
(157,392)(158,394)(159,399)(160,401)(161,400)(162,402)(163,419)(164,421)
(165,420)(166,422)(167,427)(168,429)(169,428)(170,430)(171,423)(172,425)
(173,424)(174,426)(175,431)(176,433)(177,432)(178,434)(179,403)(180,405)
(181,404)(182,406)(183,411)(184,413)(185,412)(186,414)(187,407)(188,409)
(189,408)(190,410)(191,415)(192,417)(193,416)(194,418)(195,339)(196,341)
(197,340)(198,342)(199,347)(200,349)(201,348)(202,350)(203,343)(204,345)
(205,344)(206,346)(207,351)(208,353)(209,352)(210,354)(211,371)(212,373)
(213,372)(214,374)(215,379)(216,381)(217,380)(218,382)(219,375)(220,377)
(221,376)(222,378)(223,383)(224,385)(225,384)(226,386)(227,355)(228,357)
(229,356)(230,358)(231,363)(232,365)(233,364)(234,366)(235,359)(236,361)
(237,360)(238,362)(239,367)(240,369)(241,368)(242,370)(243,291)(244,293)
(245,292)(246,294)(247,299)(248,301)(249,300)(250,302)(251,295)(252,297)
(253,296)(254,298)(255,303)(256,305)(257,304)(258,306)(259,323)(260,325)
(261,324)(262,326)(263,331)(264,333)(265,332)(266,334)(267,327)(268,329)
(269,328)(270,330)(271,335)(272,337)(273,336)(274,338)(275,307)(276,309)
(277,308)(278,310)(279,315)(280,317)(281,316)(282,318)(283,311)(284,313)
(285,312)(286,314)(287,319)(288,321)(289,320)(290,322);;
s3 := ( 3,291)( 4,292)( 5,294)( 6,293)( 7,303)( 8,304)( 9,306)( 10,305)
( 11,299)( 12,300)( 13,302)( 14,301)( 15,295)( 16,296)( 17,298)( 18,297)
( 19,323)( 20,324)( 21,326)( 22,325)( 23,335)( 24,336)( 25,338)( 26,337)
( 27,331)( 28,332)( 29,334)( 30,333)( 31,327)( 32,328)( 33,330)( 34,329)
( 35,307)( 36,308)( 37,310)( 38,309)( 39,319)( 40,320)( 41,322)( 42,321)
( 43,315)( 44,316)( 45,318)( 46,317)( 47,311)( 48,312)( 49,314)( 50,313)
( 51,403)( 52,404)( 53,406)( 54,405)( 55,415)( 56,416)( 57,418)( 58,417)
( 59,411)( 60,412)( 61,414)( 62,413)( 63,407)( 64,408)( 65,410)( 66,409)
( 67,387)( 68,388)( 69,390)( 70,389)( 71,399)( 72,400)( 73,402)( 74,401)
( 75,395)( 76,396)( 77,398)( 78,397)( 79,391)( 80,392)( 81,394)( 82,393)
( 83,419)( 84,420)( 85,422)( 86,421)( 87,431)( 88,432)( 89,434)( 90,433)
( 91,427)( 92,428)( 93,430)( 94,429)( 95,423)( 96,424)( 97,426)( 98,425)
( 99,355)(100,356)(101,358)(102,357)(103,367)(104,368)(105,370)(106,369)
(107,363)(108,364)(109,366)(110,365)(111,359)(112,360)(113,362)(114,361)
(115,339)(116,340)(117,342)(118,341)(119,351)(120,352)(121,354)(122,353)
(123,347)(124,348)(125,350)(126,349)(127,343)(128,344)(129,346)(130,345)
(131,371)(132,372)(133,374)(134,373)(135,383)(136,384)(137,386)(138,385)
(139,379)(140,380)(141,382)(142,381)(143,375)(144,376)(145,378)(146,377)
(149,150)(151,159)(152,160)(153,162)(154,161)(157,158)(163,179)(164,180)
(165,182)(166,181)(167,191)(168,192)(169,194)(170,193)(171,187)(172,188)
(173,190)(174,189)(175,183)(176,184)(177,186)(178,185)(195,259)(196,260)
(197,262)(198,261)(199,271)(200,272)(201,274)(202,273)(203,267)(204,268)
(205,270)(206,269)(207,263)(208,264)(209,266)(210,265)(211,243)(212,244)
(213,246)(214,245)(215,255)(216,256)(217,258)(218,257)(219,251)(220,252)
(221,254)(222,253)(223,247)(224,248)(225,250)(226,249)(227,275)(228,276)
(229,278)(230,277)(231,287)(232,288)(233,290)(234,289)(235,283)(236,284)
(237,286)(238,285)(239,279)(240,280)(241,282)(242,281);;
s4 := ( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)
(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145)
(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)(160,161)
(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)(176,177)
(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)(192,193)
(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)(208,209)
(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)(224,225)
(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)(240,241)
(243,246)(244,245)(247,250)(248,249)(251,254)(252,253)(255,258)(256,257)
(259,262)(260,261)(263,266)(264,265)(267,270)(268,269)(271,274)(272,273)
(275,278)(276,277)(279,282)(280,281)(283,286)(284,285)(287,290)(288,289)
(291,294)(292,293)(295,298)(296,297)(299,302)(300,301)(303,306)(304,305)
(307,310)(308,309)(311,314)(312,313)(315,318)(316,317)(319,322)(320,321)
(323,326)(324,325)(327,330)(328,329)(331,334)(332,333)(335,338)(336,337)
(339,342)(340,341)(343,346)(344,345)(347,350)(348,349)(351,354)(352,353)
(355,358)(356,357)(359,362)(360,361)(363,366)(364,365)(367,370)(368,369)
(371,374)(372,373)(375,378)(376,377)(379,382)(380,381)(383,386)(384,385)
(387,390)(388,389)(391,394)(392,393)(395,398)(396,397)(399,402)(400,401)
(403,406)(404,405)(407,410)(408,409)(411,414)(412,413)(415,418)(416,417)
(419,422)(420,421)(423,426)(424,425)(427,430)(428,429)(431,434)(432,433);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s4*s3*s2*s4*s3*s4*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(434)!(1,2);
s1 := Sym(434)!( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)
( 10, 18)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)
( 26, 34)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)
( 42, 50)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)
( 58, 66)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)
( 74, 82)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)
( 90, 98)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)
(106,114)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)
(122,130)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)
(138,146)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(153,161)
(154,162)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)
(170,178)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)
(186,194)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(201,209)
(202,210)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(217,225)
(218,226)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(233,241)
(234,242)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(249,257)
(250,258)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(265,273)
(266,274)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(281,289)
(282,290)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(297,305)
(298,306)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(313,321)
(314,322)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)(329,337)
(330,338)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)(345,353)
(346,354)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)(361,369)
(362,370)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)(377,385)
(378,386)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)(393,401)
(394,402)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)(409,417)
(410,418)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)(425,433)
(426,434);
s2 := Sym(434)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 35)
( 20, 37)( 21, 36)( 22, 38)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 39)
( 28, 41)( 29, 40)( 30, 42)( 31, 47)( 32, 49)( 33, 48)( 34, 50)( 51,115)
( 52,117)( 53,116)( 54,118)( 55,123)( 56,125)( 57,124)( 58,126)( 59,119)
( 60,121)( 61,120)( 62,122)( 63,127)( 64,129)( 65,128)( 66,130)( 67, 99)
( 68,101)( 69,100)( 70,102)( 71,107)( 72,109)( 73,108)( 74,110)( 75,103)
( 76,105)( 77,104)( 78,106)( 79,111)( 80,113)( 81,112)( 82,114)( 83,131)
( 84,133)( 85,132)( 86,134)( 87,139)( 88,141)( 89,140)( 90,142)( 91,135)
( 92,137)( 93,136)( 94,138)( 95,143)( 96,145)( 97,144)( 98,146)(147,387)
(148,389)(149,388)(150,390)(151,395)(152,397)(153,396)(154,398)(155,391)
(156,393)(157,392)(158,394)(159,399)(160,401)(161,400)(162,402)(163,419)
(164,421)(165,420)(166,422)(167,427)(168,429)(169,428)(170,430)(171,423)
(172,425)(173,424)(174,426)(175,431)(176,433)(177,432)(178,434)(179,403)
(180,405)(181,404)(182,406)(183,411)(184,413)(185,412)(186,414)(187,407)
(188,409)(189,408)(190,410)(191,415)(192,417)(193,416)(194,418)(195,339)
(196,341)(197,340)(198,342)(199,347)(200,349)(201,348)(202,350)(203,343)
(204,345)(205,344)(206,346)(207,351)(208,353)(209,352)(210,354)(211,371)
(212,373)(213,372)(214,374)(215,379)(216,381)(217,380)(218,382)(219,375)
(220,377)(221,376)(222,378)(223,383)(224,385)(225,384)(226,386)(227,355)
(228,357)(229,356)(230,358)(231,363)(232,365)(233,364)(234,366)(235,359)
(236,361)(237,360)(238,362)(239,367)(240,369)(241,368)(242,370)(243,291)
(244,293)(245,292)(246,294)(247,299)(248,301)(249,300)(250,302)(251,295)
(252,297)(253,296)(254,298)(255,303)(256,305)(257,304)(258,306)(259,323)
(260,325)(261,324)(262,326)(263,331)(264,333)(265,332)(266,334)(267,327)
(268,329)(269,328)(270,330)(271,335)(272,337)(273,336)(274,338)(275,307)
(276,309)(277,308)(278,310)(279,315)(280,317)(281,316)(282,318)(283,311)
(284,313)(285,312)(286,314)(287,319)(288,321)(289,320)(290,322);
s3 := Sym(434)!( 3,291)( 4,292)( 5,294)( 6,293)( 7,303)( 8,304)( 9,306)
( 10,305)( 11,299)( 12,300)( 13,302)( 14,301)( 15,295)( 16,296)( 17,298)
( 18,297)( 19,323)( 20,324)( 21,326)( 22,325)( 23,335)( 24,336)( 25,338)
( 26,337)( 27,331)( 28,332)( 29,334)( 30,333)( 31,327)( 32,328)( 33,330)
( 34,329)( 35,307)( 36,308)( 37,310)( 38,309)( 39,319)( 40,320)( 41,322)
( 42,321)( 43,315)( 44,316)( 45,318)( 46,317)( 47,311)( 48,312)( 49,314)
( 50,313)( 51,403)( 52,404)( 53,406)( 54,405)( 55,415)( 56,416)( 57,418)
( 58,417)( 59,411)( 60,412)( 61,414)( 62,413)( 63,407)( 64,408)( 65,410)
( 66,409)( 67,387)( 68,388)( 69,390)( 70,389)( 71,399)( 72,400)( 73,402)
( 74,401)( 75,395)( 76,396)( 77,398)( 78,397)( 79,391)( 80,392)( 81,394)
( 82,393)( 83,419)( 84,420)( 85,422)( 86,421)( 87,431)( 88,432)( 89,434)
( 90,433)( 91,427)( 92,428)( 93,430)( 94,429)( 95,423)( 96,424)( 97,426)
( 98,425)( 99,355)(100,356)(101,358)(102,357)(103,367)(104,368)(105,370)
(106,369)(107,363)(108,364)(109,366)(110,365)(111,359)(112,360)(113,362)
(114,361)(115,339)(116,340)(117,342)(118,341)(119,351)(120,352)(121,354)
(122,353)(123,347)(124,348)(125,350)(126,349)(127,343)(128,344)(129,346)
(130,345)(131,371)(132,372)(133,374)(134,373)(135,383)(136,384)(137,386)
(138,385)(139,379)(140,380)(141,382)(142,381)(143,375)(144,376)(145,378)
(146,377)(149,150)(151,159)(152,160)(153,162)(154,161)(157,158)(163,179)
(164,180)(165,182)(166,181)(167,191)(168,192)(169,194)(170,193)(171,187)
(172,188)(173,190)(174,189)(175,183)(176,184)(177,186)(178,185)(195,259)
(196,260)(197,262)(198,261)(199,271)(200,272)(201,274)(202,273)(203,267)
(204,268)(205,270)(206,269)(207,263)(208,264)(209,266)(210,265)(211,243)
(212,244)(213,246)(214,245)(215,255)(216,256)(217,258)(218,257)(219,251)
(220,252)(221,254)(222,253)(223,247)(224,248)(225,250)(226,249)(227,275)
(228,276)(229,278)(230,277)(231,287)(232,288)(233,290)(234,289)(235,283)
(236,284)(237,286)(238,285)(239,279)(240,280)(241,282)(242,281);
s4 := Sym(434)!( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)
(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)
(144,145)(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)
(160,161)(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)
(176,177)(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)
(192,193)(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)
(208,209)(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)
(224,225)(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)
(240,241)(243,246)(244,245)(247,250)(248,249)(251,254)(252,253)(255,258)
(256,257)(259,262)(260,261)(263,266)(264,265)(267,270)(268,269)(271,274)
(272,273)(275,278)(276,277)(279,282)(280,281)(283,286)(284,285)(287,290)
(288,289)(291,294)(292,293)(295,298)(296,297)(299,302)(300,301)(303,306)
(304,305)(307,310)(308,309)(311,314)(312,313)(315,318)(316,317)(319,322)
(320,321)(323,326)(324,325)(327,330)(328,329)(331,334)(332,333)(335,338)
(336,337)(339,342)(340,341)(343,346)(344,345)(347,350)(348,349)(351,354)
(352,353)(355,358)(356,357)(359,362)(360,361)(363,366)(364,365)(367,370)
(368,369)(371,374)(372,373)(375,378)(376,377)(379,382)(380,381)(383,386)
(384,385)(387,390)(388,389)(391,394)(392,393)(395,398)(396,397)(399,402)
(400,401)(403,406)(404,405)(407,410)(408,409)(411,414)(412,413)(415,418)
(416,417)(419,422)(420,421)(423,426)(424,425)(427,430)(428,429)(431,434)
(432,433);
poly := sub<Sym(434)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s1*s2,
s4*s3*s2*s4*s3*s4*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 >;
to this polytope