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