Polytope of Type {38,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,6,4}*1824b
if this polytope has a name.
Group : SmallGroup(1824,1245)
Rank : 4
Schlafli Type : {38,6,4}
Number of vertices, edges, etc : 38, 114, 12, 4
Order of s0s1s2s3 : 114
Order of s0s1s2s3s2s1 : 2
Special Properties :
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) :
19-fold quotients : {2,6,4}*96c
38-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 73)( 6, 74)( 7, 75)( 8, 76)( 9, 69)( 10, 70)( 11, 71)( 12, 72)
( 13, 65)( 14, 66)( 15, 67)( 16, 68)( 17, 61)( 18, 62)( 19, 63)( 20, 64)
( 21, 57)( 22, 58)( 23, 59)( 24, 60)( 25, 53)( 26, 54)( 27, 55)( 28, 56)
( 29, 49)( 30, 50)( 31, 51)( 32, 52)( 33, 45)( 34, 46)( 35, 47)( 36, 48)
( 37, 41)( 38, 42)( 39, 43)( 40, 44)( 81,149)( 82,150)( 83,151)( 84,152)
( 85,145)( 86,146)( 87,147)( 88,148)( 89,141)( 90,142)( 91,143)( 92,144)
( 93,137)( 94,138)( 95,139)( 96,140)( 97,133)( 98,134)( 99,135)(100,136)
(101,129)(102,130)(103,131)(104,132)(105,125)(106,126)(107,127)(108,128)
(109,121)(110,122)(111,123)(112,124)(113,117)(114,118)(115,119)(116,120)
(157,225)(158,226)(159,227)(160,228)(161,221)(162,222)(163,223)(164,224)
(165,217)(166,218)(167,219)(168,220)(169,213)(170,214)(171,215)(172,216)
(173,209)(174,210)(175,211)(176,212)(177,205)(178,206)(179,207)(180,208)
(181,201)(182,202)(183,203)(184,204)(185,197)(186,198)(187,199)(188,200)
(189,193)(190,194)(191,195)(192,196)(233,301)(234,302)(235,303)(236,304)
(237,297)(238,298)(239,299)(240,300)(241,293)(242,294)(243,295)(244,296)
(245,289)(246,290)(247,291)(248,292)(249,285)(250,286)(251,287)(252,288)
(253,281)(254,282)(255,283)(256,284)(257,277)(258,278)(259,279)(260,280)
(261,273)(262,274)(263,275)(264,276)(265,269)(266,270)(267,271)(268,272)
(309,377)(310,378)(311,379)(312,380)(313,373)(314,374)(315,375)(316,376)
(317,369)(318,370)(319,371)(320,372)(321,365)(322,366)(323,367)(324,368)
(325,361)(326,362)(327,363)(328,364)(329,357)(330,358)(331,359)(332,360)
(333,353)(334,354)(335,355)(336,356)(337,349)(338,350)(339,351)(340,352)
(341,345)(342,346)(343,347)(344,348)(385,453)(386,454)(387,455)(388,456)
(389,449)(390,450)(391,451)(392,452)(393,445)(394,446)(395,447)(396,448)
(397,441)(398,442)(399,443)(400,444)(401,437)(402,438)(403,439)(404,440)
(405,433)(406,434)(407,435)(408,436)(409,429)(410,430)(411,431)(412,432)
(413,425)(414,426)(415,427)(416,428)(417,421)(418,422)(419,423)(420,424);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 73)( 10, 74)( 11, 76)( 12, 75)
( 13, 69)( 14, 70)( 15, 72)( 16, 71)( 17, 65)( 18, 66)( 19, 68)( 20, 67)
( 21, 61)( 22, 62)( 23, 64)( 24, 63)( 25, 57)( 26, 58)( 27, 60)( 28, 59)
( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)
( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 43, 44)( 77,157)( 78,158)( 79,160)
( 80,159)( 81,153)( 82,154)( 83,156)( 84,155)( 85,225)( 86,226)( 87,228)
( 88,227)( 89,221)( 90,222)( 91,224)( 92,223)( 93,217)( 94,218)( 95,220)
( 96,219)( 97,213)( 98,214)( 99,216)(100,215)(101,209)(102,210)(103,212)
(104,211)(105,205)(106,206)(107,208)(108,207)(109,201)(110,202)(111,204)
(112,203)(113,197)(114,198)(115,200)(116,199)(117,193)(118,194)(119,196)
(120,195)(121,189)(122,190)(123,192)(124,191)(125,185)(126,186)(127,188)
(128,187)(129,181)(130,182)(131,184)(132,183)(133,177)(134,178)(135,180)
(136,179)(137,173)(138,174)(139,176)(140,175)(141,169)(142,170)(143,172)
(144,171)(145,165)(146,166)(147,168)(148,167)(149,161)(150,162)(151,164)
(152,163)(229,233)(230,234)(231,236)(232,235)(237,301)(238,302)(239,304)
(240,303)(241,297)(242,298)(243,300)(244,299)(245,293)(246,294)(247,296)
(248,295)(249,289)(250,290)(251,292)(252,291)(253,285)(254,286)(255,288)
(256,287)(257,281)(258,282)(259,284)(260,283)(261,277)(262,278)(263,280)
(264,279)(265,273)(266,274)(267,276)(268,275)(271,272)(305,385)(306,386)
(307,388)(308,387)(309,381)(310,382)(311,384)(312,383)(313,453)(314,454)
(315,456)(316,455)(317,449)(318,450)(319,452)(320,451)(321,445)(322,446)
(323,448)(324,447)(325,441)(326,442)(327,444)(328,443)(329,437)(330,438)
(331,440)(332,439)(333,433)(334,434)(335,436)(336,435)(337,429)(338,430)
(339,432)(340,431)(341,425)(342,426)(343,428)(344,427)(345,421)(346,422)
(347,424)(348,423)(349,417)(350,418)(351,420)(352,419)(353,413)(354,414)
(355,416)(356,415)(357,409)(358,410)(359,412)(360,411)(361,405)(362,406)
(363,408)(364,407)(365,401)(366,402)(367,404)(368,403)(369,397)(370,398)
(371,400)(372,399)(373,393)(374,394)(375,396)(376,395)(377,389)(378,390)
(379,392)(380,391);;
s2 := ( 1,305)( 2,308)( 3,307)( 4,306)( 5,309)( 6,312)( 7,311)( 8,310)
( 9,313)( 10,316)( 11,315)( 12,314)( 13,317)( 14,320)( 15,319)( 16,318)
( 17,321)( 18,324)( 19,323)( 20,322)( 21,325)( 22,328)( 23,327)( 24,326)
( 25,329)( 26,332)( 27,331)( 28,330)( 29,333)( 30,336)( 31,335)( 32,334)
( 33,337)( 34,340)( 35,339)( 36,338)( 37,341)( 38,344)( 39,343)( 40,342)
( 41,345)( 42,348)( 43,347)( 44,346)( 45,349)( 46,352)( 47,351)( 48,350)
( 49,353)( 50,356)( 51,355)( 52,354)( 53,357)( 54,360)( 55,359)( 56,358)
( 57,361)( 58,364)( 59,363)( 60,362)( 61,365)( 62,368)( 63,367)( 64,366)
( 65,369)( 66,372)( 67,371)( 68,370)( 69,373)( 70,376)( 71,375)( 72,374)
( 73,377)( 74,380)( 75,379)( 76,378)( 77,229)( 78,232)( 79,231)( 80,230)
( 81,233)( 82,236)( 83,235)( 84,234)( 85,237)( 86,240)( 87,239)( 88,238)
( 89,241)( 90,244)( 91,243)( 92,242)( 93,245)( 94,248)( 95,247)( 96,246)
( 97,249)( 98,252)( 99,251)(100,250)(101,253)(102,256)(103,255)(104,254)
(105,257)(106,260)(107,259)(108,258)(109,261)(110,264)(111,263)(112,262)
(113,265)(114,268)(115,267)(116,266)(117,269)(118,272)(119,271)(120,270)
(121,273)(122,276)(123,275)(124,274)(125,277)(126,280)(127,279)(128,278)
(129,281)(130,284)(131,283)(132,282)(133,285)(134,288)(135,287)(136,286)
(137,289)(138,292)(139,291)(140,290)(141,293)(142,296)(143,295)(144,294)
(145,297)(146,300)(147,299)(148,298)(149,301)(150,304)(151,303)(152,302)
(153,381)(154,384)(155,383)(156,382)(157,385)(158,388)(159,387)(160,386)
(161,389)(162,392)(163,391)(164,390)(165,393)(166,396)(167,395)(168,394)
(169,397)(170,400)(171,399)(172,398)(173,401)(174,404)(175,403)(176,402)
(177,405)(178,408)(179,407)(180,406)(181,409)(182,412)(183,411)(184,410)
(185,413)(186,416)(187,415)(188,414)(189,417)(190,420)(191,419)(192,418)
(193,421)(194,424)(195,423)(196,422)(197,425)(198,428)(199,427)(200,426)
(201,429)(202,432)(203,431)(204,430)(205,433)(206,436)(207,435)(208,434)
(209,437)(210,440)(211,439)(212,438)(213,441)(214,444)(215,443)(216,442)
(217,445)(218,448)(219,447)(220,446)(221,449)(222,452)(223,451)(224,450)
(225,453)(226,456)(227,455)(228,454);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456);;
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*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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(456)!( 5, 73)( 6, 74)( 7, 75)( 8, 76)( 9, 69)( 10, 70)( 11, 71)
( 12, 72)( 13, 65)( 14, 66)( 15, 67)( 16, 68)( 17, 61)( 18, 62)( 19, 63)
( 20, 64)( 21, 57)( 22, 58)( 23, 59)( 24, 60)( 25, 53)( 26, 54)( 27, 55)
( 28, 56)( 29, 49)( 30, 50)( 31, 51)( 32, 52)( 33, 45)( 34, 46)( 35, 47)
( 36, 48)( 37, 41)( 38, 42)( 39, 43)( 40, 44)( 81,149)( 82,150)( 83,151)
( 84,152)( 85,145)( 86,146)( 87,147)( 88,148)( 89,141)( 90,142)( 91,143)
( 92,144)( 93,137)( 94,138)( 95,139)( 96,140)( 97,133)( 98,134)( 99,135)
(100,136)(101,129)(102,130)(103,131)(104,132)(105,125)(106,126)(107,127)
(108,128)(109,121)(110,122)(111,123)(112,124)(113,117)(114,118)(115,119)
(116,120)(157,225)(158,226)(159,227)(160,228)(161,221)(162,222)(163,223)
(164,224)(165,217)(166,218)(167,219)(168,220)(169,213)(170,214)(171,215)
(172,216)(173,209)(174,210)(175,211)(176,212)(177,205)(178,206)(179,207)
(180,208)(181,201)(182,202)(183,203)(184,204)(185,197)(186,198)(187,199)
(188,200)(189,193)(190,194)(191,195)(192,196)(233,301)(234,302)(235,303)
(236,304)(237,297)(238,298)(239,299)(240,300)(241,293)(242,294)(243,295)
(244,296)(245,289)(246,290)(247,291)(248,292)(249,285)(250,286)(251,287)
(252,288)(253,281)(254,282)(255,283)(256,284)(257,277)(258,278)(259,279)
(260,280)(261,273)(262,274)(263,275)(264,276)(265,269)(266,270)(267,271)
(268,272)(309,377)(310,378)(311,379)(312,380)(313,373)(314,374)(315,375)
(316,376)(317,369)(318,370)(319,371)(320,372)(321,365)(322,366)(323,367)
(324,368)(325,361)(326,362)(327,363)(328,364)(329,357)(330,358)(331,359)
(332,360)(333,353)(334,354)(335,355)(336,356)(337,349)(338,350)(339,351)
(340,352)(341,345)(342,346)(343,347)(344,348)(385,453)(386,454)(387,455)
(388,456)(389,449)(390,450)(391,451)(392,452)(393,445)(394,446)(395,447)
(396,448)(397,441)(398,442)(399,443)(400,444)(401,437)(402,438)(403,439)
(404,440)(405,433)(406,434)(407,435)(408,436)(409,429)(410,430)(411,431)
(412,432)(413,425)(414,426)(415,427)(416,428)(417,421)(418,422)(419,423)
(420,424);
s1 := Sym(456)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 73)( 10, 74)( 11, 76)
( 12, 75)( 13, 69)( 14, 70)( 15, 72)( 16, 71)( 17, 65)( 18, 66)( 19, 68)
( 20, 67)( 21, 61)( 22, 62)( 23, 64)( 24, 63)( 25, 57)( 26, 58)( 27, 60)
( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)
( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 43, 44)( 77,157)( 78,158)
( 79,160)( 80,159)( 81,153)( 82,154)( 83,156)( 84,155)( 85,225)( 86,226)
( 87,228)( 88,227)( 89,221)( 90,222)( 91,224)( 92,223)( 93,217)( 94,218)
( 95,220)( 96,219)( 97,213)( 98,214)( 99,216)(100,215)(101,209)(102,210)
(103,212)(104,211)(105,205)(106,206)(107,208)(108,207)(109,201)(110,202)
(111,204)(112,203)(113,197)(114,198)(115,200)(116,199)(117,193)(118,194)
(119,196)(120,195)(121,189)(122,190)(123,192)(124,191)(125,185)(126,186)
(127,188)(128,187)(129,181)(130,182)(131,184)(132,183)(133,177)(134,178)
(135,180)(136,179)(137,173)(138,174)(139,176)(140,175)(141,169)(142,170)
(143,172)(144,171)(145,165)(146,166)(147,168)(148,167)(149,161)(150,162)
(151,164)(152,163)(229,233)(230,234)(231,236)(232,235)(237,301)(238,302)
(239,304)(240,303)(241,297)(242,298)(243,300)(244,299)(245,293)(246,294)
(247,296)(248,295)(249,289)(250,290)(251,292)(252,291)(253,285)(254,286)
(255,288)(256,287)(257,281)(258,282)(259,284)(260,283)(261,277)(262,278)
(263,280)(264,279)(265,273)(266,274)(267,276)(268,275)(271,272)(305,385)
(306,386)(307,388)(308,387)(309,381)(310,382)(311,384)(312,383)(313,453)
(314,454)(315,456)(316,455)(317,449)(318,450)(319,452)(320,451)(321,445)
(322,446)(323,448)(324,447)(325,441)(326,442)(327,444)(328,443)(329,437)
(330,438)(331,440)(332,439)(333,433)(334,434)(335,436)(336,435)(337,429)
(338,430)(339,432)(340,431)(341,425)(342,426)(343,428)(344,427)(345,421)
(346,422)(347,424)(348,423)(349,417)(350,418)(351,420)(352,419)(353,413)
(354,414)(355,416)(356,415)(357,409)(358,410)(359,412)(360,411)(361,405)
(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)(368,403)(369,397)
(370,398)(371,400)(372,399)(373,393)(374,394)(375,396)(376,395)(377,389)
(378,390)(379,392)(380,391);
s2 := Sym(456)!( 1,305)( 2,308)( 3,307)( 4,306)( 5,309)( 6,312)( 7,311)
( 8,310)( 9,313)( 10,316)( 11,315)( 12,314)( 13,317)( 14,320)( 15,319)
( 16,318)( 17,321)( 18,324)( 19,323)( 20,322)( 21,325)( 22,328)( 23,327)
( 24,326)( 25,329)( 26,332)( 27,331)( 28,330)( 29,333)( 30,336)( 31,335)
( 32,334)( 33,337)( 34,340)( 35,339)( 36,338)( 37,341)( 38,344)( 39,343)
( 40,342)( 41,345)( 42,348)( 43,347)( 44,346)( 45,349)( 46,352)( 47,351)
( 48,350)( 49,353)( 50,356)( 51,355)( 52,354)( 53,357)( 54,360)( 55,359)
( 56,358)( 57,361)( 58,364)( 59,363)( 60,362)( 61,365)( 62,368)( 63,367)
( 64,366)( 65,369)( 66,372)( 67,371)( 68,370)( 69,373)( 70,376)( 71,375)
( 72,374)( 73,377)( 74,380)( 75,379)( 76,378)( 77,229)( 78,232)( 79,231)
( 80,230)( 81,233)( 82,236)( 83,235)( 84,234)( 85,237)( 86,240)( 87,239)
( 88,238)( 89,241)( 90,244)( 91,243)( 92,242)( 93,245)( 94,248)( 95,247)
( 96,246)( 97,249)( 98,252)( 99,251)(100,250)(101,253)(102,256)(103,255)
(104,254)(105,257)(106,260)(107,259)(108,258)(109,261)(110,264)(111,263)
(112,262)(113,265)(114,268)(115,267)(116,266)(117,269)(118,272)(119,271)
(120,270)(121,273)(122,276)(123,275)(124,274)(125,277)(126,280)(127,279)
(128,278)(129,281)(130,284)(131,283)(132,282)(133,285)(134,288)(135,287)
(136,286)(137,289)(138,292)(139,291)(140,290)(141,293)(142,296)(143,295)
(144,294)(145,297)(146,300)(147,299)(148,298)(149,301)(150,304)(151,303)
(152,302)(153,381)(154,384)(155,383)(156,382)(157,385)(158,388)(159,387)
(160,386)(161,389)(162,392)(163,391)(164,390)(165,393)(166,396)(167,395)
(168,394)(169,397)(170,400)(171,399)(172,398)(173,401)(174,404)(175,403)
(176,402)(177,405)(178,408)(179,407)(180,406)(181,409)(182,412)(183,411)
(184,410)(185,413)(186,416)(187,415)(188,414)(189,417)(190,420)(191,419)
(192,418)(193,421)(194,424)(195,423)(196,422)(197,425)(198,428)(199,427)
(200,426)(201,429)(202,432)(203,431)(204,430)(205,433)(206,436)(207,435)
(208,434)(209,437)(210,440)(211,439)(212,438)(213,441)(214,444)(215,443)
(216,442)(217,445)(218,448)(219,447)(220,446)(221,449)(222,452)(223,451)
(224,450)(225,453)(226,456)(227,455)(228,454);
s3 := Sym(456)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456);
poly := sub<Sym(456)|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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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