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Polytope of Type {4,6,38}

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