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