Polytope of Type {2,4,28,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,28,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,336975)
Rank : 5
Schlafli Type : {2,4,28,4}
Number of vertices, edges, etc : 2, 4, 56, 56, 4
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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) :
2-fold quotients : {2,2,28,4}*896, {2,4,28,2}*896, {2,4,14,4}*896
4-fold quotients : {2,2,28,2}*448, {2,2,14,4}*448, {2,4,14,2}*448
7-fold quotients : {2,4,4,4}*256
8-fold quotients : {2,2,14,2}*224
14-fold quotients : {2,2,4,4}*128, {2,4,4,2}*128, {2,4,2,4}*128
16-fold quotients : {2,2,7,2}*112
28-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64, {2,4,2,2}*64
56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)( 8, 64)( 9, 65)( 10, 66)
( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)( 17, 73)( 18, 74)
( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)( 26, 82)
( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)( 34, 90)
( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)( 42, 98)
( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)( 50,106)
( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)( 57,113)( 58,114)
(115,171)(116,172)(117,173)(118,174)(119,175)(120,176)(121,177)(122,178)
(123,179)(124,180)(125,181)(126,182)(127,183)(128,184)(129,185)(130,186)
(131,187)(132,188)(133,189)(134,190)(135,191)(136,192)(137,193)(138,194)
(139,195)(140,196)(141,197)(142,198)(143,199)(144,200)(145,201)(146,202)
(147,203)(148,204)(149,205)(150,206)(151,207)(152,208)(153,209)(154,210)
(155,211)(156,212)(157,213)(158,214)(159,215)(160,216)(161,217)(162,218)
(163,219)(164,220)(165,221)(166,222)(167,223)(168,224)(169,225)(170,226)
(227,283)(228,284)(229,285)(230,286)(231,287)(232,288)(233,289)(234,290)
(235,291)(236,292)(237,293)(238,294)(239,295)(240,296)(241,297)(242,298)
(243,299)(244,300)(245,301)(246,302)(247,303)(248,304)(249,305)(250,306)
(251,307)(252,308)(253,309)(254,310)(255,311)(256,312)(257,313)(258,314)
(259,315)(260,316)(261,317)(262,318)(263,319)(264,320)(265,321)(266,322)
(267,323)(268,324)(269,325)(270,326)(271,327)(272,328)(273,329)(274,330)
(275,331)(276,332)(277,333)(278,334)(279,335)(280,336)(281,337)(282,338)
(339,395)(340,396)(341,397)(342,398)(343,399)(344,400)(345,401)(346,402)
(347,403)(348,404)(349,405)(350,406)(351,407)(352,408)(353,409)(354,410)
(355,411)(356,412)(357,413)(358,414)(359,415)(360,416)(361,417)(362,418)
(363,419)(364,420)(365,421)(366,422)(367,423)(368,424)(369,425)(370,426)
(371,427)(372,428)(373,429)(374,430)(375,431)(376,432)(377,433)(378,434)
(379,435)(380,436)(381,437)(382,438)(383,439)(384,440)(385,441)(386,442)
(387,443)(388,444)(389,445)(390,446)(391,447)(392,448)(393,449)(394,450);;
s2 := ( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)
( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)
( 59, 87)( 60, 93)( 61, 92)( 62, 91)( 63, 90)( 64, 89)( 65, 88)( 66, 94)
( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73,101)( 74,107)
( 75,106)( 76,105)( 77,104)( 78,103)( 79,102)( 80,108)( 81,114)( 82,113)
( 83,112)( 84,111)( 85,110)( 86,109)(115,129)(116,135)(117,134)(118,133)
(119,132)(120,131)(121,130)(122,136)(123,142)(124,141)(125,140)(126,139)
(127,138)(128,137)(143,157)(144,163)(145,162)(146,161)(147,160)(148,159)
(149,158)(150,164)(151,170)(152,169)(153,168)(154,167)(155,166)(156,165)
(171,213)(172,219)(173,218)(174,217)(175,216)(176,215)(177,214)(178,220)
(179,226)(180,225)(181,224)(182,223)(183,222)(184,221)(185,199)(186,205)
(187,204)(188,203)(189,202)(190,201)(191,200)(192,206)(193,212)(194,211)
(195,210)(196,209)(197,208)(198,207)(227,255)(228,261)(229,260)(230,259)
(231,258)(232,257)(233,256)(234,262)(235,268)(236,267)(237,266)(238,265)
(239,264)(240,263)(241,269)(242,275)(243,274)(244,273)(245,272)(246,271)
(247,270)(248,276)(249,282)(250,281)(251,280)(252,279)(253,278)(254,277)
(284,289)(285,288)(286,287)(291,296)(292,295)(293,294)(298,303)(299,302)
(300,301)(305,310)(306,309)(307,308)(312,317)(313,316)(314,315)(319,324)
(320,323)(321,322)(326,331)(327,330)(328,329)(333,338)(334,337)(335,336)
(339,381)(340,387)(341,386)(342,385)(343,384)(344,383)(345,382)(346,388)
(347,394)(348,393)(349,392)(350,391)(351,390)(352,389)(353,367)(354,373)
(355,372)(356,371)(357,370)(358,369)(359,368)(360,374)(361,380)(362,379)
(363,378)(364,377)(365,376)(366,375)(395,409)(396,415)(397,414)(398,413)
(399,412)(400,411)(401,410)(402,416)(403,422)(404,421)(405,420)(406,419)
(407,418)(408,417)(423,437)(424,443)(425,442)(426,441)(427,440)(428,439)
(429,438)(430,444)(431,450)(432,449)(433,448)(434,447)(435,446)(436,445);;
s3 := ( 3,116)( 4,115)( 5,121)( 6,120)( 7,119)( 8,118)( 9,117)( 10,123)
( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,130)( 18,129)
( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,137)( 25,136)( 26,142)
( 27,141)( 28,140)( 29,139)( 30,138)( 31,144)( 32,143)( 33,149)( 34,148)
( 35,147)( 36,146)( 37,145)( 38,151)( 39,150)( 40,156)( 41,155)( 42,154)
( 43,153)( 44,152)( 45,158)( 46,157)( 47,163)( 48,162)( 49,161)( 50,160)
( 51,159)( 52,165)( 53,164)( 54,170)( 55,169)( 56,168)( 57,167)( 58,166)
( 59,172)( 60,171)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)( 66,179)
( 67,178)( 68,184)( 69,183)( 70,182)( 71,181)( 72,180)( 73,186)( 74,185)
( 75,191)( 76,190)( 77,189)( 78,188)( 79,187)( 80,193)( 81,192)( 82,198)
( 83,197)( 84,196)( 85,195)( 86,194)( 87,200)( 88,199)( 89,205)( 90,204)
( 91,203)( 92,202)( 93,201)( 94,207)( 95,206)( 96,212)( 97,211)( 98,210)
( 99,209)(100,208)(101,214)(102,213)(103,219)(104,218)(105,217)(106,216)
(107,215)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)(114,222)
(227,340)(228,339)(229,345)(230,344)(231,343)(232,342)(233,341)(234,347)
(235,346)(236,352)(237,351)(238,350)(239,349)(240,348)(241,354)(242,353)
(243,359)(244,358)(245,357)(246,356)(247,355)(248,361)(249,360)(250,366)
(251,365)(252,364)(253,363)(254,362)(255,368)(256,367)(257,373)(258,372)
(259,371)(260,370)(261,369)(262,375)(263,374)(264,380)(265,379)(266,378)
(267,377)(268,376)(269,382)(270,381)(271,387)(272,386)(273,385)(274,384)
(275,383)(276,389)(277,388)(278,394)(279,393)(280,392)(281,391)(282,390)
(283,396)(284,395)(285,401)(286,400)(287,399)(288,398)(289,397)(290,403)
(291,402)(292,408)(293,407)(294,406)(295,405)(296,404)(297,410)(298,409)
(299,415)(300,414)(301,413)(302,412)(303,411)(304,417)(305,416)(306,422)
(307,421)(308,420)(309,419)(310,418)(311,424)(312,423)(313,429)(314,428)
(315,427)(316,426)(317,425)(318,431)(319,430)(320,436)(321,435)(322,434)
(323,433)(324,432)(325,438)(326,437)(327,443)(328,442)(329,441)(330,440)
(331,439)(332,445)(333,444)(334,450)(335,449)(336,448)(337,447)(338,446);;
s4 := ( 3,283)( 4,284)( 5,285)( 6,286)( 7,287)( 8,288)( 9,289)( 10,290)
( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,296)( 17,297)( 18,298)
( 19,299)( 20,300)( 21,301)( 22,302)( 23,303)( 24,304)( 25,305)( 26,306)
( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)( 33,313)( 34,314)
( 35,315)( 36,316)( 37,317)( 38,318)( 39,319)( 40,320)( 41,321)( 42,322)
( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)( 48,328)( 49,329)( 50,330)
( 51,331)( 52,332)( 53,333)( 54,334)( 55,335)( 56,336)( 57,337)( 58,338)
( 59,227)( 60,228)( 61,229)( 62,230)( 63,231)( 64,232)( 65,233)( 66,234)
( 67,235)( 68,236)( 69,237)( 70,238)( 71,239)( 72,240)( 73,241)( 74,242)
( 75,243)( 76,244)( 77,245)( 78,246)( 79,247)( 80,248)( 81,249)( 82,250)
( 83,251)( 84,252)( 85,253)( 86,254)( 87,255)( 88,256)( 89,257)( 90,258)
( 91,259)( 92,260)( 93,261)( 94,262)( 95,263)( 96,264)( 97,265)( 98,266)
( 99,267)(100,268)(101,269)(102,270)(103,271)(104,272)(105,273)(106,274)
(107,275)(108,276)(109,277)(110,278)(111,279)(112,280)(113,281)(114,282)
(115,402)(116,403)(117,404)(118,405)(119,406)(120,407)(121,408)(122,395)
(123,396)(124,397)(125,398)(126,399)(127,400)(128,401)(129,416)(130,417)
(131,418)(132,419)(133,420)(134,421)(135,422)(136,409)(137,410)(138,411)
(139,412)(140,413)(141,414)(142,415)(143,430)(144,431)(145,432)(146,433)
(147,434)(148,435)(149,436)(150,423)(151,424)(152,425)(153,426)(154,427)
(155,428)(156,429)(157,444)(158,445)(159,446)(160,447)(161,448)(162,449)
(163,450)(164,437)(165,438)(166,439)(167,440)(168,441)(169,442)(170,443)
(171,346)(172,347)(173,348)(174,349)(175,350)(176,351)(177,352)(178,339)
(179,340)(180,341)(181,342)(182,343)(183,344)(184,345)(185,360)(186,361)
(187,362)(188,363)(189,364)(190,365)(191,366)(192,353)(193,354)(194,355)
(195,356)(196,357)(197,358)(198,359)(199,374)(200,375)(201,376)(202,377)
(203,378)(204,379)(205,380)(206,367)(207,368)(208,369)(209,370)(210,371)
(211,372)(212,373)(213,388)(214,389)(215,390)(216,391)(217,392)(218,393)
(219,394)(220,381)(221,382)(222,383)(223,384)(224,385)(225,386)(226,387);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
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(450)!(1,2);
s1 := Sym(450)!( 3, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)( 8, 64)( 9, 65)
( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)( 17, 73)
( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)
( 26, 82)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)
( 34, 90)( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)
( 42, 98)( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)
( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)( 57,113)
( 58,114)(115,171)(116,172)(117,173)(118,174)(119,175)(120,176)(121,177)
(122,178)(123,179)(124,180)(125,181)(126,182)(127,183)(128,184)(129,185)
(130,186)(131,187)(132,188)(133,189)(134,190)(135,191)(136,192)(137,193)
(138,194)(139,195)(140,196)(141,197)(142,198)(143,199)(144,200)(145,201)
(146,202)(147,203)(148,204)(149,205)(150,206)(151,207)(152,208)(153,209)
(154,210)(155,211)(156,212)(157,213)(158,214)(159,215)(160,216)(161,217)
(162,218)(163,219)(164,220)(165,221)(166,222)(167,223)(168,224)(169,225)
(170,226)(227,283)(228,284)(229,285)(230,286)(231,287)(232,288)(233,289)
(234,290)(235,291)(236,292)(237,293)(238,294)(239,295)(240,296)(241,297)
(242,298)(243,299)(244,300)(245,301)(246,302)(247,303)(248,304)(249,305)
(250,306)(251,307)(252,308)(253,309)(254,310)(255,311)(256,312)(257,313)
(258,314)(259,315)(260,316)(261,317)(262,318)(263,319)(264,320)(265,321)
(266,322)(267,323)(268,324)(269,325)(270,326)(271,327)(272,328)(273,329)
(274,330)(275,331)(276,332)(277,333)(278,334)(279,335)(280,336)(281,337)
(282,338)(339,395)(340,396)(341,397)(342,398)(343,399)(344,400)(345,401)
(346,402)(347,403)(348,404)(349,405)(350,406)(351,407)(352,408)(353,409)
(354,410)(355,411)(356,412)(357,413)(358,414)(359,415)(360,416)(361,417)
(362,418)(363,419)(364,420)(365,421)(366,422)(367,423)(368,424)(369,425)
(370,426)(371,427)(372,428)(373,429)(374,430)(375,431)(376,432)(377,433)
(378,434)(379,435)(380,436)(381,437)(382,438)(383,439)(384,440)(385,441)
(386,442)(387,443)(388,444)(389,445)(390,446)(391,447)(392,448)(393,449)
(394,450);
s2 := Sym(450)!( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)
( 55, 56)( 59, 87)( 60, 93)( 61, 92)( 62, 91)( 63, 90)( 64, 89)( 65, 88)
( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73,101)
( 74,107)( 75,106)( 76,105)( 77,104)( 78,103)( 79,102)( 80,108)( 81,114)
( 82,113)( 83,112)( 84,111)( 85,110)( 86,109)(115,129)(116,135)(117,134)
(118,133)(119,132)(120,131)(121,130)(122,136)(123,142)(124,141)(125,140)
(126,139)(127,138)(128,137)(143,157)(144,163)(145,162)(146,161)(147,160)
(148,159)(149,158)(150,164)(151,170)(152,169)(153,168)(154,167)(155,166)
(156,165)(171,213)(172,219)(173,218)(174,217)(175,216)(176,215)(177,214)
(178,220)(179,226)(180,225)(181,224)(182,223)(183,222)(184,221)(185,199)
(186,205)(187,204)(188,203)(189,202)(190,201)(191,200)(192,206)(193,212)
(194,211)(195,210)(196,209)(197,208)(198,207)(227,255)(228,261)(229,260)
(230,259)(231,258)(232,257)(233,256)(234,262)(235,268)(236,267)(237,266)
(238,265)(239,264)(240,263)(241,269)(242,275)(243,274)(244,273)(245,272)
(246,271)(247,270)(248,276)(249,282)(250,281)(251,280)(252,279)(253,278)
(254,277)(284,289)(285,288)(286,287)(291,296)(292,295)(293,294)(298,303)
(299,302)(300,301)(305,310)(306,309)(307,308)(312,317)(313,316)(314,315)
(319,324)(320,323)(321,322)(326,331)(327,330)(328,329)(333,338)(334,337)
(335,336)(339,381)(340,387)(341,386)(342,385)(343,384)(344,383)(345,382)
(346,388)(347,394)(348,393)(349,392)(350,391)(351,390)(352,389)(353,367)
(354,373)(355,372)(356,371)(357,370)(358,369)(359,368)(360,374)(361,380)
(362,379)(363,378)(364,377)(365,376)(366,375)(395,409)(396,415)(397,414)
(398,413)(399,412)(400,411)(401,410)(402,416)(403,422)(404,421)(405,420)
(406,419)(407,418)(408,417)(423,437)(424,443)(425,442)(426,441)(427,440)
(428,439)(429,438)(430,444)(431,450)(432,449)(433,448)(434,447)(435,446)
(436,445);
s3 := Sym(450)!( 3,116)( 4,115)( 5,121)( 6,120)( 7,119)( 8,118)( 9,117)
( 10,123)( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,130)
( 18,129)( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,137)( 25,136)
( 26,142)( 27,141)( 28,140)( 29,139)( 30,138)( 31,144)( 32,143)( 33,149)
( 34,148)( 35,147)( 36,146)( 37,145)( 38,151)( 39,150)( 40,156)( 41,155)
( 42,154)( 43,153)( 44,152)( 45,158)( 46,157)( 47,163)( 48,162)( 49,161)
( 50,160)( 51,159)( 52,165)( 53,164)( 54,170)( 55,169)( 56,168)( 57,167)
( 58,166)( 59,172)( 60,171)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)
( 66,179)( 67,178)( 68,184)( 69,183)( 70,182)( 71,181)( 72,180)( 73,186)
( 74,185)( 75,191)( 76,190)( 77,189)( 78,188)( 79,187)( 80,193)( 81,192)
( 82,198)( 83,197)( 84,196)( 85,195)( 86,194)( 87,200)( 88,199)( 89,205)
( 90,204)( 91,203)( 92,202)( 93,201)( 94,207)( 95,206)( 96,212)( 97,211)
( 98,210)( 99,209)(100,208)(101,214)(102,213)(103,219)(104,218)(105,217)
(106,216)(107,215)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)
(114,222)(227,340)(228,339)(229,345)(230,344)(231,343)(232,342)(233,341)
(234,347)(235,346)(236,352)(237,351)(238,350)(239,349)(240,348)(241,354)
(242,353)(243,359)(244,358)(245,357)(246,356)(247,355)(248,361)(249,360)
(250,366)(251,365)(252,364)(253,363)(254,362)(255,368)(256,367)(257,373)
(258,372)(259,371)(260,370)(261,369)(262,375)(263,374)(264,380)(265,379)
(266,378)(267,377)(268,376)(269,382)(270,381)(271,387)(272,386)(273,385)
(274,384)(275,383)(276,389)(277,388)(278,394)(279,393)(280,392)(281,391)
(282,390)(283,396)(284,395)(285,401)(286,400)(287,399)(288,398)(289,397)
(290,403)(291,402)(292,408)(293,407)(294,406)(295,405)(296,404)(297,410)
(298,409)(299,415)(300,414)(301,413)(302,412)(303,411)(304,417)(305,416)
(306,422)(307,421)(308,420)(309,419)(310,418)(311,424)(312,423)(313,429)
(314,428)(315,427)(316,426)(317,425)(318,431)(319,430)(320,436)(321,435)
(322,434)(323,433)(324,432)(325,438)(326,437)(327,443)(328,442)(329,441)
(330,440)(331,439)(332,445)(333,444)(334,450)(335,449)(336,448)(337,447)
(338,446);
s4 := Sym(450)!( 3,283)( 4,284)( 5,285)( 6,286)( 7,287)( 8,288)( 9,289)
( 10,290)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,296)( 17,297)
( 18,298)( 19,299)( 20,300)( 21,301)( 22,302)( 23,303)( 24,304)( 25,305)
( 26,306)( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)( 33,313)
( 34,314)( 35,315)( 36,316)( 37,317)( 38,318)( 39,319)( 40,320)( 41,321)
( 42,322)( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)( 48,328)( 49,329)
( 50,330)( 51,331)( 52,332)( 53,333)( 54,334)( 55,335)( 56,336)( 57,337)
( 58,338)( 59,227)( 60,228)( 61,229)( 62,230)( 63,231)( 64,232)( 65,233)
( 66,234)( 67,235)( 68,236)( 69,237)( 70,238)( 71,239)( 72,240)( 73,241)
( 74,242)( 75,243)( 76,244)( 77,245)( 78,246)( 79,247)( 80,248)( 81,249)
( 82,250)( 83,251)( 84,252)( 85,253)( 86,254)( 87,255)( 88,256)( 89,257)
( 90,258)( 91,259)( 92,260)( 93,261)( 94,262)( 95,263)( 96,264)( 97,265)
( 98,266)( 99,267)(100,268)(101,269)(102,270)(103,271)(104,272)(105,273)
(106,274)(107,275)(108,276)(109,277)(110,278)(111,279)(112,280)(113,281)
(114,282)(115,402)(116,403)(117,404)(118,405)(119,406)(120,407)(121,408)
(122,395)(123,396)(124,397)(125,398)(126,399)(127,400)(128,401)(129,416)
(130,417)(131,418)(132,419)(133,420)(134,421)(135,422)(136,409)(137,410)
(138,411)(139,412)(140,413)(141,414)(142,415)(143,430)(144,431)(145,432)
(146,433)(147,434)(148,435)(149,436)(150,423)(151,424)(152,425)(153,426)
(154,427)(155,428)(156,429)(157,444)(158,445)(159,446)(160,447)(161,448)
(162,449)(163,450)(164,437)(165,438)(166,439)(167,440)(168,441)(169,442)
(170,443)(171,346)(172,347)(173,348)(174,349)(175,350)(176,351)(177,352)
(178,339)(179,340)(180,341)(181,342)(182,343)(183,344)(184,345)(185,360)
(186,361)(187,362)(188,363)(189,364)(190,365)(191,366)(192,353)(193,354)
(194,355)(195,356)(196,357)(197,358)(198,359)(199,374)(200,375)(201,376)
(202,377)(203,378)(204,379)(205,380)(206,367)(207,368)(208,369)(209,370)
(210,371)(211,372)(212,373)(213,388)(214,389)(215,390)(216,391)(217,392)
(218,393)(219,394)(220,381)(221,382)(222,383)(223,384)(224,385)(225,386)
(226,387);
poly := sub<Sym(450)|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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, 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