Polytope of Type {2,4,8,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,8,14}*1792b
if this polytope has a name.
Group : SmallGroup(1792,1036167)
Rank : 5
Schlafli Type : {2,4,8,14}
Number of vertices, edges, etc : 2, 4, 16, 56, 14
Order of s0s1s2s3s4 : 56
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 : {2,4,4,14}*896
   4-fold quotients : {2,2,4,14}*448, {2,4,2,14}*448
   7-fold quotients : {2,4,8,2}*256b
   8-fold quotients : {2,4,2,7}*224, {2,2,2,14}*224
   14-fold quotients : {2,4,4,2}*128
   16-fold quotients : {2,2,2,7}*112
   28-fold quotients : {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 := (  3,115)(  4,116)(  5,117)(  6,118)(  7,119)(  8,120)(  9,121)( 10,122)
( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)( 17,129)( 18,130)
( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)( 25,137)( 26,138)
( 27,139)( 28,140)( 29,141)( 30,142)( 31,150)( 32,151)( 33,152)( 34,153)
( 35,154)( 36,155)( 37,156)( 38,143)( 39,144)( 40,145)( 41,146)( 42,147)
( 43,148)( 44,149)( 45,164)( 46,165)( 47,166)( 48,167)( 49,168)( 50,169)
( 51,170)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)
( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)( 64,176)( 65,177)( 66,178)
( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)( 73,185)( 74,186)
( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)( 80,192)( 81,193)( 82,194)
( 83,195)( 84,196)( 85,197)( 86,198)( 87,206)( 88,207)( 89,208)( 90,209)
( 91,210)( 92,211)( 93,212)( 94,199)( 95,200)( 96,201)( 97,202)( 98,203)
( 99,204)(100,205)(101,220)(102,221)(103,222)(104,223)(105,224)(106,225)
(107,226)(108,213)(109,214)(110,215)(111,216)(112,217)(113,218)(114,219)
(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)(233,345)(234,346)
(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)(241,353)(242,354)
(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)(249,361)(250,362)
(251,363)(252,364)(253,365)(254,366)(255,374)(256,375)(257,376)(258,377)
(259,378)(260,379)(261,380)(262,367)(263,368)(264,369)(265,370)(266,371)
(267,372)(268,373)(269,388)(270,389)(271,390)(272,391)(273,392)(274,393)
(275,394)(276,381)(277,382)(278,383)(279,384)(280,385)(281,386)(282,387)
(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)(289,401)(290,402)
(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)(297,409)(298,410)
(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)(305,417)(306,418)
(307,419)(308,420)(309,421)(310,422)(311,430)(312,431)(313,432)(314,433)
(315,434)(316,435)(317,436)(318,423)(319,424)(320,425)(321,426)(322,427)
(323,428)(324,429)(325,444)(326,445)(327,446)(328,447)(329,448)(330,449)
(331,450)(332,437)(333,438)(334,439)(335,440)(336,441)(337,442)(338,443);;
s2 := ( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)( 45, 52)
( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 87, 94)( 88, 95)
( 89, 96)( 90, 97)( 91, 98)( 92, 99)( 93,100)(101,108)(102,109)(103,110)
(104,111)(105,112)(106,113)(107,114)(115,129)(116,130)(117,131)(118,132)
(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)
(127,141)(128,142)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)
(149,170)(150,157)(151,158)(152,159)(153,160)(154,161)(155,162)(156,163)
(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)
(179,193)(180,194)(181,195)(182,196)(183,197)(184,198)(199,220)(200,221)
(201,222)(202,223)(203,224)(204,225)(205,226)(206,213)(207,214)(208,215)
(209,216)(210,217)(211,218)(212,219)(227,255)(228,256)(229,257)(230,258)
(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)
(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)(245,273)(246,274)
(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)(253,281)(254,282)
(283,311)(284,312)(285,313)(286,314)(287,315)(288,316)(289,317)(290,318)
(291,319)(292,320)(293,321)(294,322)(295,323)(296,324)(297,325)(298,326)
(299,327)(300,328)(301,329)(302,330)(303,331)(304,332)(305,333)(306,334)
(307,335)(308,336)(309,337)(310,338)(339,388)(340,389)(341,390)(342,391)
(343,392)(344,393)(345,394)(346,381)(347,382)(348,383)(349,384)(350,385)
(351,386)(352,387)(353,374)(354,375)(355,376)(356,377)(357,378)(358,379)
(359,380)(360,367)(361,368)(362,369)(363,370)(364,371)(365,372)(366,373)
(395,444)(396,445)(397,446)(398,447)(399,448)(400,449)(401,450)(402,437)
(403,438)(404,439)(405,440)(406,441)(407,442)(408,443)(409,430)(410,431)
(411,432)(412,433)(413,434)(414,435)(415,436)(416,423)(417,424)(418,425)
(419,426)(420,427)(421,428)(422,429);;
s3 := (  3,283)(  4,289)(  5,288)(  6,287)(  7,286)(  8,285)(  9,284)( 10,290)
( 11,296)( 12,295)( 13,294)( 14,293)( 15,292)( 16,291)( 17,304)( 18,310)
( 19,309)( 20,308)( 21,307)( 22,306)( 23,305)( 24,297)( 25,303)( 26,302)
( 27,301)( 28,300)( 29,299)( 30,298)( 31,318)( 32,324)( 33,323)( 34,322)
( 35,321)( 36,320)( 37,319)( 38,311)( 39,317)( 40,316)( 41,315)( 42,314)
( 43,313)( 44,312)( 45,325)( 46,331)( 47,330)( 48,329)( 49,328)( 50,327)
( 51,326)( 52,332)( 53,338)( 54,337)( 55,336)( 56,335)( 57,334)( 58,333)
( 59,227)( 60,233)( 61,232)( 62,231)( 63,230)( 64,229)( 65,228)( 66,234)
( 67,240)( 68,239)( 69,238)( 70,237)( 71,236)( 72,235)( 73,248)( 74,254)
( 75,253)( 76,252)( 77,251)( 78,250)( 79,249)( 80,241)( 81,247)( 82,246)
( 83,245)( 84,244)( 85,243)( 86,242)( 87,262)( 88,268)( 89,267)( 90,266)
( 91,265)( 92,264)( 93,263)( 94,255)( 95,261)( 96,260)( 97,259)( 98,258)
( 99,257)(100,256)(101,269)(102,275)(103,274)(104,273)(105,272)(106,271)
(107,270)(108,276)(109,282)(110,281)(111,280)(112,279)(113,278)(114,277)
(115,395)(116,401)(117,400)(118,399)(119,398)(120,397)(121,396)(122,402)
(123,408)(124,407)(125,406)(126,405)(127,404)(128,403)(129,416)(130,422)
(131,421)(132,420)(133,419)(134,418)(135,417)(136,409)(137,415)(138,414)
(139,413)(140,412)(141,411)(142,410)(143,430)(144,436)(145,435)(146,434)
(147,433)(148,432)(149,431)(150,423)(151,429)(152,428)(153,427)(154,426)
(155,425)(156,424)(157,437)(158,443)(159,442)(160,441)(161,440)(162,439)
(163,438)(164,444)(165,450)(166,449)(167,448)(168,447)(169,446)(170,445)
(171,339)(172,345)(173,344)(174,343)(175,342)(176,341)(177,340)(178,346)
(179,352)(180,351)(181,350)(182,349)(183,348)(184,347)(185,360)(186,366)
(187,365)(188,364)(189,363)(190,362)(191,361)(192,353)(193,359)(194,358)
(195,357)(196,356)(197,355)(198,354)(199,374)(200,380)(201,379)(202,378)
(203,377)(204,376)(205,375)(206,367)(207,373)(208,372)(209,371)(210,370)
(211,369)(212,368)(213,381)(214,387)(215,386)(216,385)(217,384)(218,383)
(219,382)(220,388)(221,394)(222,393)(223,392)(224,391)(225,390)(226,389);;
s4 := (  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)( 10, 67)
( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 74)( 18, 73)
( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 81)( 25, 80)( 26, 86)
( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 88)( 32, 87)( 33, 93)( 34, 92)
( 35, 91)( 36, 90)( 37, 89)( 38, 95)( 39, 94)( 40,100)( 41, 99)( 42, 98)
( 43, 97)( 44, 96)( 45,102)( 46,101)( 47,107)( 48,106)( 49,105)( 50,104)
( 51,103)( 52,109)( 53,108)( 54,114)( 55,113)( 56,112)( 57,111)( 58,110)
(115,172)(116,171)(117,177)(118,176)(119,175)(120,174)(121,173)(122,179)
(123,178)(124,184)(125,183)(126,182)(127,181)(128,180)(129,186)(130,185)
(131,191)(132,190)(133,189)(134,188)(135,187)(136,193)(137,192)(138,198)
(139,197)(140,196)(141,195)(142,194)(143,200)(144,199)(145,205)(146,204)
(147,203)(148,202)(149,201)(150,207)(151,206)(152,212)(153,211)(154,210)
(155,209)(156,208)(157,214)(158,213)(159,219)(160,218)(161,217)(162,216)
(163,215)(164,221)(165,220)(166,226)(167,225)(168,224)(169,223)(170,222)
(227,284)(228,283)(229,289)(230,288)(231,287)(232,286)(233,285)(234,291)
(235,290)(236,296)(237,295)(238,294)(239,293)(240,292)(241,298)(242,297)
(243,303)(244,302)(245,301)(246,300)(247,299)(248,305)(249,304)(250,310)
(251,309)(252,308)(253,307)(254,306)(255,312)(256,311)(257,317)(258,316)
(259,315)(260,314)(261,313)(262,319)(263,318)(264,324)(265,323)(266,322)
(267,321)(268,320)(269,326)(270,325)(271,331)(272,330)(273,329)(274,328)
(275,327)(276,333)(277,332)(278,338)(279,337)(280,336)(281,335)(282,334)
(339,396)(340,395)(341,401)(342,400)(343,399)(344,398)(345,397)(346,403)
(347,402)(348,408)(349,407)(350,406)(351,405)(352,404)(353,410)(354,409)
(355,415)(356,414)(357,413)(358,412)(359,411)(360,417)(361,416)(362,422)
(363,421)(364,420)(365,419)(366,418)(367,424)(368,423)(369,429)(370,428)
(371,427)(372,426)(373,425)(374,431)(375,430)(376,436)(377,435)(378,434)
(379,433)(380,432)(381,438)(382,437)(383,443)(384,442)(385,441)(386,440)
(387,439)(388,445)(389,444)(390,450)(391,449)(392,448)(393,447)(394,446);;
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(450)!(1,2);
s1 := Sym(450)!(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)(  8,120)(  9,121)
( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)( 17,129)
( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)( 25,137)
( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,150)( 32,151)( 33,152)
( 34,153)( 35,154)( 36,155)( 37,156)( 38,143)( 39,144)( 40,145)( 41,146)
( 42,147)( 43,148)( 44,149)( 45,164)( 46,165)( 47,166)( 48,167)( 49,168)
( 50,169)( 51,170)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)
( 58,163)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)( 64,176)( 65,177)
( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)( 73,185)
( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)( 80,192)( 81,193)
( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,206)( 88,207)( 89,208)
( 90,209)( 91,210)( 92,211)( 93,212)( 94,199)( 95,200)( 96,201)( 97,202)
( 98,203)( 99,204)(100,205)(101,220)(102,221)(103,222)(104,223)(105,224)
(106,225)(107,226)(108,213)(109,214)(110,215)(111,216)(112,217)(113,218)
(114,219)(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)(233,345)
(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)(241,353)
(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)(249,361)
(250,362)(251,363)(252,364)(253,365)(254,366)(255,374)(256,375)(257,376)
(258,377)(259,378)(260,379)(261,380)(262,367)(263,368)(264,369)(265,370)
(266,371)(267,372)(268,373)(269,388)(270,389)(271,390)(272,391)(273,392)
(274,393)(275,394)(276,381)(277,382)(278,383)(279,384)(280,385)(281,386)
(282,387)(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)(289,401)
(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)(297,409)
(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)(305,417)
(306,418)(307,419)(308,420)(309,421)(310,422)(311,430)(312,431)(313,432)
(314,433)(315,434)(316,435)(317,436)(318,423)(319,424)(320,425)(321,426)
(322,427)(323,428)(324,429)(325,444)(326,445)(327,446)(328,447)(329,448)
(330,449)(331,450)(332,437)(333,438)(334,439)(335,440)(336,441)(337,442)
(338,443);
s2 := Sym(450)!( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)
( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 87, 94)
( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 92, 99)( 93,100)(101,108)(102,109)
(103,110)(104,111)(105,112)(106,113)(107,114)(115,129)(116,130)(117,131)
(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)
(126,140)(127,141)(128,142)(143,164)(144,165)(145,166)(146,167)(147,168)
(148,169)(149,170)(150,157)(151,158)(152,159)(153,160)(154,161)(155,162)
(156,163)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)
(178,192)(179,193)(180,194)(181,195)(182,196)(183,197)(184,198)(199,220)
(200,221)(201,222)(202,223)(203,224)(204,225)(205,226)(206,213)(207,214)
(208,215)(209,216)(210,217)(211,218)(212,219)(227,255)(228,256)(229,257)
(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)
(238,266)(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)(245,273)
(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)(253,281)
(254,282)(283,311)(284,312)(285,313)(286,314)(287,315)(288,316)(289,317)
(290,318)(291,319)(292,320)(293,321)(294,322)(295,323)(296,324)(297,325)
(298,326)(299,327)(300,328)(301,329)(302,330)(303,331)(304,332)(305,333)
(306,334)(307,335)(308,336)(309,337)(310,338)(339,388)(340,389)(341,390)
(342,391)(343,392)(344,393)(345,394)(346,381)(347,382)(348,383)(349,384)
(350,385)(351,386)(352,387)(353,374)(354,375)(355,376)(356,377)(357,378)
(358,379)(359,380)(360,367)(361,368)(362,369)(363,370)(364,371)(365,372)
(366,373)(395,444)(396,445)(397,446)(398,447)(399,448)(400,449)(401,450)
(402,437)(403,438)(404,439)(405,440)(406,441)(407,442)(408,443)(409,430)
(410,431)(411,432)(412,433)(413,434)(414,435)(415,436)(416,423)(417,424)
(418,425)(419,426)(420,427)(421,428)(422,429);
s3 := Sym(450)!(  3,283)(  4,289)(  5,288)(  6,287)(  7,286)(  8,285)(  9,284)
( 10,290)( 11,296)( 12,295)( 13,294)( 14,293)( 15,292)( 16,291)( 17,304)
( 18,310)( 19,309)( 20,308)( 21,307)( 22,306)( 23,305)( 24,297)( 25,303)
( 26,302)( 27,301)( 28,300)( 29,299)( 30,298)( 31,318)( 32,324)( 33,323)
( 34,322)( 35,321)( 36,320)( 37,319)( 38,311)( 39,317)( 40,316)( 41,315)
( 42,314)( 43,313)( 44,312)( 45,325)( 46,331)( 47,330)( 48,329)( 49,328)
( 50,327)( 51,326)( 52,332)( 53,338)( 54,337)( 55,336)( 56,335)( 57,334)
( 58,333)( 59,227)( 60,233)( 61,232)( 62,231)( 63,230)( 64,229)( 65,228)
( 66,234)( 67,240)( 68,239)( 69,238)( 70,237)( 71,236)( 72,235)( 73,248)
( 74,254)( 75,253)( 76,252)( 77,251)( 78,250)( 79,249)( 80,241)( 81,247)
( 82,246)( 83,245)( 84,244)( 85,243)( 86,242)( 87,262)( 88,268)( 89,267)
( 90,266)( 91,265)( 92,264)( 93,263)( 94,255)( 95,261)( 96,260)( 97,259)
( 98,258)( 99,257)(100,256)(101,269)(102,275)(103,274)(104,273)(105,272)
(106,271)(107,270)(108,276)(109,282)(110,281)(111,280)(112,279)(113,278)
(114,277)(115,395)(116,401)(117,400)(118,399)(119,398)(120,397)(121,396)
(122,402)(123,408)(124,407)(125,406)(126,405)(127,404)(128,403)(129,416)
(130,422)(131,421)(132,420)(133,419)(134,418)(135,417)(136,409)(137,415)
(138,414)(139,413)(140,412)(141,411)(142,410)(143,430)(144,436)(145,435)
(146,434)(147,433)(148,432)(149,431)(150,423)(151,429)(152,428)(153,427)
(154,426)(155,425)(156,424)(157,437)(158,443)(159,442)(160,441)(161,440)
(162,439)(163,438)(164,444)(165,450)(166,449)(167,448)(168,447)(169,446)
(170,445)(171,339)(172,345)(173,344)(174,343)(175,342)(176,341)(177,340)
(178,346)(179,352)(180,351)(181,350)(182,349)(183,348)(184,347)(185,360)
(186,366)(187,365)(188,364)(189,363)(190,362)(191,361)(192,353)(193,359)
(194,358)(195,357)(196,356)(197,355)(198,354)(199,374)(200,380)(201,379)
(202,378)(203,377)(204,376)(205,375)(206,367)(207,373)(208,372)(209,371)
(210,370)(211,369)(212,368)(213,381)(214,387)(215,386)(216,385)(217,384)
(218,383)(219,382)(220,388)(221,394)(222,393)(223,392)(224,391)(225,390)
(226,389);
s4 := Sym(450)!(  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)
( 10, 67)( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 74)
( 18, 73)( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 81)( 25, 80)
( 26, 86)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 88)( 32, 87)( 33, 93)
( 34, 92)( 35, 91)( 36, 90)( 37, 89)( 38, 95)( 39, 94)( 40,100)( 41, 99)
( 42, 98)( 43, 97)( 44, 96)( 45,102)( 46,101)( 47,107)( 48,106)( 49,105)
( 50,104)( 51,103)( 52,109)( 53,108)( 54,114)( 55,113)( 56,112)( 57,111)
( 58,110)(115,172)(116,171)(117,177)(118,176)(119,175)(120,174)(121,173)
(122,179)(123,178)(124,184)(125,183)(126,182)(127,181)(128,180)(129,186)
(130,185)(131,191)(132,190)(133,189)(134,188)(135,187)(136,193)(137,192)
(138,198)(139,197)(140,196)(141,195)(142,194)(143,200)(144,199)(145,205)
(146,204)(147,203)(148,202)(149,201)(150,207)(151,206)(152,212)(153,211)
(154,210)(155,209)(156,208)(157,214)(158,213)(159,219)(160,218)(161,217)
(162,216)(163,215)(164,221)(165,220)(166,226)(167,225)(168,224)(169,223)
(170,222)(227,284)(228,283)(229,289)(230,288)(231,287)(232,286)(233,285)
(234,291)(235,290)(236,296)(237,295)(238,294)(239,293)(240,292)(241,298)
(242,297)(243,303)(244,302)(245,301)(246,300)(247,299)(248,305)(249,304)
(250,310)(251,309)(252,308)(253,307)(254,306)(255,312)(256,311)(257,317)
(258,316)(259,315)(260,314)(261,313)(262,319)(263,318)(264,324)(265,323)
(266,322)(267,321)(268,320)(269,326)(270,325)(271,331)(272,330)(273,329)
(274,328)(275,327)(276,333)(277,332)(278,338)(279,337)(280,336)(281,335)
(282,334)(339,396)(340,395)(341,401)(342,400)(343,399)(344,398)(345,397)
(346,403)(347,402)(348,408)(349,407)(350,406)(351,405)(352,404)(353,410)
(354,409)(355,415)(356,414)(357,413)(358,412)(359,411)(360,417)(361,416)
(362,422)(363,421)(364,420)(365,419)(366,418)(367,424)(368,423)(369,429)
(370,428)(371,427)(372,426)(373,425)(374,431)(375,430)(376,436)(377,435)
(378,434)(379,433)(380,432)(381,438)(382,437)(383,443)(384,442)(385,441)
(386,440)(387,439)(388,445)(389,444)(390,450)(391,449)(392,448)(393,447)
(394,446);
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, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope