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

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