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}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1035859)
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, {2,2,8,14}*896
4-fold quotients : {2,2,4,14}*448, {2,4,2,14}*448
7-fold quotients : {2,4,8,2}*256a
8-fold quotients : {2,4,2,7}*224, {2,2,2,14}*224
14-fold quotients : {2,4,4,2}*128, {2,2,8,2}*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)( 31,143)( 32,144)( 33,145)( 34,146)
( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)( 41,153)( 42,154)
( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)( 49,161)( 50,162)
( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)( 57,169)( 58,170)
( 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)( 87,199)( 88,200)( 89,201)( 90,202)
( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)( 98,210)
( 99,211)(100,212)(101,213)(102,214)(103,215)(104,216)(105,217)(106,218)
(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)(113,225)(114,226)
(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)(255,367)(256,368)(257,369)(258,370)
(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)(265,377)(266,378)
(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)(273,385)(274,386)
(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)(281,393)(282,394)
(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)(311,423)(312,424)(313,425)(314,426)
(315,427)(316,428)(317,429)(318,430)(319,431)(320,432)(321,433)(322,434)
(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)(329,441)(330,442)
(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)(337,449)(338,450);;
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)(339,381)(340,382)(341,383)(342,384)
(343,385)(344,386)(345,387)(346,388)(347,389)(348,390)(349,391)(350,392)
(351,393)(352,394)(353,367)(354,368)(355,369)(356,370)(357,371)(358,372)
(359,373)(360,374)(361,375)(362,376)(363,377)(364,378)(365,379)(366,380)
(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)
(403,445)(404,446)(405,447)(406,448)(407,449)(408,450)(409,423)(410,424)
(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)
(419,433)(420,434)(421,435)(422,436);;
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)( 17,297)( 18,303)
( 19,302)( 20,301)( 21,300)( 22,299)( 23,298)( 24,304)( 25,310)( 26,309)
( 27,308)( 28,307)( 29,306)( 30,305)( 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)( 45,332)( 46,338)( 47,337)( 48,336)( 49,335)( 50,334)
( 51,333)( 52,325)( 53,331)( 54,330)( 55,329)( 56,328)( 57,327)( 58,326)
( 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)( 73,241)( 74,247)
( 75,246)( 76,245)( 77,244)( 78,243)( 79,242)( 80,248)( 81,254)( 82,253)
( 83,252)( 84,251)( 85,250)( 86,249)( 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)(101,276)(102,282)(103,281)(104,280)(105,279)(106,278)
(107,277)(108,269)(109,275)(110,274)(111,273)(112,272)(113,271)(114,270)
(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)(129,409)(130,415)
(131,414)(132,413)(133,412)(134,411)(135,410)(136,416)(137,422)(138,421)
(139,420)(140,419)(141,418)(142,417)(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)(157,444)(158,450)(159,449)(160,448)(161,447)(162,446)
(163,445)(164,437)(165,443)(166,442)(167,441)(168,440)(169,439)(170,438)
(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)(185,353)(186,359)
(187,358)(188,357)(189,356)(190,355)(191,354)(192,360)(193,366)(194,365)
(195,364)(196,363)(197,362)(198,361)(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)(213,388)(214,394)(215,393)(216,392)(217,391)(218,390)
(219,389)(220,381)(221,387)(222,386)(223,385)(224,384)(225,383)(226,382);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)( 31,143)( 32,144)( 33,145)
( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)( 41,153)
( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)( 49,161)
( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)( 57,169)
( 58,170)( 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)( 87,199)( 88,200)( 89,201)
( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)
( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)(104,216)(105,217)
(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)(113,225)
(114,226)(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)(255,367)(256,368)(257,369)
(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)(265,377)
(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)(273,385)
(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)(281,393)
(282,394)(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)(311,423)(312,424)(313,425)
(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)(320,432)(321,433)
(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)(329,441)
(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)(337,449)
(338,450);
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)(339,381)(340,382)(341,383)
(342,384)(343,385)(344,386)(345,387)(346,388)(347,389)(348,390)(349,391)
(350,392)(351,393)(352,394)(353,367)(354,368)(355,369)(356,370)(357,371)
(358,372)(359,373)(360,374)(361,375)(362,376)(363,377)(364,378)(365,379)
(366,380)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)
(402,444)(403,445)(404,446)(405,447)(406,448)(407,449)(408,450)(409,423)
(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)
(418,432)(419,433)(420,434)(421,435)(422,436);
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)( 17,297)
( 18,303)( 19,302)( 20,301)( 21,300)( 22,299)( 23,298)( 24,304)( 25,310)
( 26,309)( 27,308)( 28,307)( 29,306)( 30,305)( 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)( 45,332)( 46,338)( 47,337)( 48,336)( 49,335)
( 50,334)( 51,333)( 52,325)( 53,331)( 54,330)( 55,329)( 56,328)( 57,327)
( 58,326)( 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)( 73,241)
( 74,247)( 75,246)( 76,245)( 77,244)( 78,243)( 79,242)( 80,248)( 81,254)
( 82,253)( 83,252)( 84,251)( 85,250)( 86,249)( 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)(101,276)(102,282)(103,281)(104,280)(105,279)
(106,278)(107,277)(108,269)(109,275)(110,274)(111,273)(112,272)(113,271)
(114,270)(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)(129,409)
(130,415)(131,414)(132,413)(133,412)(134,411)(135,410)(136,416)(137,422)
(138,421)(139,420)(140,419)(141,418)(142,417)(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)(157,444)(158,450)(159,449)(160,448)(161,447)
(162,446)(163,445)(164,437)(165,443)(166,442)(167,441)(168,440)(169,439)
(170,438)(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)(185,353)
(186,359)(187,358)(188,357)(189,356)(190,355)(191,354)(192,360)(193,366)
(194,365)(195,364)(196,363)(197,362)(198,361)(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)(213,388)(214,394)(215,393)(216,392)(217,391)
(218,390)(219,389)(220,381)(221,387)(222,386)(223,385)(224,384)(225,383)
(226,382);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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