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}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1035859)
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, {2,8,2,14}*896
4-fold quotients : {2,8,2,7}*448, {2,2,4,14}*448, {2,4,2,14}*448
7-fold quotients : {2,8,4,2}*256a
8-fold quotients : {2,4,2,7}*224, {2,2,2,14}*224
14-fold quotients : {2,4,4,2}*128, {2,8,2,2}*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)( 17,241)( 18,242)
( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)( 25,249)( 26,250)
( 27,251)( 28,252)( 29,253)( 30,254)( 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)( 45,276)( 46,277)( 47,278)( 48,279)( 49,280)( 50,281)
( 51,282)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)( 57,274)( 58,275)
( 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)( 73,297)( 74,298)
( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)( 81,305)( 82,306)
( 83,307)( 84,308)( 85,309)( 86,310)( 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)(101,332)(102,333)(103,334)(104,335)(105,336)(106,337)
(107,338)(108,325)(109,326)(110,327)(111,328)(112,329)(113,330)(114,331)
(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)(129,353)(130,354)
(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)(137,361)(138,362)
(139,363)(140,364)(141,365)(142,366)(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)(157,388)(158,389)(159,390)(160,391)(161,392)(162,393)
(163,394)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)(170,387)
(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)(185,409)(186,410)
(187,411)(188,412)(189,413)(190,414)(191,415)(192,416)(193,417)(194,418)
(195,419)(196,420)(197,421)(198,422)(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)(213,444)(214,445)(215,446)(216,447)(217,448)(218,449)
(219,450)(220,437)(221,438)(222,439)(223,440)(224,441)(225,442)(226,443);;
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)(339,381)(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 := ( 3,171)( 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)( 31,199)( 32,205)( 33,204)( 34,203)
( 35,202)( 36,201)( 37,200)( 38,206)( 39,212)( 40,211)( 41,210)( 42,209)
( 43,208)( 44,207)( 45,213)( 46,219)( 47,218)( 48,217)( 49,216)( 50,215)
( 51,214)( 52,220)( 53,226)( 54,225)( 55,224)( 56,223)( 57,222)( 58,221)
( 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)( 87,143)( 88,149)( 89,148)( 90,147)
( 91,146)( 92,145)( 93,144)( 94,150)( 95,156)( 96,155)( 97,154)( 98,153)
( 99,152)(100,151)(101,157)(102,163)(103,162)(104,161)(105,160)(106,159)
(107,158)(108,164)(109,170)(110,169)(111,168)(112,167)(113,166)(114,165)
(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)(255,423)(256,429)(257,428)(258,427)
(259,426)(260,425)(261,424)(262,430)(263,436)(264,435)(265,434)(266,433)
(267,432)(268,431)(269,437)(270,443)(271,442)(272,441)(273,440)(274,439)
(275,438)(276,444)(277,450)(278,449)(279,448)(280,447)(281,446)(282,445)
(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)(311,367)(312,373)(313,372)(314,371)
(315,370)(316,369)(317,368)(318,374)(319,380)(320,379)(321,378)(322,377)
(323,376)(324,375)(325,381)(326,387)(327,386)(328,385)(329,384)(330,383)
(331,382)(332,388)(333,394)(334,393)(335,392)(336,391)(337,390)(338,389);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 17,241)
( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)( 25,249)
( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 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)( 45,276)( 46,277)( 47,278)( 48,279)( 49,280)
( 50,281)( 51,282)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)( 57,274)
( 58,275)( 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)( 73,297)
( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)( 81,305)
( 82,306)( 83,307)( 84,308)( 85,309)( 86,310)( 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)(101,332)(102,333)(103,334)(104,335)(105,336)
(106,337)(107,338)(108,325)(109,326)(110,327)(111,328)(112,329)(113,330)
(114,331)(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)(129,353)
(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)(137,361)
(138,362)(139,363)(140,364)(141,365)(142,366)(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)(157,388)(158,389)(159,390)(160,391)(161,392)
(162,393)(163,394)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)
(170,387)(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)(185,409)
(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)(192,416)(193,417)
(194,418)(195,419)(196,420)(197,421)(198,422)(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)(213,444)(214,445)(215,446)(216,447)(217,448)
(218,449)(219,450)(220,437)(221,438)(222,439)(223,440)(224,441)(225,442)
(226,443);
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)(339,381)(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)!( 3,171)( 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)( 31,199)( 32,205)( 33,204)
( 34,203)( 35,202)( 36,201)( 37,200)( 38,206)( 39,212)( 40,211)( 41,210)
( 42,209)( 43,208)( 44,207)( 45,213)( 46,219)( 47,218)( 48,217)( 49,216)
( 50,215)( 51,214)( 52,220)( 53,226)( 54,225)( 55,224)( 56,223)( 57,222)
( 58,221)( 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)( 87,143)( 88,149)( 89,148)
( 90,147)( 91,146)( 92,145)( 93,144)( 94,150)( 95,156)( 96,155)( 97,154)
( 98,153)( 99,152)(100,151)(101,157)(102,163)(103,162)(104,161)(105,160)
(106,159)(107,158)(108,164)(109,170)(110,169)(111,168)(112,167)(113,166)
(114,165)(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)(255,423)(256,429)(257,428)
(258,427)(259,426)(260,425)(261,424)(262,430)(263,436)(264,435)(265,434)
(266,433)(267,432)(268,431)(269,437)(270,443)(271,442)(272,441)(273,440)
(274,439)(275,438)(276,444)(277,450)(278,449)(279,448)(280,447)(281,446)
(282,445)(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)(311,367)(312,373)(313,372)
(314,371)(315,370)(316,369)(317,368)(318,374)(319,380)(320,379)(321,378)
(322,377)(323,376)(324,375)(325,381)(326,387)(327,386)(328,385)(329,384)
(330,383)(331,382)(332,388)(333,394)(334,393)(335,392)(336,391)(337,390)
(338,389);
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*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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