Polytope of Type {2,14,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,8,4}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1035859)
Rank : 5
Schlafli Type : {2,14,8,4}
Number of vertices, edges, etc : 2, 14, 56, 16, 4
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 : {2,14,4,4}*896, {2,14,8,2}*896
4-fold quotients : {2,14,2,4}*448, {2,14,4,2}*448
7-fold quotients : {2,2,8,4}*256a
8-fold quotients : {2,7,2,4}*224, {2,14,2,2}*224
14-fold quotients : {2,2,4,4}*128, {2,2,8,2}*128
16-fold quotients : {2,7,2,2}*112
28-fold quotients : {2,2,2,4}*64, {2,2,4,2}*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, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)( 10, 66)
( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 73)( 18, 79)
( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 74)( 24, 80)( 25, 86)( 26, 85)
( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31, 87)( 32, 93)( 33, 92)( 34, 91)
( 35, 90)( 36, 89)( 37, 88)( 38, 94)( 39,100)( 40, 99)( 41, 98)( 42, 97)
( 43, 96)( 44, 95)( 45,101)( 46,107)( 47,106)( 48,105)( 49,104)( 50,103)
( 51,102)( 52,108)( 53,114)( 54,113)( 55,112)( 56,111)( 57,110)( 58,109)
(115,171)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)(122,178)
(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,185)(130,191)
(131,190)(132,189)(133,188)(134,187)(135,186)(136,192)(137,198)(138,197)
(139,196)(140,195)(141,194)(142,193)(143,199)(144,205)(145,204)(146,203)
(147,202)(148,201)(149,200)(150,206)(151,212)(152,211)(153,210)(154,209)
(155,208)(156,207)(157,213)(158,219)(159,218)(160,217)(161,216)(162,215)
(163,214)(164,220)(165,226)(166,225)(167,224)(168,223)(169,222)(170,221)
(227,283)(228,289)(229,288)(230,287)(231,286)(232,285)(233,284)(234,290)
(235,296)(236,295)(237,294)(238,293)(239,292)(240,291)(241,297)(242,303)
(243,302)(244,301)(245,300)(246,299)(247,298)(248,304)(249,310)(250,309)
(251,308)(252,307)(253,306)(254,305)(255,311)(256,317)(257,316)(258,315)
(259,314)(260,313)(261,312)(262,318)(263,324)(264,323)(265,322)(266,321)
(267,320)(268,319)(269,325)(270,331)(271,330)(272,329)(273,328)(274,327)
(275,326)(276,332)(277,338)(278,337)(279,336)(280,335)(281,334)(282,333)
(339,395)(340,401)(341,400)(342,399)(343,398)(344,397)(345,396)(346,402)
(347,408)(348,407)(349,406)(350,405)(351,404)(352,403)(353,409)(354,415)
(355,414)(356,413)(357,412)(358,411)(359,410)(360,416)(361,422)(362,421)
(363,420)(364,419)(365,418)(366,417)(367,423)(368,429)(369,428)(370,427)
(371,426)(372,425)(373,424)(374,430)(375,436)(376,435)(377,434)(378,433)
(379,432)(380,431)(381,437)(382,443)(383,442)(384,441)(385,440)(386,439)
(387,438)(388,444)(389,450)(390,449)(391,448)(392,447)(393,446)(394,445);;
s2 := ( 3,284)( 4,283)( 5,289)( 6,288)( 7,287)( 8,286)( 9,285)( 10,291)
( 11,290)( 12,296)( 13,295)( 14,294)( 15,293)( 16,292)( 17,298)( 18,297)
( 19,303)( 20,302)( 21,301)( 22,300)( 23,299)( 24,305)( 25,304)( 26,310)
( 27,309)( 28,308)( 29,307)( 30,306)( 31,319)( 32,318)( 33,324)( 34,323)
( 35,322)( 36,321)( 37,320)( 38,312)( 39,311)( 40,317)( 41,316)( 42,315)
( 43,314)( 44,313)( 45,333)( 46,332)( 47,338)( 48,337)( 49,336)( 50,335)
( 51,334)( 52,326)( 53,325)( 54,331)( 55,330)( 56,329)( 57,328)( 58,327)
( 59,228)( 60,227)( 61,233)( 62,232)( 63,231)( 64,230)( 65,229)( 66,235)
( 67,234)( 68,240)( 69,239)( 70,238)( 71,237)( 72,236)( 73,242)( 74,241)
( 75,247)( 76,246)( 77,245)( 78,244)( 79,243)( 80,249)( 81,248)( 82,254)
( 83,253)( 84,252)( 85,251)( 86,250)( 87,263)( 88,262)( 89,268)( 90,267)
( 91,266)( 92,265)( 93,264)( 94,256)( 95,255)( 96,261)( 97,260)( 98,259)
( 99,258)(100,257)(101,277)(102,276)(103,282)(104,281)(105,280)(106,279)
(107,278)(108,270)(109,269)(110,275)(111,274)(112,273)(113,272)(114,271)
(115,396)(116,395)(117,401)(118,400)(119,399)(120,398)(121,397)(122,403)
(123,402)(124,408)(125,407)(126,406)(127,405)(128,404)(129,410)(130,409)
(131,415)(132,414)(133,413)(134,412)(135,411)(136,417)(137,416)(138,422)
(139,421)(140,420)(141,419)(142,418)(143,431)(144,430)(145,436)(146,435)
(147,434)(148,433)(149,432)(150,424)(151,423)(152,429)(153,428)(154,427)
(155,426)(156,425)(157,445)(158,444)(159,450)(160,449)(161,448)(162,447)
(163,446)(164,438)(165,437)(166,443)(167,442)(168,441)(169,440)(170,439)
(171,340)(172,339)(173,345)(174,344)(175,343)(176,342)(177,341)(178,347)
(179,346)(180,352)(181,351)(182,350)(183,349)(184,348)(185,354)(186,353)
(187,359)(188,358)(189,357)(190,356)(191,355)(192,361)(193,360)(194,366)
(195,365)(196,364)(197,363)(198,362)(199,375)(200,374)(201,380)(202,379)
(203,378)(204,377)(205,376)(206,368)(207,367)(208,373)(209,372)(210,371)
(211,370)(212,369)(213,389)(214,388)(215,394)(216,393)(217,392)(218,391)
(219,390)(220,382)(221,381)(222,387)(223,386)(224,385)(225,384)(226,383);;
s3 := ( 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);;
s4 := ( 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);;
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*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(450)!(1,2);
s1 := Sym(450)!( 3, 59)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)
( 10, 66)( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 73)
( 18, 79)( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 74)( 24, 80)( 25, 86)
( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31, 87)( 32, 93)( 33, 92)
( 34, 91)( 35, 90)( 36, 89)( 37, 88)( 38, 94)( 39,100)( 40, 99)( 41, 98)
( 42, 97)( 43, 96)( 44, 95)( 45,101)( 46,107)( 47,106)( 48,105)( 49,104)
( 50,103)( 51,102)( 52,108)( 53,114)( 54,113)( 55,112)( 56,111)( 57,110)
( 58,109)(115,171)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)
(122,178)(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,185)
(130,191)(131,190)(132,189)(133,188)(134,187)(135,186)(136,192)(137,198)
(138,197)(139,196)(140,195)(141,194)(142,193)(143,199)(144,205)(145,204)
(146,203)(147,202)(148,201)(149,200)(150,206)(151,212)(152,211)(153,210)
(154,209)(155,208)(156,207)(157,213)(158,219)(159,218)(160,217)(161,216)
(162,215)(163,214)(164,220)(165,226)(166,225)(167,224)(168,223)(169,222)
(170,221)(227,283)(228,289)(229,288)(230,287)(231,286)(232,285)(233,284)
(234,290)(235,296)(236,295)(237,294)(238,293)(239,292)(240,291)(241,297)
(242,303)(243,302)(244,301)(245,300)(246,299)(247,298)(248,304)(249,310)
(250,309)(251,308)(252,307)(253,306)(254,305)(255,311)(256,317)(257,316)
(258,315)(259,314)(260,313)(261,312)(262,318)(263,324)(264,323)(265,322)
(266,321)(267,320)(268,319)(269,325)(270,331)(271,330)(272,329)(273,328)
(274,327)(275,326)(276,332)(277,338)(278,337)(279,336)(280,335)(281,334)
(282,333)(339,395)(340,401)(341,400)(342,399)(343,398)(344,397)(345,396)
(346,402)(347,408)(348,407)(349,406)(350,405)(351,404)(352,403)(353,409)
(354,415)(355,414)(356,413)(357,412)(358,411)(359,410)(360,416)(361,422)
(362,421)(363,420)(364,419)(365,418)(366,417)(367,423)(368,429)(369,428)
(370,427)(371,426)(372,425)(373,424)(374,430)(375,436)(376,435)(377,434)
(378,433)(379,432)(380,431)(381,437)(382,443)(383,442)(384,441)(385,440)
(386,439)(387,438)(388,444)(389,450)(390,449)(391,448)(392,447)(393,446)
(394,445);
s2 := Sym(450)!( 3,284)( 4,283)( 5,289)( 6,288)( 7,287)( 8,286)( 9,285)
( 10,291)( 11,290)( 12,296)( 13,295)( 14,294)( 15,293)( 16,292)( 17,298)
( 18,297)( 19,303)( 20,302)( 21,301)( 22,300)( 23,299)( 24,305)( 25,304)
( 26,310)( 27,309)( 28,308)( 29,307)( 30,306)( 31,319)( 32,318)( 33,324)
( 34,323)( 35,322)( 36,321)( 37,320)( 38,312)( 39,311)( 40,317)( 41,316)
( 42,315)( 43,314)( 44,313)( 45,333)( 46,332)( 47,338)( 48,337)( 49,336)
( 50,335)( 51,334)( 52,326)( 53,325)( 54,331)( 55,330)( 56,329)( 57,328)
( 58,327)( 59,228)( 60,227)( 61,233)( 62,232)( 63,231)( 64,230)( 65,229)
( 66,235)( 67,234)( 68,240)( 69,239)( 70,238)( 71,237)( 72,236)( 73,242)
( 74,241)( 75,247)( 76,246)( 77,245)( 78,244)( 79,243)( 80,249)( 81,248)
( 82,254)( 83,253)( 84,252)( 85,251)( 86,250)( 87,263)( 88,262)( 89,268)
( 90,267)( 91,266)( 92,265)( 93,264)( 94,256)( 95,255)( 96,261)( 97,260)
( 98,259)( 99,258)(100,257)(101,277)(102,276)(103,282)(104,281)(105,280)
(106,279)(107,278)(108,270)(109,269)(110,275)(111,274)(112,273)(113,272)
(114,271)(115,396)(116,395)(117,401)(118,400)(119,399)(120,398)(121,397)
(122,403)(123,402)(124,408)(125,407)(126,406)(127,405)(128,404)(129,410)
(130,409)(131,415)(132,414)(133,413)(134,412)(135,411)(136,417)(137,416)
(138,422)(139,421)(140,420)(141,419)(142,418)(143,431)(144,430)(145,436)
(146,435)(147,434)(148,433)(149,432)(150,424)(151,423)(152,429)(153,428)
(154,427)(155,426)(156,425)(157,445)(158,444)(159,450)(160,449)(161,448)
(162,447)(163,446)(164,438)(165,437)(166,443)(167,442)(168,441)(169,440)
(170,439)(171,340)(172,339)(173,345)(174,344)(175,343)(176,342)(177,341)
(178,347)(179,346)(180,352)(181,351)(182,350)(183,349)(184,348)(185,354)
(186,353)(187,359)(188,358)(189,357)(190,356)(191,355)(192,361)(193,360)
(194,366)(195,365)(196,364)(197,363)(198,362)(199,375)(200,374)(201,380)
(202,379)(203,378)(204,377)(205,376)(206,368)(207,367)(208,373)(209,372)
(210,371)(211,370)(212,369)(213,389)(214,388)(215,394)(216,393)(217,392)
(218,391)(219,390)(220,382)(221,381)(222,387)(223,386)(224,385)(225,384)
(226,383);
s3 := 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);
s4 := 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);
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*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope