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

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

to this polytope