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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,14,2}*1792b
if this polytope has a name.
Group : SmallGroup(1792,1036167)
Rank : 5
Schlafli Type : {8,4,14,2}
Number of vertices, edges, etc : 8, 16, 28, 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 : {8,4,2,2}*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 := (  1,225)(  2,226)(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)
(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,246)( 16,247)
( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)( 24,241)
( 25,242)( 26,243)( 27,244)( 28,245)( 29,260)( 30,261)( 31,262)( 32,263)
( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)( 40,257)
( 41,258)( 42,259)( 43,267)( 44,268)( 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)( 71,302)( 72,303)
( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)( 80,297)
( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)( 88,319)
( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)( 96,313)
( 97,314)( 98,315)( 99,323)(100,324)(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)(127,358)(128,359)
(129,360)(130,361)(131,362)(132,363)(133,364)(134,351)(135,352)(136,353)
(137,354)(138,355)(139,356)(140,357)(141,372)(142,373)(143,374)(144,375)
(145,376)(146,377)(147,378)(148,365)(149,366)(150,367)(151,368)(152,369)
(153,370)(154,371)(155,379)(156,380)(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)(183,414)(184,415)
(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)(192,409)
(193,410)(194,411)(195,412)(196,413)(197,428)(198,429)(199,430)(200,431)
(201,432)(202,433)(203,434)(204,421)(205,422)(206,423)(207,424)(208,425)
(209,426)(210,427)(211,435)(212,436)(213,437)(214,438)(215,439)(216,440)
(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)(224,448);;
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 := (  1,169)(  2,175)(  3,174)(  4,173)(  5,172)(  6,171)(  7,170)(  8,176)
(  9,182)( 10,181)( 11,180)( 12,179)( 13,178)( 14,177)( 15,183)( 16,189)
( 17,188)( 18,187)( 19,186)( 20,185)( 21,184)( 22,190)( 23,196)( 24,195)
( 25,194)( 26,193)( 27,192)( 28,191)( 29,204)( 30,210)( 31,209)( 32,208)
( 33,207)( 34,206)( 35,205)( 36,197)( 37,203)( 38,202)( 39,201)( 40,200)
( 41,199)( 42,198)( 43,218)( 44,224)( 45,223)( 46,222)( 47,221)( 48,220)
( 49,219)( 50,211)( 51,217)( 52,216)( 53,215)( 54,214)( 55,213)( 56,212)
( 57,113)( 58,119)( 59,118)( 60,117)( 61,116)( 62,115)( 63,114)( 64,120)
( 65,126)( 66,125)( 67,124)( 68,123)( 69,122)( 70,121)( 71,127)( 72,133)
( 73,132)( 74,131)( 75,130)( 76,129)( 77,128)( 78,134)( 79,140)( 80,139)
( 81,138)( 82,137)( 83,136)( 84,135)( 85,148)( 86,154)( 87,153)( 88,152)
( 89,151)( 90,150)( 91,149)( 92,141)( 93,147)( 94,146)( 95,145)( 96,144)
( 97,143)( 98,142)( 99,162)(100,168)(101,167)(102,166)(103,165)(104,164)
(105,163)(106,155)(107,161)(108,160)(109,159)(110,158)(111,157)(112,156)
(225,393)(226,399)(227,398)(228,397)(229,396)(230,395)(231,394)(232,400)
(233,406)(234,405)(235,404)(236,403)(237,402)(238,401)(239,407)(240,413)
(241,412)(242,411)(243,410)(244,409)(245,408)(246,414)(247,420)(248,419)
(249,418)(250,417)(251,416)(252,415)(253,428)(254,434)(255,433)(256,432)
(257,431)(258,430)(259,429)(260,421)(261,427)(262,426)(263,425)(264,424)
(265,423)(266,422)(267,442)(268,448)(269,447)(270,446)(271,445)(272,444)
(273,443)(274,435)(275,441)(276,440)(277,439)(278,438)(279,437)(280,436)
(281,337)(282,343)(283,342)(284,341)(285,340)(286,339)(287,338)(288,344)
(289,350)(290,349)(291,348)(292,347)(293,346)(294,345)(295,351)(296,357)
(297,356)(298,355)(299,354)(300,353)(301,352)(302,358)(303,364)(304,363)
(305,362)(306,361)(307,360)(308,359)(309,372)(310,378)(311,377)(312,376)
(313,375)(314,374)(315,373)(316,365)(317,371)(318,370)(319,369)(320,368)
(321,367)(322,366)(323,386)(324,392)(325,391)(326,390)(327,389)(328,388)
(329,387)(330,379)(331,385)(332,384)(333,383)(334,382)(335,381)(336,380);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*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)!(  1,225)(  2,226)(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)
(  8,232)(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,246)
( 16,247)( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)
( 24,241)( 25,242)( 26,243)( 27,244)( 28,245)( 29,260)( 30,261)( 31,262)
( 32,263)( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)
( 40,257)( 41,258)( 42,259)( 43,267)( 44,268)( 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)( 71,302)
( 72,303)( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)
( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)
( 88,319)( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)
( 96,313)( 97,314)( 98,315)( 99,323)(100,324)(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)(127,358)
(128,359)(129,360)(130,361)(131,362)(132,363)(133,364)(134,351)(135,352)
(136,353)(137,354)(138,355)(139,356)(140,357)(141,372)(142,373)(143,374)
(144,375)(145,376)(146,377)(147,378)(148,365)(149,366)(150,367)(151,368)
(152,369)(153,370)(154,371)(155,379)(156,380)(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)(183,414)
(184,415)(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)
(192,409)(193,410)(194,411)(195,412)(196,413)(197,428)(198,429)(199,430)
(200,431)(201,432)(202,433)(203,434)(204,421)(205,422)(206,423)(207,424)
(208,425)(209,426)(210,427)(211,435)(212,436)(213,437)(214,438)(215,439)
(216,440)(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)
(224,448);
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)!(  1,169)(  2,175)(  3,174)(  4,173)(  5,172)(  6,171)(  7,170)
(  8,176)(  9,182)( 10,181)( 11,180)( 12,179)( 13,178)( 14,177)( 15,183)
( 16,189)( 17,188)( 18,187)( 19,186)( 20,185)( 21,184)( 22,190)( 23,196)
( 24,195)( 25,194)( 26,193)( 27,192)( 28,191)( 29,204)( 30,210)( 31,209)
( 32,208)( 33,207)( 34,206)( 35,205)( 36,197)( 37,203)( 38,202)( 39,201)
( 40,200)( 41,199)( 42,198)( 43,218)( 44,224)( 45,223)( 46,222)( 47,221)
( 48,220)( 49,219)( 50,211)( 51,217)( 52,216)( 53,215)( 54,214)( 55,213)
( 56,212)( 57,113)( 58,119)( 59,118)( 60,117)( 61,116)( 62,115)( 63,114)
( 64,120)( 65,126)( 66,125)( 67,124)( 68,123)( 69,122)( 70,121)( 71,127)
( 72,133)( 73,132)( 74,131)( 75,130)( 76,129)( 77,128)( 78,134)( 79,140)
( 80,139)( 81,138)( 82,137)( 83,136)( 84,135)( 85,148)( 86,154)( 87,153)
( 88,152)( 89,151)( 90,150)( 91,149)( 92,141)( 93,147)( 94,146)( 95,145)
( 96,144)( 97,143)( 98,142)( 99,162)(100,168)(101,167)(102,166)(103,165)
(104,164)(105,163)(106,155)(107,161)(108,160)(109,159)(110,158)(111,157)
(112,156)(225,393)(226,399)(227,398)(228,397)(229,396)(230,395)(231,394)
(232,400)(233,406)(234,405)(235,404)(236,403)(237,402)(238,401)(239,407)
(240,413)(241,412)(242,411)(243,410)(244,409)(245,408)(246,414)(247,420)
(248,419)(249,418)(250,417)(251,416)(252,415)(253,428)(254,434)(255,433)
(256,432)(257,431)(258,430)(259,429)(260,421)(261,427)(262,426)(263,425)
(264,424)(265,423)(266,422)(267,442)(268,448)(269,447)(270,446)(271,445)
(272,444)(273,443)(274,435)(275,441)(276,440)(277,439)(278,438)(279,437)
(280,436)(281,337)(282,343)(283,342)(284,341)(285,340)(286,339)(287,338)
(288,344)(289,350)(290,349)(291,348)(292,347)(293,346)(294,345)(295,351)
(296,357)(297,356)(298,355)(299,354)(300,353)(301,352)(302,358)(303,364)
(304,363)(305,362)(306,361)(307,360)(308,359)(309,372)(310,378)(311,377)
(312,376)(313,375)(314,374)(315,373)(316,365)(317,371)(318,370)(319,369)
(320,368)(321,367)(322,366)(323,386)(324,392)(325,391)(326,390)(327,389)
(328,388)(329,387)(330,379)(331,385)(332,384)(333,383)(334,382)(335,381)
(336,380);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*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