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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}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1035859)
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, {8,2,14,2}*896
   4-fold quotients : {8,2,7,2}*448, {2,4,14,2}*448, {4,2,14,2}*448
   7-fold quotients : {8,4,2,2}*256a
   8-fold quotients : {4,2,7,2}*224, {2,2,14,2}*224
   14-fold quotients : {4,4,2,2}*128, {8,2,2,2}*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)( 15,239)( 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)( 29,260)( 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)( 43,274)( 44,275)( 45,276)( 46,277)( 47,278)( 48,279)
( 49,280)( 50,267)( 51,268)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)
( 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)( 71,295)( 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)( 85,316)( 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)( 99,330)(100,331)(101,332)(102,333)(103,334)(104,335)
(105,336)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)(112,329)
(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)(127,351)(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)(141,372)(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)(155,386)(156,387)(157,388)(158,389)(159,390)(160,391)
(161,392)(162,379)(163,380)(164,381)(165,382)(166,383)(167,384)(168,385)
(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)(183,407)(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)(197,428)(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)(211,442)(212,443)(213,444)(214,445)(215,446)(216,447)
(217,448)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)(224,441);;
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)(337,379)(338,380)(339,381)(340,382)
(341,383)(342,384)(343,385)(344,386)(345,387)(346,388)(347,389)(348,390)
(349,391)(350,392)(351,365)(352,366)(353,367)(354,368)(355,369)(356,370)
(357,371)(358,372)(359,373)(360,374)(361,375)(362,376)(363,377)(364,378)
(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)
(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)(408,422)
(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)
(417,431)(418,432)(419,433)(420,434);;
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)( 29,197)( 30,203)( 31,202)( 32,201)
( 33,200)( 34,199)( 35,198)( 36,204)( 37,210)( 38,209)( 39,208)( 40,207)
( 41,206)( 42,205)( 43,211)( 44,217)( 45,216)( 46,215)( 47,214)( 48,213)
( 49,212)( 50,218)( 51,224)( 52,223)( 53,222)( 54,221)( 55,220)( 56,219)
( 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)( 85,141)( 86,147)( 87,146)( 88,145)
( 89,144)( 90,143)( 91,142)( 92,148)( 93,154)( 94,153)( 95,152)( 96,151)
( 97,150)( 98,149)( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)
(105,156)(106,162)(107,168)(108,167)(109,166)(110,165)(111,164)(112,163)
(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)(253,421)(254,427)(255,426)(256,425)
(257,424)(258,423)(259,422)(260,428)(261,434)(262,433)(263,432)(264,431)
(265,430)(266,429)(267,435)(268,441)(269,440)(270,439)(271,438)(272,437)
(273,436)(274,442)(275,448)(276,447)(277,446)(278,445)(279,444)(280,443)
(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)(309,365)(310,371)(311,370)(312,369)
(313,368)(314,367)(315,366)(316,372)(317,378)(318,377)(319,376)(320,375)
(321,374)(322,373)(323,379)(324,385)(325,384)(326,383)(327,382)(328,381)
(329,380)(330,386)(331,392)(332,391)(333,390)(334,389)(335,388)(336,387);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 15,239)
( 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)( 29,260)( 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)( 43,274)( 44,275)( 45,276)( 46,277)( 47,278)
( 48,279)( 49,280)( 50,267)( 51,268)( 52,269)( 53,270)( 54,271)( 55,272)
( 56,273)( 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)( 71,295)
( 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)( 85,316)( 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)( 99,330)(100,331)(101,332)(102,333)(103,334)
(104,335)(105,336)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)
(112,329)(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)(127,351)
(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)(141,372)(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)(155,386)(156,387)(157,388)(158,389)(159,390)
(160,391)(161,392)(162,379)(163,380)(164,381)(165,382)(166,383)(167,384)
(168,385)(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)(183,407)
(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)(197,428)(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)(211,442)(212,443)(213,444)(214,445)(215,446)
(216,447)(217,448)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)
(224,441);
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)(337,379)(338,380)(339,381)
(340,382)(341,383)(342,384)(343,385)(344,386)(345,387)(346,388)(347,389)
(348,390)(349,391)(350,392)(351,365)(352,366)(353,367)(354,368)(355,369)
(356,370)(357,371)(358,372)(359,373)(360,374)(361,375)(362,376)(363,377)
(364,378)(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)
(400,442)(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)
(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)
(416,430)(417,431)(418,432)(419,433)(420,434);
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)( 29,197)( 30,203)( 31,202)
( 32,201)( 33,200)( 34,199)( 35,198)( 36,204)( 37,210)( 38,209)( 39,208)
( 40,207)( 41,206)( 42,205)( 43,211)( 44,217)( 45,216)( 46,215)( 47,214)
( 48,213)( 49,212)( 50,218)( 51,224)( 52,223)( 53,222)( 54,221)( 55,220)
( 56,219)( 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)( 85,141)( 86,147)( 87,146)
( 88,145)( 89,144)( 90,143)( 91,142)( 92,148)( 93,154)( 94,153)( 95,152)
( 96,151)( 97,150)( 98,149)( 99,155)(100,161)(101,160)(102,159)(103,158)
(104,157)(105,156)(106,162)(107,168)(108,167)(109,166)(110,165)(111,164)
(112,163)(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)(253,421)(254,427)(255,426)
(256,425)(257,424)(258,423)(259,422)(260,428)(261,434)(262,433)(263,432)
(264,431)(265,430)(266,429)(267,435)(268,441)(269,440)(270,439)(271,438)
(272,437)(273,436)(274,442)(275,448)(276,447)(277,446)(278,445)(279,444)
(280,443)(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)(309,365)(310,371)(311,370)
(312,369)(313,368)(314,367)(315,366)(316,372)(317,378)(318,377)(319,376)
(320,375)(321,374)(322,373)(323,379)(324,385)(325,384)(326,383)(327,382)
(328,381)(329,380)(330,386)(331,392)(332,391)(333,390)(334,389)(335,388)
(336,387);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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