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

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

to this polytope