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