Polytope of Type {28,4,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,4,4,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,336974)
Rank : 5
Schlafli Type : {28,4,4,2}
Number of vertices, edges, etc : 28, 56, 8, 4, 2
Order of s0s1s2s3s4 : 28
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 : {28,4,2,2}*896, {28,2,4,2}*896, {14,4,4,2}*896
4-fold quotients : {28,2,2,2}*448, {14,2,4,2}*448, {14,4,2,2}*448
7-fold quotients : {4,4,4,2}*256
8-fold quotients : {7,2,4,2}*224, {14,2,2,2}*224
14-fold quotients : {2,4,4,2}*128, {4,4,2,2}*128, {4,2,4,2}*128
16-fold quotients : {7,2,2,2}*112
28-fold quotients : {2,2,4,2}*64, {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 := ( 1,281)( 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)( 15,295)( 16,301)
( 17,300)( 18,299)( 19,298)( 20,297)( 21,296)( 22,302)( 23,308)( 24,307)
( 25,306)( 26,305)( 27,304)( 28,303)( 29,309)( 30,315)( 31,314)( 32,313)
( 33,312)( 34,311)( 35,310)( 36,316)( 37,322)( 38,321)( 39,320)( 40,319)
( 41,318)( 42,317)( 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)( 71,239)( 72,245)
( 73,244)( 74,243)( 75,242)( 76,241)( 77,240)( 78,246)( 79,252)( 80,251)
( 81,250)( 82,249)( 83,248)( 84,247)( 85,253)( 86,259)( 87,258)( 88,257)
( 89,256)( 90,255)( 91,254)( 92,260)( 93,266)( 94,265)( 95,264)( 96,263)
( 97,262)( 98,261)( 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)
(113,400)(114,406)(115,405)(116,404)(117,403)(118,402)(119,401)(120,393)
(121,399)(122,398)(123,397)(124,396)(125,395)(126,394)(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)(155,442)(156,448)(157,447)(158,446)(159,445)(160,444)
(161,443)(162,435)(163,441)(164,440)(165,439)(166,438)(167,437)(168,436)
(169,344)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)(176,337)
(177,343)(178,342)(179,341)(180,340)(181,339)(182,338)(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)(211,386)(212,392)(213,391)(214,390)(215,389)(216,388)
(217,387)(218,379)(219,385)(220,384)(221,383)(222,382)(223,381)(224,380);;
s1 := ( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)( 8,121)
( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)( 16,127)
( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)( 24,140)
( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)( 32,146)
( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)
( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)
( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)
( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,177)
( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)( 72,183)
( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)( 80,196)
( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)( 88,202)
( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)( 96,208)
( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)(104,214)
(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220)
(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)(232,345)
(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)(240,351)
(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)(248,364)
(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)(256,370)
(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)(264,376)
(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)(272,382)
(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)(280,388)
(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)(288,401)
(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)(296,407)
(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)(304,420)
(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)(312,426)
(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)(320,432)
(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)(328,438)
(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)(336,444);;
s2 := ( 57, 85)( 58, 86)( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)
( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 97)( 70, 98)( 71, 99)( 72,100)
( 73,101)( 74,102)( 75,103)( 76,104)( 77,105)( 78,106)( 79,107)( 80,108)
( 81,109)( 82,110)( 83,111)( 84,112)(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)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)
(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)
(169,211)(170,212)(171,213)(172,214)(173,215)(174,216)(175,217)(176,218)
(177,219)(178,220)(179,221)(180,222)(181,223)(182,224)(183,197)(184,198)
(185,199)(186,200)(187,201)(188,202)(189,203)(190,204)(191,205)(192,206)
(193,207)(194,208)(195,209)(196,210)(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)
(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)(393,407)(394,408)(395,409)(396,410)
(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)
(405,419)(406,420)(421,435)(422,436)(423,437)(424,438)(425,439)(426,440)
(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448);;
s3 := ( 1, 57)( 2, 58)( 3, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)( 8, 64)
( 9, 65)( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)
( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)
( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)( 32, 88)
( 33, 89)( 34, 90)( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)
( 41, 97)( 42, 98)( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)( 48,104)
( 49,105)( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)
(113,169)(114,170)(115,171)(116,172)(117,173)(118,174)(119,175)(120,176)
(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,183)(128,184)
(129,185)(130,186)(131,187)(132,188)(133,189)(134,190)(135,191)(136,192)
(137,193)(138,194)(139,195)(140,196)(141,197)(142,198)(143,199)(144,200)
(145,201)(146,202)(147,203)(148,204)(149,205)(150,206)(151,207)(152,208)
(153,209)(154,210)(155,211)(156,212)(157,213)(158,214)(159,215)(160,216)
(161,217)(162,218)(163,219)(164,220)(165,221)(166,222)(167,223)(168,224)
(225,281)(226,282)(227,283)(228,284)(229,285)(230,286)(231,287)(232,288)
(233,289)(234,290)(235,291)(236,292)(237,293)(238,294)(239,295)(240,296)
(241,297)(242,298)(243,299)(244,300)(245,301)(246,302)(247,303)(248,304)
(249,305)(250,306)(251,307)(252,308)(253,309)(254,310)(255,311)(256,312)
(257,313)(258,314)(259,315)(260,316)(261,317)(262,318)(263,319)(264,320)
(265,321)(266,322)(267,323)(268,324)(269,325)(270,326)(271,327)(272,328)
(273,329)(274,330)(275,331)(276,332)(277,333)(278,334)(279,335)(280,336)
(337,393)(338,394)(339,395)(340,396)(341,397)(342,398)(343,399)(344,400)
(345,401)(346,402)(347,403)(348,404)(349,405)(350,406)(351,407)(352,408)
(353,409)(354,410)(355,411)(356,412)(357,413)(358,414)(359,415)(360,416)
(361,417)(362,418)(363,419)(364,420)(365,421)(366,422)(367,423)(368,424)
(369,425)(370,426)(371,427)(372,428)(373,429)(374,430)(375,431)(376,432)
(377,433)(378,434)(379,435)(380,436)(381,437)(382,438)(383,439)(384,440)
(385,441)(386,442)(387,443)(388,444)(389,445)(390,446)(391,447)(392,448);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
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*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)!( 1,281)( 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)( 15,295)
( 16,301)( 17,300)( 18,299)( 19,298)( 20,297)( 21,296)( 22,302)( 23,308)
( 24,307)( 25,306)( 26,305)( 27,304)( 28,303)( 29,309)( 30,315)( 31,314)
( 32,313)( 33,312)( 34,311)( 35,310)( 36,316)( 37,322)( 38,321)( 39,320)
( 40,319)( 41,318)( 42,317)( 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)( 71,239)
( 72,245)( 73,244)( 74,243)( 75,242)( 76,241)( 77,240)( 78,246)( 79,252)
( 80,251)( 81,250)( 82,249)( 83,248)( 84,247)( 85,253)( 86,259)( 87,258)
( 88,257)( 89,256)( 90,255)( 91,254)( 92,260)( 93,266)( 94,265)( 95,264)
( 96,263)( 97,262)( 98,261)( 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)(113,400)(114,406)(115,405)(116,404)(117,403)(118,402)(119,401)
(120,393)(121,399)(122,398)(123,397)(124,396)(125,395)(126,394)(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)(155,442)(156,448)(157,447)(158,446)(159,445)
(160,444)(161,443)(162,435)(163,441)(164,440)(165,439)(166,438)(167,437)
(168,436)(169,344)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)
(176,337)(177,343)(178,342)(179,341)(180,340)(181,339)(182,338)(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)(211,386)(212,392)(213,391)(214,390)(215,389)
(216,388)(217,387)(218,379)(219,385)(220,384)(221,383)(222,382)(223,381)
(224,380);
s1 := Sym(450)!( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)
( 8,121)( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)
( 16,127)( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)
( 24,140)( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)
( 32,146)( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)
( 40,152)( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)
( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)
( 56,164)( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)
( 64,177)( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)
( 72,183)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)
( 80,196)( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)
( 88,202)( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)
( 96,208)( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)
(104,214)(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)
(112,220)(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)
(232,345)(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)
(240,351)(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)
(248,364)(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)
(256,370)(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)
(264,376)(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)
(272,382)(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)
(280,388)(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)
(288,401)(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)
(296,407)(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)
(304,420)(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)
(312,426)(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)
(320,432)(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)
(328,438)(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)
(336,444);
s2 := Sym(450)!( 57, 85)( 58, 86)( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)
( 64, 92)( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 97)( 70, 98)( 71, 99)
( 72,100)( 73,101)( 74,102)( 75,103)( 76,104)( 77,105)( 78,106)( 79,107)
( 80,108)( 81,109)( 82,110)( 83,111)( 84,112)(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)(141,155)(142,156)(143,157)(144,158)(145,159)
(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)
(154,168)(169,211)(170,212)(171,213)(172,214)(173,215)(174,216)(175,217)
(176,218)(177,219)(178,220)(179,221)(180,222)(181,223)(182,224)(183,197)
(184,198)(185,199)(186,200)(187,201)(188,202)(189,203)(190,204)(191,205)
(192,206)(193,207)(194,208)(195,209)(196,210)(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)(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)(393,407)(394,408)(395,409)
(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)
(404,418)(405,419)(406,420)(421,435)(422,436)(423,437)(424,438)(425,439)
(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)
(434,448);
s3 := Sym(450)!( 1, 57)( 2, 58)( 3, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)
( 8, 64)( 9, 65)( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)
( 16, 72)( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)
( 24, 80)( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)
( 32, 88)( 33, 89)( 34, 90)( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)
( 40, 96)( 41, 97)( 42, 98)( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)
( 48,104)( 49,105)( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)
( 56,112)(113,169)(114,170)(115,171)(116,172)(117,173)(118,174)(119,175)
(120,176)(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,183)
(128,184)(129,185)(130,186)(131,187)(132,188)(133,189)(134,190)(135,191)
(136,192)(137,193)(138,194)(139,195)(140,196)(141,197)(142,198)(143,199)
(144,200)(145,201)(146,202)(147,203)(148,204)(149,205)(150,206)(151,207)
(152,208)(153,209)(154,210)(155,211)(156,212)(157,213)(158,214)(159,215)
(160,216)(161,217)(162,218)(163,219)(164,220)(165,221)(166,222)(167,223)
(168,224)(225,281)(226,282)(227,283)(228,284)(229,285)(230,286)(231,287)
(232,288)(233,289)(234,290)(235,291)(236,292)(237,293)(238,294)(239,295)
(240,296)(241,297)(242,298)(243,299)(244,300)(245,301)(246,302)(247,303)
(248,304)(249,305)(250,306)(251,307)(252,308)(253,309)(254,310)(255,311)
(256,312)(257,313)(258,314)(259,315)(260,316)(261,317)(262,318)(263,319)
(264,320)(265,321)(266,322)(267,323)(268,324)(269,325)(270,326)(271,327)
(272,328)(273,329)(274,330)(275,331)(276,332)(277,333)(278,334)(279,335)
(280,336)(337,393)(338,394)(339,395)(340,396)(341,397)(342,398)(343,399)
(344,400)(345,401)(346,402)(347,403)(348,404)(349,405)(350,406)(351,407)
(352,408)(353,409)(354,410)(355,411)(356,412)(357,413)(358,414)(359,415)
(360,416)(361,417)(362,418)(363,419)(364,420)(365,421)(366,422)(367,423)
(368,424)(369,425)(370,426)(371,427)(372,428)(373,429)(374,430)(375,431)
(376,432)(377,433)(378,434)(379,435)(380,436)(381,437)(382,438)(383,439)
(384,440)(385,441)(386,442)(387,443)(388,444)(389,445)(390,446)(391,447)
(392,448);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, 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*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