Polytope of Type {4,28,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,28,4,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,336975)
Rank : 5
Schlafli Type : {4,28,4,2}
Number of vertices, edges, etc : 4, 56, 56, 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 : {2,28,4,2}*896, {4,28,2,2}*896, {4,14,4,2}*896
4-fold quotients : {2,28,2,2}*448, {2,14,4,2}*448, {4,14,2,2}*448
7-fold quotients : {4,4,4,2}*256
8-fold quotients : {2,14,2,2}*224
14-fold quotients : {2,4,4,2}*128, {4,4,2,2}*128, {4,2,4,2}*128
16-fold quotients : {2,7,2,2}*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, 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);;
s1 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)( 57, 85)( 58, 91)( 59, 90)( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 99)( 72,105)( 73,104)( 74,103)( 75,102)( 76,101)( 77,100)( 78,106)( 79,112)( 80,111)( 81,110)( 82,109)( 83,108)( 84,107)(113,127)(114,133)(115,132)(116,131)(117,130)(118,129)(119,128)(120,134)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(141,155)(142,161)(143,160)(144,159)(145,158)(146,157)(147,156)(148,162)(149,168)(150,167)(151,166)(152,165)(153,164)(154,163)(169,211)(170,217)(171,216)(172,215)(173,214)(174,213)(175,212)(176,218)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)(183,197)(184,203)(185,202)(186,201)(187,200)(188,199)(189,198)(190,204)(191,210)(192,209)(193,208)(194,207)(195,206)(196,205)(225,253)(226,259)(227,258)(228,257)(229,256)(230,255)(231,254)(232,260)(233,266)(234,265)(235,264)(236,263)(237,262)(238,261)(239,267)(240,273)(241,272)(242,271)(243,270)(244,269)(245,268)(246,274)(247,280)(248,279)(249,278)(250,277)(251,276)(252,275)(282,287)(283,286)(284,285)(289,294)(290,293)(291,292)(296,301)(297,300)(298,299)(303,308)(304,307)(305,306)(310,315)(311,314)(312,313)(317,322)(318,321)(319,320)(324,329)(325,328)(326,327)(331,336)(332,335)(333,334)(337,379)(338,385)(339,384)(340,383)(341,382)(342,381)(343,380)(344,386)(345,392)(346,391)(347,390)(348,389)(349,388)(350,387)(351,365)(352,371)(353,370)(354,369)(355,368)(356,367)(357,366)(358,372)(359,378)(360,377)(361,376)(362,375)(363,374)(364,373)(393,407)(394,413)(395,412)(396,411)(397,410)(398,409)(399,408)(400,414)(401,420)(402,419)(403,418)(404,417)(405,416)(406,415)(421,435)(422,441)(423,440)(424,439)(425,438)(426,437)(427,436)(428,442)(429,448)(430,447)(431,446)(432,445)(433,444)(434,443);;
s2 := ( 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);;
s3 := ( 1,281)( 2,282)( 3,283)( 4,284)( 5,285)( 6,286)( 7,287)( 8,288)( 9,289)( 10,290)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,296)( 17,297)( 18,298)( 19,299)( 20,300)( 21,301)( 22,302)( 23,303)( 24,304)( 25,305)( 26,306)( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)( 33,313)( 34,314)( 35,315)( 36,316)( 37,317)( 38,318)( 39,319)( 40,320)( 41,321)( 42,322)( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)( 48,328)( 49,329)( 50,330)( 51,331)( 52,332)( 53,333)( 54,334)( 55,335)( 56,336)( 57,225)( 58,226)( 59,227)( 60,228)( 61,229)( 62,230)( 63,231)( 64,232)( 65,233)( 66,234)( 67,235)( 68,236)( 69,237)( 70,238)( 71,239)( 72,240)( 73,241)( 74,242)( 75,243)( 76,244)( 77,245)( 78,246)( 79,247)( 80,248)( 81,249)( 82,250)( 83,251)( 84,252)( 85,253)( 86,254)( 87,255)( 88,256)( 89,257)( 90,258)( 91,259)( 92,260)( 93,261)( 94,262)( 95,263)( 96,264)( 97,265)( 98,266)( 99,267)(100,268)(101,269)(102,270)(103,271)(104,272)(105,273)(106,274)(107,275)(108,276)(109,277)(110,278)(111,279)(112,280)(113,400)(114,401)(115,402)(116,403)(117,404)(118,405)(119,406)(120,393)(121,394)(122,395)(123,396)(124,397)(125,398)(126,399)(127,414)(128,415)(129,416)(130,417)(131,418)(132,419)(133,420)(134,407)(135,408)(136,409)(137,410)(138,411)(139,412)(140,413)(141,428)(142,429)(143,430)(144,431)(145,432)(146,433)(147,434)(148,421)(149,422)(150,423)(151,424)(152,425)(153,426)(154,427)(155,442)(156,443)(157,444)(158,445)(159,446)(160,447)(161,448)(162,435)(163,436)(164,437)(165,438)(166,439)(167,440)(168,441)(169,344)(170,345)(171,346)(172,347)(173,348)(174,349)(175,350)(176,337)(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,358)(184,359)(185,360)(186,361)(187,362)(188,363)(189,364)(190,351)(191,352)(192,353)(193,354)(194,355)(195,356)(196,357)(197,372)(198,373)(199,374)(200,375)(201,376)(202,377)(203,378)(204,365)(205,366)(206,367)(207,368)(208,369)(209,370)(210,371)(211,386)(212,387)(213,388)(214,389)(215,390)(216,391)(217,392)(218,379)(219,380)(220,381)(221,382)(222,383)(223,384)(224,385);;
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*s0*s1*s0*s1*s0*s1, 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(450)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)( 57, 85)( 58, 91)( 59, 90)( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 99)( 72,105)( 73,104)( 74,103)( 75,102)( 76,101)( 77,100)( 78,106)( 79,112)( 80,111)( 81,110)( 82,109)( 83,108)( 84,107)(113,127)(114,133)(115,132)(116,131)(117,130)(118,129)(119,128)(120,134)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(141,155)(142,161)(143,160)(144,159)(145,158)(146,157)(147,156)(148,162)(149,168)(150,167)(151,166)(152,165)(153,164)(154,163)(169,211)(170,217)(171,216)(172,215)(173,214)(174,213)(175,212)(176,218)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)(183,197)(184,203)(185,202)(186,201)(187,200)(188,199)(189,198)(190,204)(191,210)(192,209)(193,208)(194,207)(195,206)(196,205)(225,253)(226,259)(227,258)(228,257)(229,256)(230,255)(231,254)(232,260)(233,266)(234,265)(235,264)(236,263)(237,262)(238,261)(239,267)(240,273)(241,272)(242,271)(243,270)(244,269)(245,268)(246,274)(247,280)(248,279)(249,278)(250,277)(251,276)(252,275)(282,287)(283,286)(284,285)(289,294)(290,293)(291,292)(296,301)(297,300)(298,299)(303,308)(304,307)(305,306)(310,315)(311,314)(312,313)(317,322)(318,321)(319,320)(324,329)(325,328)(326,327)(331,336)(332,335)(333,334)(337,379)(338,385)(339,384)(340,383)(341,382)(342,381)(343,380)(344,386)(345,392)(346,391)(347,390)(348,389)(349,388)(350,387)(351,365)(352,371)(353,370)(354,369)(355,368)(356,367)(357,366)(358,372)(359,378)(360,377)(361,376)(362,375)(363,374)(364,373)(393,407)(394,413)(395,412)(396,411)(397,410)(398,409)(399,408)(400,414)(401,420)(402,419)(403,418)(404,417)(405,416)(406,415)(421,435)(422,441)(423,440)(424,439)(425,438)(426,437)(427,436)(428,442)(429,448)(430,447)(431,446)(432,445)(433,444)(434,443);
s2 := 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);
s3 := Sym(450)!( 1,281)( 2,282)( 3,283)( 4,284)( 5,285)( 6,286)( 7,287)( 8,288)( 9,289)( 10,290)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,296)( 17,297)( 18,298)( 19,299)( 20,300)( 21,301)( 22,302)( 23,303)( 24,304)( 25,305)( 26,306)( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)( 33,313)( 34,314)( 35,315)( 36,316)( 37,317)( 38,318)( 39,319)( 40,320)( 41,321)( 42,322)( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)( 48,328)( 49,329)( 50,330)( 51,331)( 52,332)( 53,333)( 54,334)( 55,335)( 56,336)( 57,225)( 58,226)( 59,227)( 60,228)( 61,229)( 62,230)( 63,231)( 64,232)( 65,233)( 66,234)( 67,235)( 68,236)( 69,237)( 70,238)( 71,239)( 72,240)( 73,241)( 74,242)( 75,243)( 76,244)( 77,245)( 78,246)( 79,247)( 80,248)( 81,249)( 82,250)( 83,251)( 84,252)( 85,253)( 86,254)( 87,255)( 88,256)( 89,257)( 90,258)( 91,259)( 92,260)( 93,261)( 94,262)( 95,263)( 96,264)( 97,265)( 98,266)( 99,267)(100,268)(101,269)(102,270)(103,271)(104,272)(105,273)(106,274)(107,275)(108,276)(109,277)(110,278)(111,279)(112,280)(113,400)(114,401)(115,402)(116,403)(117,404)(118,405)(119,406)(120,393)(121,394)(122,395)(123,396)(124,397)(125,398)(126,399)(127,414)(128,415)(129,416)(130,417)(131,418)(132,419)(133,420)(134,407)(135,408)(136,409)(137,410)(138,411)(139,412)(140,413)(141,428)(142,429)(143,430)(144,431)(145,432)(146,433)(147,434)(148,421)(149,422)(150,423)(151,424)(152,425)(153,426)(154,427)(155,442)(156,443)(157,444)(158,445)(159,446)(160,447)(161,448)(162,435)(163,436)(164,437)(165,438)(166,439)(167,440)(168,441)(169,344)(170,345)(171,346)(172,347)(173,348)(174,349)(175,350)(176,337)(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,358)(184,359)(185,360)(186,361)(187,362)(188,363)(189,364)(190,351)(191,352)(192,353)(193,354)(194,355)(195,356)(196,357)(197,372)(198,373)(199,374)(200,375)(201,376)(202,377)(203,378)(204,365)(205,366)(206,367)(207,368)(208,369)(209,370)(210,371)(211,386)(212,387)(213,388)(214,389)(215,390)(216,391)(217,392)(218,379)(219,380)(220,381)(221,382)(222,383)(223,384)(224,385);
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*s0*s1*s0*s1*s0*s1,
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope