Polytope of Type {2,8,14,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,14,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,1044756)
Rank : 5
Schlafli Type : {2,8,14,4}
Number of vertices, edges, etc : 2, 8, 56, 28, 4
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 : {2,4,14,4}*896, {2,8,14,2}*896
4-fold quotients : {2,2,14,4}*448, {2,4,14,2}*448
7-fold quotients : {2,8,2,4}*256
8-fold quotients : {2,2,14,2}*224
14-fold quotients : {2,4,2,4}*128, {2,8,2,2}*128
16-fold quotients : {2,2,7,2}*112
28-fold quotients : {2,2,2,4}*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 := (1,2);;
s1 := ( 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, 94)( 32, 95)( 33, 96)( 34, 97)
( 35, 98)( 36, 99)( 37,100)( 38, 87)( 39, 88)( 40, 89)( 41, 90)( 42, 91)
( 43, 92)( 44, 93)( 45,108)( 46,109)( 47,110)( 48,111)( 49,112)( 50,113)
( 51,114)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)( 57,106)( 58,107)
(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)(143,206)(144,207)(145,208)(146,209)
(147,210)(148,211)(149,212)(150,199)(151,200)(152,201)(153,202)(154,203)
(155,204)(156,205)(157,220)(158,221)(159,222)(160,223)(161,224)(162,225)
(163,226)(164,213)(165,214)(166,215)(167,216)(168,217)(169,218)(170,219)
(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)(255,318)(256,319)(257,320)(258,321)
(259,322)(260,323)(261,324)(262,311)(263,312)(264,313)(265,314)(266,315)
(267,316)(268,317)(269,332)(270,333)(271,334)(272,335)(273,336)(274,337)
(275,338)(276,325)(277,326)(278,327)(279,328)(280,329)(281,330)(282,331)
(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)(367,430)(368,431)(369,432)(370,433)
(371,434)(372,435)(373,436)(374,423)(375,424)(376,425)(377,426)(378,427)
(379,428)(380,429)(381,444)(382,445)(383,446)(384,447)(385,448)(386,449)
(387,450)(388,437)(389,438)(390,439)(391,440)(392,441)(393,442)(394,443);;
s2 := ( 3,227)( 4,233)( 5,232)( 6,231)( 7,230)( 8,229)( 9,228)( 10,234)
( 11,240)( 12,239)( 13,238)( 14,237)( 15,236)( 16,235)( 17,241)( 18,247)
( 19,246)( 20,245)( 21,244)( 22,243)( 23,242)( 24,248)( 25,254)( 26,253)
( 27,252)( 28,251)( 29,250)( 30,249)( 31,262)( 32,268)( 33,267)( 34,266)
( 35,265)( 36,264)( 37,263)( 38,255)( 39,261)( 40,260)( 41,259)( 42,258)
( 43,257)( 44,256)( 45,276)( 46,282)( 47,281)( 48,280)( 49,279)( 50,278)
( 51,277)( 52,269)( 53,275)( 54,274)( 55,273)( 56,272)( 57,271)( 58,270)
( 59,311)( 60,317)( 61,316)( 62,315)( 63,314)( 64,313)( 65,312)( 66,318)
( 67,324)( 68,323)( 69,322)( 70,321)( 71,320)( 72,319)( 73,325)( 74,331)
( 75,330)( 76,329)( 77,328)( 78,327)( 79,326)( 80,332)( 81,338)( 82,337)
( 83,336)( 84,335)( 85,334)( 86,333)( 87,283)( 88,289)( 89,288)( 90,287)
( 91,286)( 92,285)( 93,284)( 94,290)( 95,296)( 96,295)( 97,294)( 98,293)
( 99,292)(100,291)(101,297)(102,303)(103,302)(104,301)(105,300)(106,299)
(107,298)(108,304)(109,310)(110,309)(111,308)(112,307)(113,306)(114,305)
(115,339)(116,345)(117,344)(118,343)(119,342)(120,341)(121,340)(122,346)
(123,352)(124,351)(125,350)(126,349)(127,348)(128,347)(129,353)(130,359)
(131,358)(132,357)(133,356)(134,355)(135,354)(136,360)(137,366)(138,365)
(139,364)(140,363)(141,362)(142,361)(143,374)(144,380)(145,379)(146,378)
(147,377)(148,376)(149,375)(150,367)(151,373)(152,372)(153,371)(154,370)
(155,369)(156,368)(157,388)(158,394)(159,393)(160,392)(161,391)(162,390)
(163,389)(164,381)(165,387)(166,386)(167,385)(168,384)(169,383)(170,382)
(171,423)(172,429)(173,428)(174,427)(175,426)(176,425)(177,424)(178,430)
(179,436)(180,435)(181,434)(182,433)(183,432)(184,431)(185,437)(186,443)
(187,442)(188,441)(189,440)(190,439)(191,438)(192,444)(193,450)(194,449)
(195,448)(196,447)(197,446)(198,445)(199,395)(200,401)(201,400)(202,399)
(203,398)(204,397)(205,396)(206,402)(207,408)(208,407)(209,406)(210,405)
(211,404)(212,403)(213,409)(214,415)(215,414)(216,413)(217,412)(218,411)
(219,410)(220,416)(221,422)(222,421)(223,420)(224,419)(225,418)(226,417);;
s3 := ( 3, 88)( 4, 87)( 5, 93)( 6, 92)( 7, 91)( 8, 90)( 9, 89)( 10, 95)
( 11, 94)( 12,100)( 13, 99)( 14, 98)( 15, 97)( 16, 96)( 17,102)( 18,101)
( 19,107)( 20,106)( 21,105)( 22,104)( 23,103)( 24,109)( 25,108)( 26,114)
( 27,113)( 28,112)( 29,111)( 30,110)( 31, 67)( 32, 66)( 33, 72)( 34, 71)
( 35, 70)( 36, 69)( 37, 68)( 38, 60)( 39, 59)( 40, 65)( 41, 64)( 42, 63)
( 43, 62)( 44, 61)( 45, 81)( 46, 80)( 47, 86)( 48, 85)( 49, 84)( 50, 83)
( 51, 82)( 52, 74)( 53, 73)( 54, 79)( 55, 78)( 56, 77)( 57, 76)( 58, 75)
(115,214)(116,213)(117,219)(118,218)(119,217)(120,216)(121,215)(122,221)
(123,220)(124,226)(125,225)(126,224)(127,223)(128,222)(129,200)(130,199)
(131,205)(132,204)(133,203)(134,202)(135,201)(136,207)(137,206)(138,212)
(139,211)(140,210)(141,209)(142,208)(143,193)(144,192)(145,198)(146,197)
(147,196)(148,195)(149,194)(150,186)(151,185)(152,191)(153,190)(154,189)
(155,188)(156,187)(157,179)(158,178)(159,184)(160,183)(161,182)(162,181)
(163,180)(164,172)(165,171)(166,177)(167,176)(168,175)(169,174)(170,173)
(227,284)(228,283)(229,289)(230,288)(231,287)(232,286)(233,285)(234,291)
(235,290)(236,296)(237,295)(238,294)(239,293)(240,292)(241,298)(242,297)
(243,303)(244,302)(245,301)(246,300)(247,299)(248,305)(249,304)(250,310)
(251,309)(252,308)(253,307)(254,306)(255,312)(256,311)(257,317)(258,316)
(259,315)(260,314)(261,313)(262,319)(263,318)(264,324)(265,323)(266,322)
(267,321)(268,320)(269,326)(270,325)(271,331)(272,330)(273,329)(274,328)
(275,327)(276,333)(277,332)(278,338)(279,337)(280,336)(281,335)(282,334)
(339,410)(340,409)(341,415)(342,414)(343,413)(344,412)(345,411)(346,417)
(347,416)(348,422)(349,421)(350,420)(351,419)(352,418)(353,396)(354,395)
(355,401)(356,400)(357,399)(358,398)(359,397)(360,403)(361,402)(362,408)
(363,407)(364,406)(365,405)(366,404)(367,438)(368,437)(369,443)(370,442)
(371,441)(372,440)(373,439)(374,445)(375,444)(376,450)(377,449)(378,448)
(379,447)(380,446)(381,424)(382,423)(383,429)(384,428)(385,427)(386,426)
(387,425)(388,431)(389,430)(390,436)(391,435)(392,434)(393,433)(394,432);;
s4 := ( 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)(113,225)(114,226)
(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)(337,449)(338,450);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!(1,2);
s1 := Sym(450)!( 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, 94)( 32, 95)( 33, 96)
( 34, 97)( 35, 98)( 36, 99)( 37,100)( 38, 87)( 39, 88)( 40, 89)( 41, 90)
( 42, 91)( 43, 92)( 44, 93)( 45,108)( 46,109)( 47,110)( 48,111)( 49,112)
( 50,113)( 51,114)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)( 57,106)
( 58,107)(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)(143,206)(144,207)(145,208)
(146,209)(147,210)(148,211)(149,212)(150,199)(151,200)(152,201)(153,202)
(154,203)(155,204)(156,205)(157,220)(158,221)(159,222)(160,223)(161,224)
(162,225)(163,226)(164,213)(165,214)(166,215)(167,216)(168,217)(169,218)
(170,219)(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)(255,318)(256,319)(257,320)
(258,321)(259,322)(260,323)(261,324)(262,311)(263,312)(264,313)(265,314)
(266,315)(267,316)(268,317)(269,332)(270,333)(271,334)(272,335)(273,336)
(274,337)(275,338)(276,325)(277,326)(278,327)(279,328)(280,329)(281,330)
(282,331)(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)(367,430)(368,431)(369,432)
(370,433)(371,434)(372,435)(373,436)(374,423)(375,424)(376,425)(377,426)
(378,427)(379,428)(380,429)(381,444)(382,445)(383,446)(384,447)(385,448)
(386,449)(387,450)(388,437)(389,438)(390,439)(391,440)(392,441)(393,442)
(394,443);
s2 := Sym(450)!( 3,227)( 4,233)( 5,232)( 6,231)( 7,230)( 8,229)( 9,228)
( 10,234)( 11,240)( 12,239)( 13,238)( 14,237)( 15,236)( 16,235)( 17,241)
( 18,247)( 19,246)( 20,245)( 21,244)( 22,243)( 23,242)( 24,248)( 25,254)
( 26,253)( 27,252)( 28,251)( 29,250)( 30,249)( 31,262)( 32,268)( 33,267)
( 34,266)( 35,265)( 36,264)( 37,263)( 38,255)( 39,261)( 40,260)( 41,259)
( 42,258)( 43,257)( 44,256)( 45,276)( 46,282)( 47,281)( 48,280)( 49,279)
( 50,278)( 51,277)( 52,269)( 53,275)( 54,274)( 55,273)( 56,272)( 57,271)
( 58,270)( 59,311)( 60,317)( 61,316)( 62,315)( 63,314)( 64,313)( 65,312)
( 66,318)( 67,324)( 68,323)( 69,322)( 70,321)( 71,320)( 72,319)( 73,325)
( 74,331)( 75,330)( 76,329)( 77,328)( 78,327)( 79,326)( 80,332)( 81,338)
( 82,337)( 83,336)( 84,335)( 85,334)( 86,333)( 87,283)( 88,289)( 89,288)
( 90,287)( 91,286)( 92,285)( 93,284)( 94,290)( 95,296)( 96,295)( 97,294)
( 98,293)( 99,292)(100,291)(101,297)(102,303)(103,302)(104,301)(105,300)
(106,299)(107,298)(108,304)(109,310)(110,309)(111,308)(112,307)(113,306)
(114,305)(115,339)(116,345)(117,344)(118,343)(119,342)(120,341)(121,340)
(122,346)(123,352)(124,351)(125,350)(126,349)(127,348)(128,347)(129,353)
(130,359)(131,358)(132,357)(133,356)(134,355)(135,354)(136,360)(137,366)
(138,365)(139,364)(140,363)(141,362)(142,361)(143,374)(144,380)(145,379)
(146,378)(147,377)(148,376)(149,375)(150,367)(151,373)(152,372)(153,371)
(154,370)(155,369)(156,368)(157,388)(158,394)(159,393)(160,392)(161,391)
(162,390)(163,389)(164,381)(165,387)(166,386)(167,385)(168,384)(169,383)
(170,382)(171,423)(172,429)(173,428)(174,427)(175,426)(176,425)(177,424)
(178,430)(179,436)(180,435)(181,434)(182,433)(183,432)(184,431)(185,437)
(186,443)(187,442)(188,441)(189,440)(190,439)(191,438)(192,444)(193,450)
(194,449)(195,448)(196,447)(197,446)(198,445)(199,395)(200,401)(201,400)
(202,399)(203,398)(204,397)(205,396)(206,402)(207,408)(208,407)(209,406)
(210,405)(211,404)(212,403)(213,409)(214,415)(215,414)(216,413)(217,412)
(218,411)(219,410)(220,416)(221,422)(222,421)(223,420)(224,419)(225,418)
(226,417);
s3 := Sym(450)!( 3, 88)( 4, 87)( 5, 93)( 6, 92)( 7, 91)( 8, 90)( 9, 89)
( 10, 95)( 11, 94)( 12,100)( 13, 99)( 14, 98)( 15, 97)( 16, 96)( 17,102)
( 18,101)( 19,107)( 20,106)( 21,105)( 22,104)( 23,103)( 24,109)( 25,108)
( 26,114)( 27,113)( 28,112)( 29,111)( 30,110)( 31, 67)( 32, 66)( 33, 72)
( 34, 71)( 35, 70)( 36, 69)( 37, 68)( 38, 60)( 39, 59)( 40, 65)( 41, 64)
( 42, 63)( 43, 62)( 44, 61)( 45, 81)( 46, 80)( 47, 86)( 48, 85)( 49, 84)
( 50, 83)( 51, 82)( 52, 74)( 53, 73)( 54, 79)( 55, 78)( 56, 77)( 57, 76)
( 58, 75)(115,214)(116,213)(117,219)(118,218)(119,217)(120,216)(121,215)
(122,221)(123,220)(124,226)(125,225)(126,224)(127,223)(128,222)(129,200)
(130,199)(131,205)(132,204)(133,203)(134,202)(135,201)(136,207)(137,206)
(138,212)(139,211)(140,210)(141,209)(142,208)(143,193)(144,192)(145,198)
(146,197)(147,196)(148,195)(149,194)(150,186)(151,185)(152,191)(153,190)
(154,189)(155,188)(156,187)(157,179)(158,178)(159,184)(160,183)(161,182)
(162,181)(163,180)(164,172)(165,171)(166,177)(167,176)(168,175)(169,174)
(170,173)(227,284)(228,283)(229,289)(230,288)(231,287)(232,286)(233,285)
(234,291)(235,290)(236,296)(237,295)(238,294)(239,293)(240,292)(241,298)
(242,297)(243,303)(244,302)(245,301)(246,300)(247,299)(248,305)(249,304)
(250,310)(251,309)(252,308)(253,307)(254,306)(255,312)(256,311)(257,317)
(258,316)(259,315)(260,314)(261,313)(262,319)(263,318)(264,324)(265,323)
(266,322)(267,321)(268,320)(269,326)(270,325)(271,331)(272,330)(273,329)
(274,328)(275,327)(276,333)(277,332)(278,338)(279,337)(280,336)(281,335)
(282,334)(339,410)(340,409)(341,415)(342,414)(343,413)(344,412)(345,411)
(346,417)(347,416)(348,422)(349,421)(350,420)(351,419)(352,418)(353,396)
(354,395)(355,401)(356,400)(357,399)(358,398)(359,397)(360,403)(361,402)
(362,408)(363,407)(364,406)(365,405)(366,404)(367,438)(368,437)(369,443)
(370,442)(371,441)(372,440)(373,439)(374,445)(375,444)(376,450)(377,449)
(378,448)(379,447)(380,446)(381,424)(382,423)(383,429)(384,428)(385,427)
(386,426)(387,425)(388,431)(389,430)(390,436)(391,435)(392,434)(393,433)
(394,432);
s4 := Sym(450)!( 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)(113,225)
(114,226)(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)(337,449)
(338,450);
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*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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