Polytope of Type {2,28,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,4,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,336974)
Rank : 5
Schlafli Type : {2,28,4,4}
Number of vertices, edges, etc : 2, 28, 56, 8, 4
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, {2,28,2,4}*896, {2,14,4,4}*896
4-fold quotients : {2,28,2,2}*448, {2,14,2,4}*448, {2,14,4,2}*448
7-fold quotients : {2,4,4,4}*256
8-fold quotients : {2,7,2,4}*224, {2,14,2,2}*224
14-fold quotients : {2,2,4,4}*128, {2,4,4,2}*128, {2,4,2,4}*128
16-fold quotients : {2,7,2,2}*112
28-fold quotients : {2,2,2,4}*64, {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 := (1,2);;
s1 := ( 3,283)( 4,289)( 5,288)( 6,287)( 7,286)( 8,285)( 9,284)( 10,290)
( 11,296)( 12,295)( 13,294)( 14,293)( 15,292)( 16,291)( 17,297)( 18,303)
( 19,302)( 20,301)( 21,300)( 22,299)( 23,298)( 24,304)( 25,310)( 26,309)
( 27,308)( 28,307)( 29,306)( 30,305)( 31,311)( 32,317)( 33,316)( 34,315)
( 35,314)( 36,313)( 37,312)( 38,318)( 39,324)( 40,323)( 41,322)( 42,321)
( 43,320)( 44,319)( 45,325)( 46,331)( 47,330)( 48,329)( 49,328)( 50,327)
( 51,326)( 52,332)( 53,338)( 54,337)( 55,336)( 56,335)( 57,334)( 58,333)
( 59,227)( 60,233)( 61,232)( 62,231)( 63,230)( 64,229)( 65,228)( 66,234)
( 67,240)( 68,239)( 69,238)( 70,237)( 71,236)( 72,235)( 73,241)( 74,247)
( 75,246)( 76,245)( 77,244)( 78,243)( 79,242)( 80,248)( 81,254)( 82,253)
( 83,252)( 84,251)( 85,250)( 86,249)( 87,255)( 88,261)( 89,260)( 90,259)
( 91,258)( 92,257)( 93,256)( 94,262)( 95,268)( 96,267)( 97,266)( 98,265)
( 99,264)(100,263)(101,269)(102,275)(103,274)(104,273)(105,272)(106,271)
(107,270)(108,276)(109,282)(110,281)(111,280)(112,279)(113,278)(114,277)
(115,402)(116,408)(117,407)(118,406)(119,405)(120,404)(121,403)(122,395)
(123,401)(124,400)(125,399)(126,398)(127,397)(128,396)(129,416)(130,422)
(131,421)(132,420)(133,419)(134,418)(135,417)(136,409)(137,415)(138,414)
(139,413)(140,412)(141,411)(142,410)(143,430)(144,436)(145,435)(146,434)
(147,433)(148,432)(149,431)(150,423)(151,429)(152,428)(153,427)(154,426)
(155,425)(156,424)(157,444)(158,450)(159,449)(160,448)(161,447)(162,446)
(163,445)(164,437)(165,443)(166,442)(167,441)(168,440)(169,439)(170,438)
(171,346)(172,352)(173,351)(174,350)(175,349)(176,348)(177,347)(178,339)
(179,345)(180,344)(181,343)(182,342)(183,341)(184,340)(185,360)(186,366)
(187,365)(188,364)(189,363)(190,362)(191,361)(192,353)(193,359)(194,358)
(195,357)(196,356)(197,355)(198,354)(199,374)(200,380)(201,379)(202,378)
(203,377)(204,376)(205,375)(206,367)(207,373)(208,372)(209,371)(210,370)
(211,369)(212,368)(213,388)(214,394)(215,393)(216,392)(217,391)(218,390)
(219,389)(220,381)(221,387)(222,386)(223,385)(224,384)(225,383)(226,382);;
s2 := ( 3,116)( 4,115)( 5,121)( 6,120)( 7,119)( 8,118)( 9,117)( 10,123)
( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,130)( 18,129)
( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,137)( 25,136)( 26,142)
( 27,141)( 28,140)( 29,139)( 30,138)( 31,144)( 32,143)( 33,149)( 34,148)
( 35,147)( 36,146)( 37,145)( 38,151)( 39,150)( 40,156)( 41,155)( 42,154)
( 43,153)( 44,152)( 45,158)( 46,157)( 47,163)( 48,162)( 49,161)( 50,160)
( 51,159)( 52,165)( 53,164)( 54,170)( 55,169)( 56,168)( 57,167)( 58,166)
( 59,172)( 60,171)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)( 66,179)
( 67,178)( 68,184)( 69,183)( 70,182)( 71,181)( 72,180)( 73,186)( 74,185)
( 75,191)( 76,190)( 77,189)( 78,188)( 79,187)( 80,193)( 81,192)( 82,198)
( 83,197)( 84,196)( 85,195)( 86,194)( 87,200)( 88,199)( 89,205)( 90,204)
( 91,203)( 92,202)( 93,201)( 94,207)( 95,206)( 96,212)( 97,211)( 98,210)
( 99,209)(100,208)(101,214)(102,213)(103,219)(104,218)(105,217)(106,216)
(107,215)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)(114,222)
(227,340)(228,339)(229,345)(230,344)(231,343)(232,342)(233,341)(234,347)
(235,346)(236,352)(237,351)(238,350)(239,349)(240,348)(241,354)(242,353)
(243,359)(244,358)(245,357)(246,356)(247,355)(248,361)(249,360)(250,366)
(251,365)(252,364)(253,363)(254,362)(255,368)(256,367)(257,373)(258,372)
(259,371)(260,370)(261,369)(262,375)(263,374)(264,380)(265,379)(266,378)
(267,377)(268,376)(269,382)(270,381)(271,387)(272,386)(273,385)(274,384)
(275,383)(276,389)(277,388)(278,394)(279,393)(280,392)(281,391)(282,390)
(283,396)(284,395)(285,401)(286,400)(287,399)(288,398)(289,397)(290,403)
(291,402)(292,408)(293,407)(294,406)(295,405)(296,404)(297,410)(298,409)
(299,415)(300,414)(301,413)(302,412)(303,411)(304,417)(305,416)(306,422)
(307,421)(308,420)(309,419)(310,418)(311,424)(312,423)(313,429)(314,428)
(315,427)(316,426)(317,425)(318,431)(319,430)(320,436)(321,435)(322,434)
(323,433)(324,432)(325,438)(326,437)(327,443)(328,442)(329,441)(330,440)
(331,439)(332,445)(333,444)(334,450)(335,449)(336,448)(337,447)(338,446);;
s3 := ( 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)( 85,113)( 86,114)(115,129)(116,130)(117,131)(118,132)
(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)
(127,141)(128,142)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)
(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(155,169)(156,170)
(171,213)(172,214)(173,215)(174,216)(175,217)(176,218)(177,219)(178,220)
(179,221)(180,222)(181,223)(182,224)(183,225)(184,226)(185,199)(186,200)
(187,201)(188,202)(189,203)(190,204)(191,205)(192,206)(193,207)(194,208)
(195,209)(196,210)(197,211)(198,212)(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)(253,281)(254,282)
(339,381)(340,382)(341,383)(342,384)(343,385)(344,386)(345,387)(346,388)
(347,389)(348,390)(349,391)(350,392)(351,393)(352,394)(353,367)(354,368)
(355,369)(356,370)(357,371)(358,372)(359,373)(360,374)(361,375)(362,376)
(363,377)(364,378)(365,379)(366,380)(395,409)(396,410)(397,411)(398,412)
(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)(406,420)
(407,421)(408,422)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)
(429,443)(430,444)(431,445)(432,446)(433,447)(434,448)(435,449)(436,450);;
s4 := ( 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)( 57,113)( 58,114)
(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)(169,225)(170,226)
(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)(281,337)(282,338)
(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)(393,449)(394,450);;
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*s2*s3*s2*s3*s2*s3,
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*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)!(1,2);
s1 := Sym(450)!( 3,283)( 4,289)( 5,288)( 6,287)( 7,286)( 8,285)( 9,284)
( 10,290)( 11,296)( 12,295)( 13,294)( 14,293)( 15,292)( 16,291)( 17,297)
( 18,303)( 19,302)( 20,301)( 21,300)( 22,299)( 23,298)( 24,304)( 25,310)
( 26,309)( 27,308)( 28,307)( 29,306)( 30,305)( 31,311)( 32,317)( 33,316)
( 34,315)( 35,314)( 36,313)( 37,312)( 38,318)( 39,324)( 40,323)( 41,322)
( 42,321)( 43,320)( 44,319)( 45,325)( 46,331)( 47,330)( 48,329)( 49,328)
( 50,327)( 51,326)( 52,332)( 53,338)( 54,337)( 55,336)( 56,335)( 57,334)
( 58,333)( 59,227)( 60,233)( 61,232)( 62,231)( 63,230)( 64,229)( 65,228)
( 66,234)( 67,240)( 68,239)( 69,238)( 70,237)( 71,236)( 72,235)( 73,241)
( 74,247)( 75,246)( 76,245)( 77,244)( 78,243)( 79,242)( 80,248)( 81,254)
( 82,253)( 83,252)( 84,251)( 85,250)( 86,249)( 87,255)( 88,261)( 89,260)
( 90,259)( 91,258)( 92,257)( 93,256)( 94,262)( 95,268)( 96,267)( 97,266)
( 98,265)( 99,264)(100,263)(101,269)(102,275)(103,274)(104,273)(105,272)
(106,271)(107,270)(108,276)(109,282)(110,281)(111,280)(112,279)(113,278)
(114,277)(115,402)(116,408)(117,407)(118,406)(119,405)(120,404)(121,403)
(122,395)(123,401)(124,400)(125,399)(126,398)(127,397)(128,396)(129,416)
(130,422)(131,421)(132,420)(133,419)(134,418)(135,417)(136,409)(137,415)
(138,414)(139,413)(140,412)(141,411)(142,410)(143,430)(144,436)(145,435)
(146,434)(147,433)(148,432)(149,431)(150,423)(151,429)(152,428)(153,427)
(154,426)(155,425)(156,424)(157,444)(158,450)(159,449)(160,448)(161,447)
(162,446)(163,445)(164,437)(165,443)(166,442)(167,441)(168,440)(169,439)
(170,438)(171,346)(172,352)(173,351)(174,350)(175,349)(176,348)(177,347)
(178,339)(179,345)(180,344)(181,343)(182,342)(183,341)(184,340)(185,360)
(186,366)(187,365)(188,364)(189,363)(190,362)(191,361)(192,353)(193,359)
(194,358)(195,357)(196,356)(197,355)(198,354)(199,374)(200,380)(201,379)
(202,378)(203,377)(204,376)(205,375)(206,367)(207,373)(208,372)(209,371)
(210,370)(211,369)(212,368)(213,388)(214,394)(215,393)(216,392)(217,391)
(218,390)(219,389)(220,381)(221,387)(222,386)(223,385)(224,384)(225,383)
(226,382);
s2 := Sym(450)!( 3,116)( 4,115)( 5,121)( 6,120)( 7,119)( 8,118)( 9,117)
( 10,123)( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,130)
( 18,129)( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,137)( 25,136)
( 26,142)( 27,141)( 28,140)( 29,139)( 30,138)( 31,144)( 32,143)( 33,149)
( 34,148)( 35,147)( 36,146)( 37,145)( 38,151)( 39,150)( 40,156)( 41,155)
( 42,154)( 43,153)( 44,152)( 45,158)( 46,157)( 47,163)( 48,162)( 49,161)
( 50,160)( 51,159)( 52,165)( 53,164)( 54,170)( 55,169)( 56,168)( 57,167)
( 58,166)( 59,172)( 60,171)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)
( 66,179)( 67,178)( 68,184)( 69,183)( 70,182)( 71,181)( 72,180)( 73,186)
( 74,185)( 75,191)( 76,190)( 77,189)( 78,188)( 79,187)( 80,193)( 81,192)
( 82,198)( 83,197)( 84,196)( 85,195)( 86,194)( 87,200)( 88,199)( 89,205)
( 90,204)( 91,203)( 92,202)( 93,201)( 94,207)( 95,206)( 96,212)( 97,211)
( 98,210)( 99,209)(100,208)(101,214)(102,213)(103,219)(104,218)(105,217)
(106,216)(107,215)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)
(114,222)(227,340)(228,339)(229,345)(230,344)(231,343)(232,342)(233,341)
(234,347)(235,346)(236,352)(237,351)(238,350)(239,349)(240,348)(241,354)
(242,353)(243,359)(244,358)(245,357)(246,356)(247,355)(248,361)(249,360)
(250,366)(251,365)(252,364)(253,363)(254,362)(255,368)(256,367)(257,373)
(258,372)(259,371)(260,370)(261,369)(262,375)(263,374)(264,380)(265,379)
(266,378)(267,377)(268,376)(269,382)(270,381)(271,387)(272,386)(273,385)
(274,384)(275,383)(276,389)(277,388)(278,394)(279,393)(280,392)(281,391)
(282,390)(283,396)(284,395)(285,401)(286,400)(287,399)(288,398)(289,397)
(290,403)(291,402)(292,408)(293,407)(294,406)(295,405)(296,404)(297,410)
(298,409)(299,415)(300,414)(301,413)(302,412)(303,411)(304,417)(305,416)
(306,422)(307,421)(308,420)(309,419)(310,418)(311,424)(312,423)(313,429)
(314,428)(315,427)(316,426)(317,425)(318,431)(319,430)(320,436)(321,435)
(322,434)(323,433)(324,432)(325,438)(326,437)(327,443)(328,442)(329,441)
(330,440)(331,439)(332,445)(333,444)(334,450)(335,449)(336,448)(337,447)
(338,446);
s3 := Sym(450)!( 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)( 85,113)( 86,114)(115,129)(116,130)(117,131)
(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)
(126,140)(127,141)(128,142)(143,157)(144,158)(145,159)(146,160)(147,161)
(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(155,169)
(156,170)(171,213)(172,214)(173,215)(174,216)(175,217)(176,218)(177,219)
(178,220)(179,221)(180,222)(181,223)(182,224)(183,225)(184,226)(185,199)
(186,200)(187,201)(188,202)(189,203)(190,204)(191,205)(192,206)(193,207)
(194,208)(195,209)(196,210)(197,211)(198,212)(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)(253,281)
(254,282)(339,381)(340,382)(341,383)(342,384)(343,385)(344,386)(345,387)
(346,388)(347,389)(348,390)(349,391)(350,392)(351,393)(352,394)(353,367)
(354,368)(355,369)(356,370)(357,371)(358,372)(359,373)(360,374)(361,375)
(362,376)(363,377)(364,378)(365,379)(366,380)(395,409)(396,410)(397,411)
(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)
(406,420)(407,421)(408,422)(423,437)(424,438)(425,439)(426,440)(427,441)
(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448)(435,449)
(436,450);
s4 := 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, 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)( 57,113)
( 58,114)(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)(169,225)
(170,226)(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)(281,337)
(282,338)(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)(393,449)
(394,450);
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*s2*s3*s2*s3*s2*s3, 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*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