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