Polytope of Type {2,14,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,4,8}*1792b
if this polytope has a name.
Group : SmallGroup(1792,1036167)
Rank : 5
Schlafli Type : {2,14,4,8}
Number of vertices, edges, etc : 2, 14, 28, 16, 8
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 : {2,14,4,4}*896
4-fold quotients : {2,14,2,4}*448, {2,14,4,2}*448
7-fold quotients : {2,2,4,8}*256b
8-fold quotients : {2,7,2,4}*224, {2,14,2,2}*224
14-fold quotients : {2,2,4,4}*128
16-fold quotients : {2,7,2,2}*112
28-fold quotients : {2,2,2,4}*64, {2,2,4,2}*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, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)( 10, 66)
( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 73)( 18, 79)
( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 74)( 24, 80)( 25, 86)( 26, 85)
( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31, 87)( 32, 93)( 33, 92)( 34, 91)
( 35, 90)( 36, 89)( 37, 88)( 38, 94)( 39,100)( 40, 99)( 41, 98)( 42, 97)
( 43, 96)( 44, 95)( 45,101)( 46,107)( 47,106)( 48,105)( 49,104)( 50,103)
( 51,102)( 52,108)( 53,114)( 54,113)( 55,112)( 56,111)( 57,110)( 58,109)
(115,171)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)(122,178)
(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,185)(130,191)
(131,190)(132,189)(133,188)(134,187)(135,186)(136,192)(137,198)(138,197)
(139,196)(140,195)(141,194)(142,193)(143,199)(144,205)(145,204)(146,203)
(147,202)(148,201)(149,200)(150,206)(151,212)(152,211)(153,210)(154,209)
(155,208)(156,207)(157,213)(158,219)(159,218)(160,217)(161,216)(162,215)
(163,214)(164,220)(165,226)(166,225)(167,224)(168,223)(169,222)(170,221)
(227,283)(228,289)(229,288)(230,287)(231,286)(232,285)(233,284)(234,290)
(235,296)(236,295)(237,294)(238,293)(239,292)(240,291)(241,297)(242,303)
(243,302)(244,301)(245,300)(246,299)(247,298)(248,304)(249,310)(250,309)
(251,308)(252,307)(253,306)(254,305)(255,311)(256,317)(257,316)(258,315)
(259,314)(260,313)(261,312)(262,318)(263,324)(264,323)(265,322)(266,321)
(267,320)(268,319)(269,325)(270,331)(271,330)(272,329)(273,328)(274,327)
(275,326)(276,332)(277,338)(278,337)(279,336)(280,335)(281,334)(282,333)
(339,395)(340,401)(341,400)(342,399)(343,398)(344,397)(345,396)(346,402)
(347,408)(348,407)(349,406)(350,405)(351,404)(352,403)(353,409)(354,415)
(355,414)(356,413)(357,412)(358,411)(359,410)(360,416)(361,422)(362,421)
(363,420)(364,419)(365,418)(366,417)(367,423)(368,429)(369,428)(370,427)
(371,426)(372,425)(373,424)(374,430)(375,436)(376,435)(377,434)(378,433)
(379,432)(380,431)(381,437)(382,443)(383,442)(384,441)(385,440)(386,439)
(387,438)(388,444)(389,450)(390,449)(391,448)(392,447)(393,446)(394,445);;
s2 := ( 3,172)( 4,171)( 5,177)( 6,176)( 7,175)( 8,174)( 9,173)( 10,179)
( 11,178)( 12,184)( 13,183)( 14,182)( 15,181)( 16,180)( 17,186)( 18,185)
( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)( 24,193)( 25,192)( 26,198)
( 27,197)( 28,196)( 29,195)( 30,194)( 31,207)( 32,206)( 33,212)( 34,211)
( 35,210)( 36,209)( 37,208)( 38,200)( 39,199)( 40,205)( 41,204)( 42,203)
( 43,202)( 44,201)( 45,221)( 46,220)( 47,226)( 48,225)( 49,224)( 50,223)
( 51,222)( 52,214)( 53,213)( 54,219)( 55,218)( 56,217)( 57,216)( 58,215)
( 59,116)( 60,115)( 61,121)( 62,120)( 63,119)( 64,118)( 65,117)( 66,123)
( 67,122)( 68,128)( 69,127)( 70,126)( 71,125)( 72,124)( 73,130)( 74,129)
( 75,135)( 76,134)( 77,133)( 78,132)( 79,131)( 80,137)( 81,136)( 82,142)
( 83,141)( 84,140)( 85,139)( 86,138)( 87,151)( 88,150)( 89,156)( 90,155)
( 91,154)( 92,153)( 93,152)( 94,144)( 95,143)( 96,149)( 97,148)( 98,147)
( 99,146)(100,145)(101,165)(102,164)(103,170)(104,169)(105,168)(106,167)
(107,166)(108,158)(109,157)(110,163)(111,162)(112,161)(113,160)(114,159)
(227,396)(228,395)(229,401)(230,400)(231,399)(232,398)(233,397)(234,403)
(235,402)(236,408)(237,407)(238,406)(239,405)(240,404)(241,410)(242,409)
(243,415)(244,414)(245,413)(246,412)(247,411)(248,417)(249,416)(250,422)
(251,421)(252,420)(253,419)(254,418)(255,431)(256,430)(257,436)(258,435)
(259,434)(260,433)(261,432)(262,424)(263,423)(264,429)(265,428)(266,427)
(267,426)(268,425)(269,445)(270,444)(271,450)(272,449)(273,448)(274,447)
(275,446)(276,438)(277,437)(278,443)(279,442)(280,441)(281,440)(282,439)
(283,340)(284,339)(285,345)(286,344)(287,343)(288,342)(289,341)(290,347)
(291,346)(292,352)(293,351)(294,350)(295,349)(296,348)(297,354)(298,353)
(299,359)(300,358)(301,357)(302,356)(303,355)(304,361)(305,360)(306,366)
(307,365)(308,364)(309,363)(310,362)(311,375)(312,374)(313,380)(314,379)
(315,378)(316,377)(317,376)(318,368)(319,367)(320,373)(321,372)(322,371)
(323,370)(324,369)(325,389)(326,388)(327,394)(328,393)(329,392)(330,391)
(331,390)(332,382)(333,381)(334,387)(335,386)(336,385)(337,384)(338,383);;
s3 := ( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)( 45, 52)
( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 87, 94)( 88, 95)
( 89, 96)( 90, 97)( 91, 98)( 92, 99)( 93,100)(101,108)(102,109)(103,110)
(104,111)(105,112)(106,113)(107,114)(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)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)
(149,170)(150,157)(151,158)(152,159)(153,160)(154,161)(155,162)(156,163)
(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)
(179,193)(180,194)(181,195)(182,196)(183,197)(184,198)(199,220)(200,221)
(201,222)(202,223)(203,224)(204,225)(205,226)(206,213)(207,214)(208,215)
(209,216)(210,217)(211,218)(212,219)(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)
(283,311)(284,312)(285,313)(286,314)(287,315)(288,316)(289,317)(290,318)
(291,319)(292,320)(293,321)(294,322)(295,323)(296,324)(297,325)(298,326)
(299,327)(300,328)(301,329)(302,330)(303,331)(304,332)(305,333)(306,334)
(307,335)(308,336)(309,337)(310,338)(339,388)(340,389)(341,390)(342,391)
(343,392)(344,393)(345,394)(346,381)(347,382)(348,383)(349,384)(350,385)
(351,386)(352,387)(353,374)(354,375)(355,376)(356,377)(357,378)(358,379)
(359,380)(360,367)(361,368)(362,369)(363,370)(364,371)(365,372)(366,373)
(395,444)(396,445)(397,446)(398,447)(399,448)(400,449)(401,450)(402,437)
(403,438)(404,439)(405,440)(406,441)(407,442)(408,443)(409,430)(410,431)
(411,432)(412,433)(413,434)(414,435)(415,436)(416,423)(417,424)(418,425)
(419,426)(420,427)(421,428)(422,429);;
s4 := ( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)( 8,232)( 9,233)( 10,234)
( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,248)( 18,249)
( 19,250)( 20,251)( 21,252)( 22,253)( 23,254)( 24,241)( 25,242)( 26,243)
( 27,244)( 28,245)( 29,246)( 30,247)( 31,262)( 32,263)( 33,264)( 34,265)
( 35,266)( 36,267)( 37,268)( 38,255)( 39,256)( 40,257)( 41,258)( 42,259)
( 43,260)( 44,261)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)( 50,274)
( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,281)( 58,282)
( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)( 64,288)( 65,289)( 66,290)
( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)( 72,296)( 73,304)( 74,305)
( 75,306)( 76,307)( 77,308)( 78,309)( 79,310)( 80,297)( 81,298)( 82,299)
( 83,300)( 84,301)( 85,302)( 86,303)( 87,318)( 88,319)( 89,320)( 90,321)
( 91,322)( 92,323)( 93,324)( 94,311)( 95,312)( 96,313)( 97,314)( 98,315)
( 99,316)(100,317)(101,325)(102,326)(103,327)(104,328)(105,329)(106,330)
(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)(113,337)(114,338)
(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)(122,346)
(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,360)(130,361)
(131,362)(132,363)(133,364)(134,365)(135,366)(136,353)(137,354)(138,355)
(139,356)(140,357)(141,358)(142,359)(143,374)(144,375)(145,376)(146,377)
(147,378)(148,379)(149,380)(150,367)(151,368)(152,369)(153,370)(154,371)
(155,372)(156,373)(157,381)(158,382)(159,383)(160,384)(161,385)(162,386)
(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,393)(170,394)
(171,395)(172,396)(173,397)(174,398)(175,399)(176,400)(177,401)(178,402)
(179,403)(180,404)(181,405)(182,406)(183,407)(184,408)(185,416)(186,417)
(187,418)(188,419)(189,420)(190,421)(191,422)(192,409)(193,410)(194,411)
(195,412)(196,413)(197,414)(198,415)(199,430)(200,431)(201,432)(202,433)
(203,434)(204,435)(205,436)(206,423)(207,424)(208,425)(209,426)(210,427)
(211,428)(212,429)(213,437)(214,438)(215,439)(216,440)(217,441)(218,442)
(219,443)(220,444)(221,445)(222,446)(223,447)(224,448)(225,449)(226,450);;
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,
s4*s2*s3*s4*s3*s4*s2*s3*s4*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(450)!(1,2);
s1 := Sym(450)!( 3, 59)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)
( 10, 66)( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 73)
( 18, 79)( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 74)( 24, 80)( 25, 86)
( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31, 87)( 32, 93)( 33, 92)
( 34, 91)( 35, 90)( 36, 89)( 37, 88)( 38, 94)( 39,100)( 40, 99)( 41, 98)
( 42, 97)( 43, 96)( 44, 95)( 45,101)( 46,107)( 47,106)( 48,105)( 49,104)
( 50,103)( 51,102)( 52,108)( 53,114)( 54,113)( 55,112)( 56,111)( 57,110)
( 58,109)(115,171)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)
(122,178)(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,185)
(130,191)(131,190)(132,189)(133,188)(134,187)(135,186)(136,192)(137,198)
(138,197)(139,196)(140,195)(141,194)(142,193)(143,199)(144,205)(145,204)
(146,203)(147,202)(148,201)(149,200)(150,206)(151,212)(152,211)(153,210)
(154,209)(155,208)(156,207)(157,213)(158,219)(159,218)(160,217)(161,216)
(162,215)(163,214)(164,220)(165,226)(166,225)(167,224)(168,223)(169,222)
(170,221)(227,283)(228,289)(229,288)(230,287)(231,286)(232,285)(233,284)
(234,290)(235,296)(236,295)(237,294)(238,293)(239,292)(240,291)(241,297)
(242,303)(243,302)(244,301)(245,300)(246,299)(247,298)(248,304)(249,310)
(250,309)(251,308)(252,307)(253,306)(254,305)(255,311)(256,317)(257,316)
(258,315)(259,314)(260,313)(261,312)(262,318)(263,324)(264,323)(265,322)
(266,321)(267,320)(268,319)(269,325)(270,331)(271,330)(272,329)(273,328)
(274,327)(275,326)(276,332)(277,338)(278,337)(279,336)(280,335)(281,334)
(282,333)(339,395)(340,401)(341,400)(342,399)(343,398)(344,397)(345,396)
(346,402)(347,408)(348,407)(349,406)(350,405)(351,404)(352,403)(353,409)
(354,415)(355,414)(356,413)(357,412)(358,411)(359,410)(360,416)(361,422)
(362,421)(363,420)(364,419)(365,418)(366,417)(367,423)(368,429)(369,428)
(370,427)(371,426)(372,425)(373,424)(374,430)(375,436)(376,435)(377,434)
(378,433)(379,432)(380,431)(381,437)(382,443)(383,442)(384,441)(385,440)
(386,439)(387,438)(388,444)(389,450)(390,449)(391,448)(392,447)(393,446)
(394,445);
s2 := Sym(450)!( 3,172)( 4,171)( 5,177)( 6,176)( 7,175)( 8,174)( 9,173)
( 10,179)( 11,178)( 12,184)( 13,183)( 14,182)( 15,181)( 16,180)( 17,186)
( 18,185)( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)( 24,193)( 25,192)
( 26,198)( 27,197)( 28,196)( 29,195)( 30,194)( 31,207)( 32,206)( 33,212)
( 34,211)( 35,210)( 36,209)( 37,208)( 38,200)( 39,199)( 40,205)( 41,204)
( 42,203)( 43,202)( 44,201)( 45,221)( 46,220)( 47,226)( 48,225)( 49,224)
( 50,223)( 51,222)( 52,214)( 53,213)( 54,219)( 55,218)( 56,217)( 57,216)
( 58,215)( 59,116)( 60,115)( 61,121)( 62,120)( 63,119)( 64,118)( 65,117)
( 66,123)( 67,122)( 68,128)( 69,127)( 70,126)( 71,125)( 72,124)( 73,130)
( 74,129)( 75,135)( 76,134)( 77,133)( 78,132)( 79,131)( 80,137)( 81,136)
( 82,142)( 83,141)( 84,140)( 85,139)( 86,138)( 87,151)( 88,150)( 89,156)
( 90,155)( 91,154)( 92,153)( 93,152)( 94,144)( 95,143)( 96,149)( 97,148)
( 98,147)( 99,146)(100,145)(101,165)(102,164)(103,170)(104,169)(105,168)
(106,167)(107,166)(108,158)(109,157)(110,163)(111,162)(112,161)(113,160)
(114,159)(227,396)(228,395)(229,401)(230,400)(231,399)(232,398)(233,397)
(234,403)(235,402)(236,408)(237,407)(238,406)(239,405)(240,404)(241,410)
(242,409)(243,415)(244,414)(245,413)(246,412)(247,411)(248,417)(249,416)
(250,422)(251,421)(252,420)(253,419)(254,418)(255,431)(256,430)(257,436)
(258,435)(259,434)(260,433)(261,432)(262,424)(263,423)(264,429)(265,428)
(266,427)(267,426)(268,425)(269,445)(270,444)(271,450)(272,449)(273,448)
(274,447)(275,446)(276,438)(277,437)(278,443)(279,442)(280,441)(281,440)
(282,439)(283,340)(284,339)(285,345)(286,344)(287,343)(288,342)(289,341)
(290,347)(291,346)(292,352)(293,351)(294,350)(295,349)(296,348)(297,354)
(298,353)(299,359)(300,358)(301,357)(302,356)(303,355)(304,361)(305,360)
(306,366)(307,365)(308,364)(309,363)(310,362)(311,375)(312,374)(313,380)
(314,379)(315,378)(316,377)(317,376)(318,368)(319,367)(320,373)(321,372)
(322,371)(323,370)(324,369)(325,389)(326,388)(327,394)(328,393)(329,392)
(330,391)(331,390)(332,382)(333,381)(334,387)(335,386)(336,385)(337,384)
(338,383);
s3 := Sym(450)!( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)
( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 87, 94)
( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 92, 99)( 93,100)(101,108)(102,109)
(103,110)(104,111)(105,112)(106,113)(107,114)(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)(143,164)(144,165)(145,166)(146,167)(147,168)
(148,169)(149,170)(150,157)(151,158)(152,159)(153,160)(154,161)(155,162)
(156,163)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)
(178,192)(179,193)(180,194)(181,195)(182,196)(183,197)(184,198)(199,220)
(200,221)(201,222)(202,223)(203,224)(204,225)(205,226)(206,213)(207,214)
(208,215)(209,216)(210,217)(211,218)(212,219)(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)(283,311)(284,312)(285,313)(286,314)(287,315)(288,316)(289,317)
(290,318)(291,319)(292,320)(293,321)(294,322)(295,323)(296,324)(297,325)
(298,326)(299,327)(300,328)(301,329)(302,330)(303,331)(304,332)(305,333)
(306,334)(307,335)(308,336)(309,337)(310,338)(339,388)(340,389)(341,390)
(342,391)(343,392)(344,393)(345,394)(346,381)(347,382)(348,383)(349,384)
(350,385)(351,386)(352,387)(353,374)(354,375)(355,376)(356,377)(357,378)
(358,379)(359,380)(360,367)(361,368)(362,369)(363,370)(364,371)(365,372)
(366,373)(395,444)(396,445)(397,446)(398,447)(399,448)(400,449)(401,450)
(402,437)(403,438)(404,439)(405,440)(406,441)(407,442)(408,443)(409,430)
(410,431)(411,432)(412,433)(413,434)(414,435)(415,436)(416,423)(417,424)
(418,425)(419,426)(420,427)(421,428)(422,429);
s4 := Sym(450)!( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)( 8,232)( 9,233)
( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,248)
( 18,249)( 19,250)( 20,251)( 21,252)( 22,253)( 23,254)( 24,241)( 25,242)
( 26,243)( 27,244)( 28,245)( 29,246)( 30,247)( 31,262)( 32,263)( 33,264)
( 34,265)( 35,266)( 36,267)( 37,268)( 38,255)( 39,256)( 40,257)( 41,258)
( 42,259)( 43,260)( 44,261)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)
( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,281)
( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)( 64,288)( 65,289)
( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)( 72,296)( 73,304)
( 74,305)( 75,306)( 76,307)( 77,308)( 78,309)( 79,310)( 80,297)( 81,298)
( 82,299)( 83,300)( 84,301)( 85,302)( 86,303)( 87,318)( 88,319)( 89,320)
( 90,321)( 91,322)( 92,323)( 93,324)( 94,311)( 95,312)( 96,313)( 97,314)
( 98,315)( 99,316)(100,317)(101,325)(102,326)(103,327)(104,328)(105,329)
(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)(113,337)
(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)
(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,360)
(130,361)(131,362)(132,363)(133,364)(134,365)(135,366)(136,353)(137,354)
(138,355)(139,356)(140,357)(141,358)(142,359)(143,374)(144,375)(145,376)
(146,377)(147,378)(148,379)(149,380)(150,367)(151,368)(152,369)(153,370)
(154,371)(155,372)(156,373)(157,381)(158,382)(159,383)(160,384)(161,385)
(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,393)
(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)(176,400)(177,401)
(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)(184,408)(185,416)
(186,417)(187,418)(188,419)(189,420)(190,421)(191,422)(192,409)(193,410)
(194,411)(195,412)(196,413)(197,414)(198,415)(199,430)(200,431)(201,432)
(202,433)(203,434)(204,435)(205,436)(206,423)(207,424)(208,425)(209,426)
(210,427)(211,428)(212,429)(213,437)(214,438)(215,439)(216,440)(217,441)
(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)(224,448)(225,449)
(226,450);
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, s4*s2*s3*s4*s3*s4*s2*s3*s4*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 >;
to this polytope