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}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1035859)
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, {2,14,2,8}*896
4-fold quotients : {2,7,2,8}*448, {2,14,2,4}*448, {2,14,4,2}*448
7-fold quotients : {2,2,4,8}*256a
8-fold quotients : {2,7,2,4}*224, {2,14,2,2}*224
14-fold quotients : {2,2,4,4}*128, {2,2,2,8}*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)( 31,200)( 32,199)( 33,205)( 34,204)
( 35,203)( 36,202)( 37,201)( 38,207)( 39,206)( 40,212)( 41,211)( 42,210)
( 43,209)( 44,208)( 45,214)( 46,213)( 47,219)( 48,218)( 49,217)( 50,216)
( 51,215)( 52,221)( 53,220)( 54,226)( 55,225)( 56,224)( 57,223)( 58,222)
( 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)( 87,144)( 88,143)( 89,149)( 90,148)
( 91,147)( 92,146)( 93,145)( 94,151)( 95,150)( 96,156)( 97,155)( 98,154)
( 99,153)(100,152)(101,158)(102,157)(103,163)(104,162)(105,161)(106,160)
(107,159)(108,165)(109,164)(110,170)(111,169)(112,168)(113,167)(114,166)
(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)(255,424)(256,423)(257,429)(258,428)
(259,427)(260,426)(261,425)(262,431)(263,430)(264,436)(265,435)(266,434)
(267,433)(268,432)(269,438)(270,437)(271,443)(272,442)(273,441)(274,440)
(275,439)(276,445)(277,444)(278,450)(279,449)(280,448)(281,447)(282,446)
(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)(311,368)(312,367)(313,373)(314,372)
(315,371)(316,370)(317,369)(318,375)(319,374)(320,380)(321,379)(322,378)
(323,377)(324,376)(325,382)(326,381)(327,387)(328,386)(329,385)(330,384)
(331,383)(332,389)(333,388)(334,394)(335,393)(336,392)(337,391)(338,390);;
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)(339,381)(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)
(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)
(403,445)(404,446)(405,447)(406,448)(407,449)(408,450)(409,423)(410,424)
(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)
(419,433)(420,434)(421,435)(422,436);;
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)( 17,241)( 18,242)
( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)( 25,249)( 26,250)
( 27,251)( 28,252)( 29,253)( 30,254)( 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)( 45,276)( 46,277)( 47,278)( 48,279)( 49,280)( 50,281)
( 51,282)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)( 57,274)( 58,275)
( 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)( 73,297)( 74,298)
( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)( 81,305)( 82,306)
( 83,307)( 84,308)( 85,309)( 86,310)( 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)(101,332)(102,333)(103,334)(104,335)(105,336)(106,337)
(107,338)(108,325)(109,326)(110,327)(111,328)(112,329)(113,330)(114,331)
(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)(129,353)(130,354)
(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)(137,361)(138,362)
(139,363)(140,364)(141,365)(142,366)(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)(157,388)(158,389)(159,390)(160,391)(161,392)(162,393)
(163,394)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)(170,387)
(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)(185,409)(186,410)
(187,411)(188,412)(189,413)(190,414)(191,415)(192,416)(193,417)(194,418)
(195,419)(196,420)(197,421)(198,422)(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)(213,444)(214,445)(215,446)(216,447)(217,448)(218,449)
(219,450)(220,437)(221,438)(222,439)(223,440)(224,441)(225,442)(226,443);;
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*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 ];;
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)( 31,200)( 32,199)( 33,205)
( 34,204)( 35,203)( 36,202)( 37,201)( 38,207)( 39,206)( 40,212)( 41,211)
( 42,210)( 43,209)( 44,208)( 45,214)( 46,213)( 47,219)( 48,218)( 49,217)
( 50,216)( 51,215)( 52,221)( 53,220)( 54,226)( 55,225)( 56,224)( 57,223)
( 58,222)( 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)( 87,144)( 88,143)( 89,149)
( 90,148)( 91,147)( 92,146)( 93,145)( 94,151)( 95,150)( 96,156)( 97,155)
( 98,154)( 99,153)(100,152)(101,158)(102,157)(103,163)(104,162)(105,161)
(106,160)(107,159)(108,165)(109,164)(110,170)(111,169)(112,168)(113,167)
(114,166)(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)(255,424)(256,423)(257,429)
(258,428)(259,427)(260,426)(261,425)(262,431)(263,430)(264,436)(265,435)
(266,434)(267,433)(268,432)(269,438)(270,437)(271,443)(272,442)(273,441)
(274,440)(275,439)(276,445)(277,444)(278,450)(279,449)(280,448)(281,447)
(282,446)(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)(311,368)(312,367)(313,373)
(314,372)(315,371)(316,370)(317,369)(318,375)(319,374)(320,380)(321,379)
(322,378)(323,377)(324,376)(325,382)(326,381)(327,387)(328,386)(329,385)
(330,384)(331,383)(332,389)(333,388)(334,394)(335,393)(336,392)(337,391)
(338,390);
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)(339,381)(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)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)
(402,444)(403,445)(404,446)(405,447)(406,448)(407,449)(408,450)(409,423)
(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)
(418,432)(419,433)(420,434)(421,435)(422,436);
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)( 17,241)
( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)( 25,249)
( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 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)( 45,276)( 46,277)( 47,278)( 48,279)( 49,280)
( 50,281)( 51,282)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)( 57,274)
( 58,275)( 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)( 73,297)
( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)( 81,305)
( 82,306)( 83,307)( 84,308)( 85,309)( 86,310)( 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)(101,332)(102,333)(103,334)(104,335)(105,336)
(106,337)(107,338)(108,325)(109,326)(110,327)(111,328)(112,329)(113,330)
(114,331)(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)(129,353)
(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)(137,361)
(138,362)(139,363)(140,364)(141,365)(142,366)(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)(157,388)(158,389)(159,390)(160,391)(161,392)
(162,393)(163,394)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)
(170,387)(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)(185,409)
(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)(192,416)(193,417)
(194,418)(195,419)(196,420)(197,421)(198,422)(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)(213,444)(214,445)(215,446)(216,447)(217,448)
(218,449)(219,450)(220,437)(221,438)(222,439)(223,440)(224,441)(225,442)
(226,443);
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*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 >;
to this polytope