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