Polytope of Type {8,14,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,14,4,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1044756)
Rank : 5
Schlafli Type : {8,14,4,2}
Number of vertices, edges, etc : 8, 56, 28, 4, 2
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 : {4,14,4,2}*896, {8,14,2,2}*896
4-fold quotients : {2,14,4,2}*448, {4,14,2,2}*448
7-fold quotients : {8,2,4,2}*256
8-fold quotients : {2,14,2,2}*224
14-fold quotients : {4,2,4,2}*128, {8,2,2,2}*128
16-fold quotients : {2,7,2,2}*112
28-fold quotients : {2,2,4,2}*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, 92)( 30, 93)( 31, 94)( 32, 95)
( 33, 96)( 34, 97)( 35, 98)( 36, 85)( 37, 86)( 38, 87)( 39, 88)( 40, 89)
( 41, 90)( 42, 91)( 43,106)( 44,107)( 45,108)( 46,109)( 47,110)( 48,111)
( 49,112)( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)
(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)(141,204)(142,205)(143,206)(144,207)
(145,208)(146,209)(147,210)(148,197)(149,198)(150,199)(151,200)(152,201)
(153,202)(154,203)(155,218)(156,219)(157,220)(158,221)(159,222)(160,223)
(161,224)(162,211)(163,212)(164,213)(165,214)(166,215)(167,216)(168,217)
(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)(253,316)(254,317)(255,318)(256,319)
(257,320)(258,321)(259,322)(260,309)(261,310)(262,311)(263,312)(264,313)
(265,314)(266,315)(267,330)(268,331)(269,332)(270,333)(271,334)(272,335)
(273,336)(274,323)(275,324)(276,325)(277,326)(278,327)(279,328)(280,329)
(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)(365,428)(366,429)(367,430)(368,431)
(369,432)(370,433)(371,434)(372,421)(373,422)(374,423)(375,424)(376,425)
(377,426)(378,427)(379,442)(380,443)(381,444)(382,445)(383,446)(384,447)
(385,448)(386,435)(387,436)(388,437)(389,438)(390,439)(391,440)(392,441);;
s1 := ( 1,225)( 2,231)( 3,230)( 4,229)( 5,228)( 6,227)( 7,226)( 8,232)
( 9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,239)( 16,245)
( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,246)( 23,252)( 24,251)
( 25,250)( 26,249)( 27,248)( 28,247)( 29,260)( 30,266)( 31,265)( 32,264)
( 33,263)( 34,262)( 35,261)( 36,253)( 37,259)( 38,258)( 39,257)( 40,256)
( 41,255)( 42,254)( 43,274)( 44,280)( 45,279)( 46,278)( 47,277)( 48,276)
( 49,275)( 50,267)( 51,273)( 52,272)( 53,271)( 54,270)( 55,269)( 56,268)
( 57,309)( 58,315)( 59,314)( 60,313)( 61,312)( 62,311)( 63,310)( 64,316)
( 65,322)( 66,321)( 67,320)( 68,319)( 69,318)( 70,317)( 71,323)( 72,329)
( 73,328)( 74,327)( 75,326)( 76,325)( 77,324)( 78,330)( 79,336)( 80,335)
( 81,334)( 82,333)( 83,332)( 84,331)( 85,281)( 86,287)( 87,286)( 88,285)
( 89,284)( 90,283)( 91,282)( 92,288)( 93,294)( 94,293)( 95,292)( 96,291)
( 97,290)( 98,289)( 99,295)(100,301)(101,300)(102,299)(103,298)(104,297)
(105,296)(106,302)(107,308)(108,307)(109,306)(110,305)(111,304)(112,303)
(113,337)(114,343)(115,342)(116,341)(117,340)(118,339)(119,338)(120,344)
(121,350)(122,349)(123,348)(124,347)(125,346)(126,345)(127,351)(128,357)
(129,356)(130,355)(131,354)(132,353)(133,352)(134,358)(135,364)(136,363)
(137,362)(138,361)(139,360)(140,359)(141,372)(142,378)(143,377)(144,376)
(145,375)(146,374)(147,373)(148,365)(149,371)(150,370)(151,369)(152,368)
(153,367)(154,366)(155,386)(156,392)(157,391)(158,390)(159,389)(160,388)
(161,387)(162,379)(163,385)(164,384)(165,383)(166,382)(167,381)(168,380)
(169,421)(170,427)(171,426)(172,425)(173,424)(174,423)(175,422)(176,428)
(177,434)(178,433)(179,432)(180,431)(181,430)(182,429)(183,435)(184,441)
(185,440)(186,439)(187,438)(188,437)(189,436)(190,442)(191,448)(192,447)
(193,446)(194,445)(195,444)(196,443)(197,393)(198,399)(199,398)(200,397)
(201,396)(202,395)(203,394)(204,400)(205,406)(206,405)(207,404)(208,403)
(209,402)(210,401)(211,407)(212,413)(213,412)(214,411)(215,410)(216,409)
(217,408)(218,414)(219,420)(220,419)(221,418)(222,417)(223,416)(224,415);;
s2 := ( 1, 86)( 2, 85)( 3, 91)( 4, 90)( 5, 89)( 6, 88)( 7, 87)( 8, 93)
( 9, 92)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15,100)( 16, 99)
( 17,105)( 18,104)( 19,103)( 20,102)( 21,101)( 22,107)( 23,106)( 24,112)
( 25,111)( 26,110)( 27,109)( 28,108)( 29, 65)( 30, 64)( 31, 70)( 32, 69)
( 33, 68)( 34, 67)( 35, 66)( 36, 58)( 37, 57)( 38, 63)( 39, 62)( 40, 61)
( 41, 60)( 42, 59)( 43, 79)( 44, 78)( 45, 84)( 46, 83)( 47, 82)( 48, 81)
( 49, 80)( 50, 72)( 51, 71)( 52, 77)( 53, 76)( 54, 75)( 55, 74)( 56, 73)
(113,212)(114,211)(115,217)(116,216)(117,215)(118,214)(119,213)(120,219)
(121,218)(122,224)(123,223)(124,222)(125,221)(126,220)(127,198)(128,197)
(129,203)(130,202)(131,201)(132,200)(133,199)(134,205)(135,204)(136,210)
(137,209)(138,208)(139,207)(140,206)(141,191)(142,190)(143,196)(144,195)
(145,194)(146,193)(147,192)(148,184)(149,183)(150,189)(151,188)(152,187)
(153,186)(154,185)(155,177)(156,176)(157,182)(158,181)(159,180)(160,179)
(161,178)(162,170)(163,169)(164,175)(165,174)(166,173)(167,172)(168,171)
(225,282)(226,281)(227,287)(228,286)(229,285)(230,284)(231,283)(232,289)
(233,288)(234,294)(235,293)(236,292)(237,291)(238,290)(239,296)(240,295)
(241,301)(242,300)(243,299)(244,298)(245,297)(246,303)(247,302)(248,308)
(249,307)(250,306)(251,305)(252,304)(253,310)(254,309)(255,315)(256,314)
(257,313)(258,312)(259,311)(260,317)(261,316)(262,322)(263,321)(264,320)
(265,319)(266,318)(267,324)(268,323)(269,329)(270,328)(271,327)(272,326)
(273,325)(274,331)(275,330)(276,336)(277,335)(278,334)(279,333)(280,332)
(337,408)(338,407)(339,413)(340,412)(341,411)(342,410)(343,409)(344,415)
(345,414)(346,420)(347,419)(348,418)(349,417)(350,416)(351,394)(352,393)
(353,399)(354,398)(355,397)(356,396)(357,395)(358,401)(359,400)(360,406)
(361,405)(362,404)(363,403)(364,402)(365,436)(366,435)(367,441)(368,440)
(369,439)(370,438)(371,437)(372,443)(373,442)(374,448)(375,447)(376,446)
(377,445)(378,444)(379,422)(380,421)(381,427)(382,426)(383,425)(384,424)
(385,423)(386,429)(387,428)(388,434)(389,433)(390,432)(391,431)(392,430);;
s3 := ( 1,113)( 2,114)( 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)
(225,337)(226,338)(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);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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, 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, 92)( 30, 93)( 31, 94)
( 32, 95)( 33, 96)( 34, 97)( 35, 98)( 36, 85)( 37, 86)( 38, 87)( 39, 88)
( 40, 89)( 41, 90)( 42, 91)( 43,106)( 44,107)( 45,108)( 46,109)( 47,110)
( 48,111)( 49,112)( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)
( 56,105)(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)(141,204)(142,205)(143,206)
(144,207)(145,208)(146,209)(147,210)(148,197)(149,198)(150,199)(151,200)
(152,201)(153,202)(154,203)(155,218)(156,219)(157,220)(158,221)(159,222)
(160,223)(161,224)(162,211)(163,212)(164,213)(165,214)(166,215)(167,216)
(168,217)(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)(253,316)(254,317)(255,318)
(256,319)(257,320)(258,321)(259,322)(260,309)(261,310)(262,311)(263,312)
(264,313)(265,314)(266,315)(267,330)(268,331)(269,332)(270,333)(271,334)
(272,335)(273,336)(274,323)(275,324)(276,325)(277,326)(278,327)(279,328)
(280,329)(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)(365,428)(366,429)(367,430)
(368,431)(369,432)(370,433)(371,434)(372,421)(373,422)(374,423)(375,424)
(376,425)(377,426)(378,427)(379,442)(380,443)(381,444)(382,445)(383,446)
(384,447)(385,448)(386,435)(387,436)(388,437)(389,438)(390,439)(391,440)
(392,441);
s1 := Sym(450)!( 1,225)( 2,231)( 3,230)( 4,229)( 5,228)( 6,227)( 7,226)
( 8,232)( 9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,239)
( 16,245)( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,246)( 23,252)
( 24,251)( 25,250)( 26,249)( 27,248)( 28,247)( 29,260)( 30,266)( 31,265)
( 32,264)( 33,263)( 34,262)( 35,261)( 36,253)( 37,259)( 38,258)( 39,257)
( 40,256)( 41,255)( 42,254)( 43,274)( 44,280)( 45,279)( 46,278)( 47,277)
( 48,276)( 49,275)( 50,267)( 51,273)( 52,272)( 53,271)( 54,270)( 55,269)
( 56,268)( 57,309)( 58,315)( 59,314)( 60,313)( 61,312)( 62,311)( 63,310)
( 64,316)( 65,322)( 66,321)( 67,320)( 68,319)( 69,318)( 70,317)( 71,323)
( 72,329)( 73,328)( 74,327)( 75,326)( 76,325)( 77,324)( 78,330)( 79,336)
( 80,335)( 81,334)( 82,333)( 83,332)( 84,331)( 85,281)( 86,287)( 87,286)
( 88,285)( 89,284)( 90,283)( 91,282)( 92,288)( 93,294)( 94,293)( 95,292)
( 96,291)( 97,290)( 98,289)( 99,295)(100,301)(101,300)(102,299)(103,298)
(104,297)(105,296)(106,302)(107,308)(108,307)(109,306)(110,305)(111,304)
(112,303)(113,337)(114,343)(115,342)(116,341)(117,340)(118,339)(119,338)
(120,344)(121,350)(122,349)(123,348)(124,347)(125,346)(126,345)(127,351)
(128,357)(129,356)(130,355)(131,354)(132,353)(133,352)(134,358)(135,364)
(136,363)(137,362)(138,361)(139,360)(140,359)(141,372)(142,378)(143,377)
(144,376)(145,375)(146,374)(147,373)(148,365)(149,371)(150,370)(151,369)
(152,368)(153,367)(154,366)(155,386)(156,392)(157,391)(158,390)(159,389)
(160,388)(161,387)(162,379)(163,385)(164,384)(165,383)(166,382)(167,381)
(168,380)(169,421)(170,427)(171,426)(172,425)(173,424)(174,423)(175,422)
(176,428)(177,434)(178,433)(179,432)(180,431)(181,430)(182,429)(183,435)
(184,441)(185,440)(186,439)(187,438)(188,437)(189,436)(190,442)(191,448)
(192,447)(193,446)(194,445)(195,444)(196,443)(197,393)(198,399)(199,398)
(200,397)(201,396)(202,395)(203,394)(204,400)(205,406)(206,405)(207,404)
(208,403)(209,402)(210,401)(211,407)(212,413)(213,412)(214,411)(215,410)
(216,409)(217,408)(218,414)(219,420)(220,419)(221,418)(222,417)(223,416)
(224,415);
s2 := Sym(450)!( 1, 86)( 2, 85)( 3, 91)( 4, 90)( 5, 89)( 6, 88)( 7, 87)
( 8, 93)( 9, 92)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15,100)
( 16, 99)( 17,105)( 18,104)( 19,103)( 20,102)( 21,101)( 22,107)( 23,106)
( 24,112)( 25,111)( 26,110)( 27,109)( 28,108)( 29, 65)( 30, 64)( 31, 70)
( 32, 69)( 33, 68)( 34, 67)( 35, 66)( 36, 58)( 37, 57)( 38, 63)( 39, 62)
( 40, 61)( 41, 60)( 42, 59)( 43, 79)( 44, 78)( 45, 84)( 46, 83)( 47, 82)
( 48, 81)( 49, 80)( 50, 72)( 51, 71)( 52, 77)( 53, 76)( 54, 75)( 55, 74)
( 56, 73)(113,212)(114,211)(115,217)(116,216)(117,215)(118,214)(119,213)
(120,219)(121,218)(122,224)(123,223)(124,222)(125,221)(126,220)(127,198)
(128,197)(129,203)(130,202)(131,201)(132,200)(133,199)(134,205)(135,204)
(136,210)(137,209)(138,208)(139,207)(140,206)(141,191)(142,190)(143,196)
(144,195)(145,194)(146,193)(147,192)(148,184)(149,183)(150,189)(151,188)
(152,187)(153,186)(154,185)(155,177)(156,176)(157,182)(158,181)(159,180)
(160,179)(161,178)(162,170)(163,169)(164,175)(165,174)(166,173)(167,172)
(168,171)(225,282)(226,281)(227,287)(228,286)(229,285)(230,284)(231,283)
(232,289)(233,288)(234,294)(235,293)(236,292)(237,291)(238,290)(239,296)
(240,295)(241,301)(242,300)(243,299)(244,298)(245,297)(246,303)(247,302)
(248,308)(249,307)(250,306)(251,305)(252,304)(253,310)(254,309)(255,315)
(256,314)(257,313)(258,312)(259,311)(260,317)(261,316)(262,322)(263,321)
(264,320)(265,319)(266,318)(267,324)(268,323)(269,329)(270,328)(271,327)
(272,326)(273,325)(274,331)(275,330)(276,336)(277,335)(278,334)(279,333)
(280,332)(337,408)(338,407)(339,413)(340,412)(341,411)(342,410)(343,409)
(344,415)(345,414)(346,420)(347,419)(348,418)(349,417)(350,416)(351,394)
(352,393)(353,399)(354,398)(355,397)(356,396)(357,395)(358,401)(359,400)
(360,406)(361,405)(362,404)(363,403)(364,402)(365,436)(366,435)(367,441)
(368,440)(369,439)(370,438)(371,437)(372,443)(373,442)(374,448)(375,447)
(376,446)(377,445)(378,444)(379,422)(380,421)(381,427)(382,426)(383,425)
(384,424)(385,423)(386,429)(387,428)(388,434)(389,433)(390,432)(391,431)
(392,430);
s3 := Sym(450)!( 1,113)( 2,114)( 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)(225,337)(226,338)(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);
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*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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