Polytope of Type {8,3,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,3,6,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,30298)
Rank : 5
Schlafli Type : {8,3,6,3}
Number of vertices, edges, etc : 16, 24, 18, 9, 3
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
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 : {4,3,6,3}*864
3-fold quotients : {8,3,2,3}*576
4-fold quotients : {4,3,6,3}*432
6-fold quotients : {4,3,2,3}*288
8-fold quotients : {2,3,6,3}*216
12-fold quotients : {4,3,2,3}*144
24-fold quotients : {2,3,2,3}*72
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)( 8,220)
( 9,229)( 10,230)( 11,232)( 12,231)( 13,226)( 14,225)( 15,227)( 16,228)
( 17,237)( 18,238)( 19,240)( 20,239)( 21,234)( 22,233)( 23,235)( 24,236)
( 25,245)( 26,246)( 27,248)( 28,247)( 29,242)( 30,241)( 31,243)( 32,244)
( 33,253)( 34,254)( 35,256)( 36,255)( 37,250)( 38,249)( 39,251)( 40,252)
( 41,261)( 42,262)( 43,264)( 44,263)( 45,258)( 46,257)( 47,259)( 48,260)
( 49,269)( 50,270)( 51,272)( 52,271)( 53,266)( 54,265)( 55,267)( 56,268)
( 57,277)( 58,278)( 59,280)( 60,279)( 61,274)( 62,273)( 63,275)( 64,276)
( 65,285)( 66,286)( 67,288)( 68,287)( 69,282)( 70,281)( 71,283)( 72,284)
( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)( 80,292)
( 81,301)( 82,302)( 83,304)( 84,303)( 85,298)( 86,297)( 87,299)( 88,300)
( 89,309)( 90,310)( 91,312)( 92,311)( 93,306)( 94,305)( 95,307)( 96,308)
( 97,317)( 98,318)( 99,320)(100,319)(101,314)(102,313)(103,315)(104,316)
(105,325)(106,326)(107,328)(108,327)(109,322)(110,321)(111,323)(112,324)
(113,333)(114,334)(115,336)(116,335)(117,330)(118,329)(119,331)(120,332)
(121,341)(122,342)(123,344)(124,343)(125,338)(126,337)(127,339)(128,340)
(129,349)(130,350)(131,352)(132,351)(133,346)(134,345)(135,347)(136,348)
(137,357)(138,358)(139,360)(140,359)(141,354)(142,353)(143,355)(144,356)
(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)(152,364)
(153,373)(154,374)(155,376)(156,375)(157,370)(158,369)(159,371)(160,372)
(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)(168,380)
(169,389)(170,390)(171,392)(172,391)(173,386)(174,385)(175,387)(176,388)
(177,397)(178,398)(179,400)(180,399)(181,394)(182,393)(183,395)(184,396)
(185,405)(186,406)(187,408)(188,407)(189,402)(190,401)(191,403)(192,404)
(193,413)(194,414)(195,416)(196,415)(197,410)(198,409)(199,411)(200,412)
(201,421)(202,422)(203,424)(204,423)(205,418)(206,417)(207,419)(208,420)
(209,429)(210,430)(211,432)(212,431)(213,426)(214,425)(215,427)(216,428);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 27, 28)( 29, 31)( 30, 32)( 33, 41)( 34, 42)
( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 51, 52)( 53, 55)
( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)
( 64, 70)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)
( 80,150)( 81,161)( 82,162)( 83,164)( 84,163)( 85,167)( 86,168)( 87,165)
( 88,166)( 89,153)( 90,154)( 91,156)( 92,155)( 93,159)( 94,160)( 95,157)
( 96,158)( 97,169)( 98,170)( 99,172)(100,171)(101,175)(102,176)(103,173)
(104,174)(105,185)(106,186)(107,188)(108,187)(109,191)(110,192)(111,189)
(112,190)(113,177)(114,178)(115,180)(116,179)(117,183)(118,184)(119,181)
(120,182)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)(127,197)
(128,198)(129,209)(130,210)(131,212)(132,211)(133,215)(134,216)(135,213)
(136,214)(137,201)(138,202)(139,204)(140,203)(141,207)(142,208)(143,205)
(144,206)(217,218)(221,224)(222,223)(225,234)(226,233)(227,235)(228,236)
(229,240)(230,239)(231,238)(232,237)(241,242)(245,248)(246,247)(249,258)
(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)(256,261)(265,266)
(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)(277,288)(278,287)
(279,286)(280,285)(289,362)(290,361)(291,363)(292,364)(293,368)(294,367)
(295,366)(296,365)(297,378)(298,377)(299,379)(300,380)(301,384)(302,383)
(303,382)(304,381)(305,370)(306,369)(307,371)(308,372)(309,376)(310,375)
(311,374)(312,373)(313,386)(314,385)(315,387)(316,388)(317,392)(318,391)
(319,390)(320,389)(321,402)(322,401)(323,403)(324,404)(325,408)(326,407)
(327,406)(328,405)(329,394)(330,393)(331,395)(332,396)(333,400)(334,399)
(335,398)(336,397)(337,410)(338,409)(339,411)(340,412)(341,416)(342,415)
(343,414)(344,413)(345,426)(346,425)(347,427)(348,428)(349,432)(350,431)
(351,430)(352,429)(353,418)(354,417)(355,419)(356,420)(357,424)(358,423)
(359,422)(360,421);;
s2 := ( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)( 8, 76)
( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)( 16, 92)
( 17, 81)( 18, 82)( 19, 87)( 20, 88)( 21, 86)( 22, 85)( 23, 83)( 24, 84)
( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)( 32,108)
( 33, 97)( 34, 98)( 35,103)( 36,104)( 37,102)( 38,101)( 39, 99)( 40,100)
( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)( 48,116)
( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)( 56,140)
( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)( 64,132)
( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)( 72,124)
(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)(157,166)
(158,165)(159,163)(160,164)(169,177)(170,178)(171,183)(172,184)(173,182)
(174,181)(175,179)(176,180)(187,191)(188,192)(189,190)(193,209)(194,210)
(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)(204,208)
(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)(223,292)
(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)(231,308)
(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)(239,300)
(240,299)(241,322)(242,321)(243,328)(244,327)(245,325)(246,326)(247,324)
(248,323)(249,314)(250,313)(251,320)(252,319)(253,317)(254,318)(255,316)
(256,315)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)(263,332)
(264,331)(265,354)(266,353)(267,360)(268,359)(269,357)(270,358)(271,356)
(272,355)(273,346)(274,345)(275,352)(276,351)(277,349)(278,350)(279,348)
(280,347)(281,338)(282,337)(283,344)(284,343)(285,341)(286,342)(287,340)
(288,339)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)(372,383)
(373,381)(374,382)(375,380)(376,379)(385,394)(386,393)(387,400)(388,399)
(389,397)(390,398)(391,396)(392,395)(401,402)(403,408)(404,407)(409,426)
(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)(417,418)
(419,424)(420,423);;
s3 := ( 1, 25)( 2, 26)( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)( 8, 32)
( 9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)( 16, 48)
( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 73, 97)( 74, 98)( 75, 99)( 76,100)( 77,101)( 78,102)( 79,103)( 80,104)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)( 88,120)
( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,169)(146,170)(147,171)(148,172)(149,173)(150,174)(151,175)(152,176)
(153,185)(154,186)(155,187)(156,188)(157,189)(158,190)(159,191)(160,192)
(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)
(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)
(217,241)(218,242)(219,243)(220,244)(221,245)(222,246)(223,247)(224,248)
(225,257)(226,258)(227,259)(228,260)(229,261)(230,262)(231,263)(232,264)
(233,249)(234,250)(235,251)(236,252)(237,253)(238,254)(239,255)(240,256)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)
(289,313)(290,314)(291,315)(292,316)(293,317)(294,318)(295,319)(296,320)
(297,329)(298,330)(299,331)(300,332)(301,333)(302,334)(303,335)(304,336)
(305,321)(306,322)(307,323)(308,324)(309,325)(310,326)(311,327)(312,328)
(345,353)(346,354)(347,355)(348,356)(349,357)(350,358)(351,359)(352,360)
(361,385)(362,386)(363,387)(364,388)(365,389)(366,390)(367,391)(368,392)
(369,401)(370,402)(371,403)(372,404)(373,405)(374,406)(375,407)(376,408)
(377,393)(378,394)(379,395)(380,396)(381,397)(382,398)(383,399)(384,400)
(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432);;
s4 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)( 32, 56)
( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)( 40, 72)
( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)
(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)(112,144)
(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)(120,136)
(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)(160,168)
(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)
(177,209)(178,210)(179,211)(180,212)(181,213)(182,214)(183,215)(184,216)
(185,201)(186,202)(187,203)(188,204)(189,205)(190,206)(191,207)(192,208)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)
(249,281)(250,282)(251,283)(252,284)(253,285)(254,286)(255,287)(256,288)
(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)(264,280)
(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)(304,312)
(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)(320,344)
(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)(328,360)
(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)(336,352)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)(392,416)
(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)(400,432)
(401,417)(402,418)(403,419)(404,420)(405,421)(406,422)(407,423)(408,424);;
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, s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)
( 8,220)( 9,229)( 10,230)( 11,232)( 12,231)( 13,226)( 14,225)( 15,227)
( 16,228)( 17,237)( 18,238)( 19,240)( 20,239)( 21,234)( 22,233)( 23,235)
( 24,236)( 25,245)( 26,246)( 27,248)( 28,247)( 29,242)( 30,241)( 31,243)
( 32,244)( 33,253)( 34,254)( 35,256)( 36,255)( 37,250)( 38,249)( 39,251)
( 40,252)( 41,261)( 42,262)( 43,264)( 44,263)( 45,258)( 46,257)( 47,259)
( 48,260)( 49,269)( 50,270)( 51,272)( 52,271)( 53,266)( 54,265)( 55,267)
( 56,268)( 57,277)( 58,278)( 59,280)( 60,279)( 61,274)( 62,273)( 63,275)
( 64,276)( 65,285)( 66,286)( 67,288)( 68,287)( 69,282)( 70,281)( 71,283)
( 72,284)( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)
( 80,292)( 81,301)( 82,302)( 83,304)( 84,303)( 85,298)( 86,297)( 87,299)
( 88,300)( 89,309)( 90,310)( 91,312)( 92,311)( 93,306)( 94,305)( 95,307)
( 96,308)( 97,317)( 98,318)( 99,320)(100,319)(101,314)(102,313)(103,315)
(104,316)(105,325)(106,326)(107,328)(108,327)(109,322)(110,321)(111,323)
(112,324)(113,333)(114,334)(115,336)(116,335)(117,330)(118,329)(119,331)
(120,332)(121,341)(122,342)(123,344)(124,343)(125,338)(126,337)(127,339)
(128,340)(129,349)(130,350)(131,352)(132,351)(133,346)(134,345)(135,347)
(136,348)(137,357)(138,358)(139,360)(140,359)(141,354)(142,353)(143,355)
(144,356)(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)
(152,364)(153,373)(154,374)(155,376)(156,375)(157,370)(158,369)(159,371)
(160,372)(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)
(168,380)(169,389)(170,390)(171,392)(172,391)(173,386)(174,385)(175,387)
(176,388)(177,397)(178,398)(179,400)(180,399)(181,394)(182,393)(183,395)
(184,396)(185,405)(186,406)(187,408)(188,407)(189,402)(190,401)(191,403)
(192,404)(193,413)(194,414)(195,416)(196,415)(197,410)(198,409)(199,411)
(200,412)(201,421)(202,422)(203,424)(204,423)(205,418)(206,417)(207,419)
(208,420)(209,429)(210,430)(211,432)(212,431)(213,426)(214,425)(215,427)
(216,428);
s1 := Sym(432)!( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 27, 28)( 29, 31)( 30, 32)( 33, 41)
( 34, 42)( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 51, 52)
( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)
( 63, 69)( 64, 70)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)
( 79,149)( 80,150)( 81,161)( 82,162)( 83,164)( 84,163)( 85,167)( 86,168)
( 87,165)( 88,166)( 89,153)( 90,154)( 91,156)( 92,155)( 93,159)( 94,160)
( 95,157)( 96,158)( 97,169)( 98,170)( 99,172)(100,171)(101,175)(102,176)
(103,173)(104,174)(105,185)(106,186)(107,188)(108,187)(109,191)(110,192)
(111,189)(112,190)(113,177)(114,178)(115,180)(116,179)(117,183)(118,184)
(119,181)(120,182)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)
(127,197)(128,198)(129,209)(130,210)(131,212)(132,211)(133,215)(134,216)
(135,213)(136,214)(137,201)(138,202)(139,204)(140,203)(141,207)(142,208)
(143,205)(144,206)(217,218)(221,224)(222,223)(225,234)(226,233)(227,235)
(228,236)(229,240)(230,239)(231,238)(232,237)(241,242)(245,248)(246,247)
(249,258)(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)(256,261)
(265,266)(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)(277,288)
(278,287)(279,286)(280,285)(289,362)(290,361)(291,363)(292,364)(293,368)
(294,367)(295,366)(296,365)(297,378)(298,377)(299,379)(300,380)(301,384)
(302,383)(303,382)(304,381)(305,370)(306,369)(307,371)(308,372)(309,376)
(310,375)(311,374)(312,373)(313,386)(314,385)(315,387)(316,388)(317,392)
(318,391)(319,390)(320,389)(321,402)(322,401)(323,403)(324,404)(325,408)
(326,407)(327,406)(328,405)(329,394)(330,393)(331,395)(332,396)(333,400)
(334,399)(335,398)(336,397)(337,410)(338,409)(339,411)(340,412)(341,416)
(342,415)(343,414)(344,413)(345,426)(346,425)(347,427)(348,428)(349,432)
(350,431)(351,430)(352,429)(353,418)(354,417)(355,419)(356,420)(357,424)
(358,423)(359,422)(360,421);
s2 := Sym(432)!( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)
( 8, 76)( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)
( 16, 92)( 17, 81)( 18, 82)( 19, 87)( 20, 88)( 21, 86)( 22, 85)( 23, 83)
( 24, 84)( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)
( 32,108)( 33, 97)( 34, 98)( 35,103)( 36,104)( 37,102)( 38,101)( 39, 99)
( 40,100)( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)
( 48,116)( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)
( 56,140)( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)
( 64,132)( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)
( 72,124)(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)
(157,166)(158,165)(159,163)(160,164)(169,177)(170,178)(171,183)(172,184)
(173,182)(174,181)(175,179)(176,180)(187,191)(188,192)(189,190)(193,209)
(194,210)(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)
(204,208)(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)
(223,292)(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)
(231,308)(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)
(239,300)(240,299)(241,322)(242,321)(243,328)(244,327)(245,325)(246,326)
(247,324)(248,323)(249,314)(250,313)(251,320)(252,319)(253,317)(254,318)
(255,316)(256,315)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)
(263,332)(264,331)(265,354)(266,353)(267,360)(268,359)(269,357)(270,358)
(271,356)(272,355)(273,346)(274,345)(275,352)(276,351)(277,349)(278,350)
(279,348)(280,347)(281,338)(282,337)(283,344)(284,343)(285,341)(286,342)
(287,340)(288,339)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)
(372,383)(373,381)(374,382)(375,380)(376,379)(385,394)(386,393)(387,400)
(388,399)(389,397)(390,398)(391,396)(392,395)(401,402)(403,408)(404,407)
(409,426)(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)
(417,418)(419,424)(420,423);
s3 := Sym(432)!( 1, 25)( 2, 26)( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)
( 8, 32)( 9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)
( 16, 48)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)
( 24, 40)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 73, 97)( 74, 98)( 75, 99)( 76,100)( 77,101)( 78,102)( 79,103)
( 80,104)( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)
( 88,120)( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)
( 96,112)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,169)(146,170)(147,171)(148,172)(149,173)(150,174)(151,175)
(152,176)(153,185)(154,186)(155,187)(156,188)(157,189)(158,190)(159,191)
(160,192)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)
(168,184)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)
(208,216)(217,241)(218,242)(219,243)(220,244)(221,245)(222,246)(223,247)
(224,248)(225,257)(226,258)(227,259)(228,260)(229,261)(230,262)(231,263)
(232,264)(233,249)(234,250)(235,251)(236,252)(237,253)(238,254)(239,255)
(240,256)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288)(289,313)(290,314)(291,315)(292,316)(293,317)(294,318)(295,319)
(296,320)(297,329)(298,330)(299,331)(300,332)(301,333)(302,334)(303,335)
(304,336)(305,321)(306,322)(307,323)(308,324)(309,325)(310,326)(311,327)
(312,328)(345,353)(346,354)(347,355)(348,356)(349,357)(350,358)(351,359)
(352,360)(361,385)(362,386)(363,387)(364,388)(365,389)(366,390)(367,391)
(368,392)(369,401)(370,402)(371,403)(372,404)(373,405)(374,406)(375,407)
(376,408)(377,393)(378,394)(379,395)(380,396)(381,397)(382,398)(383,399)
(384,400)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)
(424,432);
s4 := Sym(432)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)
( 32, 56)( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)
( 40, 72)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)
( 48, 64)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)
(104,128)(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)
(112,144)(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)
(120,136)(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)
(160,168)(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)
(176,200)(177,209)(178,210)(179,211)(180,212)(181,213)(182,214)(183,215)
(184,216)(185,201)(186,202)(187,203)(188,204)(189,205)(190,206)(191,207)
(192,208)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)
(248,272)(249,281)(250,282)(251,283)(252,284)(253,285)(254,286)(255,287)
(256,288)(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)
(264,280)(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)
(304,312)(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)
(320,344)(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)
(328,360)(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)
(336,352)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)
(392,416)(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)
(400,432)(401,417)(402,418)(403,419)(404,420)(405,421)(406,422)(407,423)
(408,424);
poly := sub<Sym(432)|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, s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope