Polytope of Type {4,6,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,30804)
Rank : 5
Schlafli Type : {4,6,6,6}
Number of vertices, edges, etc : 4, 12, 18, 18, 6
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 : {4,6,6,3}*864a, {2,6,6,6}*864a
3-fold quotients : {4,6,2,6}*576a
4-fold quotients : {2,3,6,6}*432a, {2,6,6,3}*432a
6-fold quotients : {4,6,2,3}*288a, {2,6,2,6}*288
8-fold quotients : {2,3,6,3}*216
9-fold quotients : {4,2,2,6}*192, {4,6,2,2}*192a
12-fold quotients : {2,3,2,6}*144, {2,6,2,3}*144
18-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96, {2,6,2,2}*96
24-fold quotients : {2,3,2,3}*72
27-fold quotients : {4,2,2,2}*64
36-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48
54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,109)( 2,110)( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)( 8,116)
( 9,117)( 10,118)( 11,119)( 12,120)( 13,121)( 14,122)( 15,123)( 16,124)
( 17,125)( 18,126)( 19,127)( 20,128)( 21,129)( 22,130)( 23,131)( 24,132)
( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)( 32,140)
( 33,141)( 34,142)( 35,143)( 36,144)( 37,145)( 38,146)( 39,147)( 40,148)
( 41,149)( 42,150)( 43,151)( 44,152)( 45,153)( 46,154)( 47,155)( 48,156)
( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,190)( 56,191)
( 57,192)( 58,193)( 59,194)( 60,195)( 61,196)( 62,197)( 63,198)( 64,199)
( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)
( 73,208)( 74,209)( 75,210)( 76,211)( 77,212)( 78,213)( 79,214)( 80,215)
( 81,216)( 82,163)( 83,164)( 84,165)( 85,166)( 86,167)( 87,168)( 88,169)
( 89,170)( 90,171)( 91,172)( 92,173)( 93,174)( 94,175)( 95,176)( 96,177)
( 97,178)( 98,179)( 99,180)(100,181)(101,182)(102,183)(103,184)(104,185)
(105,186)(106,187)(107,188)(108,189)(217,325)(218,326)(219,327)(220,328)
(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)(228,336)
(229,337)(230,338)(231,339)(232,340)(233,341)(234,342)(235,343)(236,344)
(237,345)(238,346)(239,347)(240,348)(241,349)(242,350)(243,351)(244,352)
(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)(252,360)
(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)(260,368)
(261,369)(262,370)(263,371)(264,372)(265,373)(266,374)(267,375)(268,376)
(269,377)(270,378)(271,406)(272,407)(273,408)(274,409)(275,410)(276,411)
(277,412)(278,413)(279,414)(280,415)(281,416)(282,417)(283,418)(284,419)
(285,420)(286,421)(287,422)(288,423)(289,424)(290,425)(291,426)(292,427)
(293,428)(294,429)(295,430)(296,431)(297,432)(298,379)(299,380)(300,381)
(301,382)(302,383)(303,384)(304,385)(305,386)(306,387)(307,388)(308,389)
(309,390)(310,391)(311,392)(312,393)(313,394)(314,395)(315,396)(316,397)
(317,398)(318,399)(319,400)(320,401)(321,402)(322,403)(323,404)(324,405);;
s1 := ( 1, 55)( 2, 57)( 3, 56)( 4, 58)( 5, 60)( 6, 59)( 7, 61)( 8, 63)
( 9, 62)( 10, 73)( 11, 75)( 12, 74)( 13, 76)( 14, 78)( 15, 77)( 16, 79)
( 17, 81)( 18, 80)( 19, 64)( 20, 66)( 21, 65)( 22, 67)( 23, 69)( 24, 68)
( 25, 70)( 26, 72)( 27, 71)( 28, 82)( 29, 84)( 30, 83)( 31, 85)( 32, 87)
( 33, 86)( 34, 88)( 35, 90)( 36, 89)( 37,100)( 38,102)( 39,101)( 40,103)
( 41,105)( 42,104)( 43,106)( 44,108)( 45,107)( 46, 91)( 47, 93)( 48, 92)
( 49, 94)( 50, 96)( 51, 95)( 52, 97)( 53, 99)( 54, 98)(109,163)(110,165)
(111,164)(112,166)(113,168)(114,167)(115,169)(116,171)(117,170)(118,181)
(119,183)(120,182)(121,184)(122,186)(123,185)(124,187)(125,189)(126,188)
(127,172)(128,174)(129,173)(130,175)(131,177)(132,176)(133,178)(134,180)
(135,179)(136,190)(137,192)(138,191)(139,193)(140,195)(141,194)(142,196)
(143,198)(144,197)(145,208)(146,210)(147,209)(148,211)(149,213)(150,212)
(151,214)(152,216)(153,215)(154,199)(155,201)(156,200)(157,202)(158,204)
(159,203)(160,205)(161,207)(162,206)(217,271)(218,273)(219,272)(220,274)
(221,276)(222,275)(223,277)(224,279)(225,278)(226,289)(227,291)(228,290)
(229,292)(230,294)(231,293)(232,295)(233,297)(234,296)(235,280)(236,282)
(237,281)(238,283)(239,285)(240,284)(241,286)(242,288)(243,287)(244,298)
(245,300)(246,299)(247,301)(248,303)(249,302)(250,304)(251,306)(252,305)
(253,316)(254,318)(255,317)(256,319)(257,321)(258,320)(259,322)(260,324)
(261,323)(262,307)(263,309)(264,308)(265,310)(266,312)(267,311)(268,313)
(269,315)(270,314)(325,379)(326,381)(327,380)(328,382)(329,384)(330,383)
(331,385)(332,387)(333,386)(334,397)(335,399)(336,398)(337,400)(338,402)
(339,401)(340,403)(341,405)(342,404)(343,388)(344,390)(345,389)(346,391)
(347,393)(348,392)(349,394)(350,396)(351,395)(352,406)(353,408)(354,407)
(355,409)(356,411)(357,410)(358,412)(359,414)(360,413)(361,424)(362,426)
(363,425)(364,427)(365,429)(366,428)(367,430)(368,432)(369,431)(370,415)
(371,417)(372,416)(373,418)(374,420)(375,419)(376,421)(377,423)(378,422);;
s2 := ( 1, 10)( 2, 12)( 3, 11)( 4, 14)( 5, 13)( 6, 15)( 7, 18)( 8, 17)
( 9, 16)( 20, 21)( 22, 23)( 25, 27)( 28, 37)( 29, 39)( 30, 38)( 31, 41)
( 32, 40)( 33, 42)( 34, 45)( 35, 44)( 36, 43)( 47, 48)( 49, 50)( 52, 54)
( 55, 64)( 56, 66)( 57, 65)( 58, 68)( 59, 67)( 60, 69)( 61, 72)( 62, 71)
( 63, 70)( 74, 75)( 76, 77)( 79, 81)( 82, 91)( 83, 93)( 84, 92)( 85, 95)
( 86, 94)( 87, 96)( 88, 99)( 89, 98)( 90, 97)(101,102)(103,104)(106,108)
(109,118)(110,120)(111,119)(112,122)(113,121)(114,123)(115,126)(116,125)
(117,124)(128,129)(130,131)(133,135)(136,145)(137,147)(138,146)(139,149)
(140,148)(141,150)(142,153)(143,152)(144,151)(155,156)(157,158)(160,162)
(163,172)(164,174)(165,173)(166,176)(167,175)(168,177)(169,180)(170,179)
(171,178)(182,183)(184,185)(187,189)(190,199)(191,201)(192,200)(193,203)
(194,202)(195,204)(196,207)(197,206)(198,205)(209,210)(211,212)(214,216)
(217,226)(218,228)(219,227)(220,230)(221,229)(222,231)(223,234)(224,233)
(225,232)(236,237)(238,239)(241,243)(244,253)(245,255)(246,254)(247,257)
(248,256)(249,258)(250,261)(251,260)(252,259)(263,264)(265,266)(268,270)
(271,280)(272,282)(273,281)(274,284)(275,283)(276,285)(277,288)(278,287)
(279,286)(290,291)(292,293)(295,297)(298,307)(299,309)(300,308)(301,311)
(302,310)(303,312)(304,315)(305,314)(306,313)(317,318)(319,320)(322,324)
(325,334)(326,336)(327,335)(328,338)(329,337)(330,339)(331,342)(332,341)
(333,340)(344,345)(346,347)(349,351)(352,361)(353,363)(354,362)(355,365)
(356,364)(357,366)(358,369)(359,368)(360,367)(371,372)(373,374)(376,378)
(379,388)(380,390)(381,389)(382,392)(383,391)(384,393)(385,396)(386,395)
(387,394)(398,399)(400,401)(403,405)(406,415)(407,417)(408,416)(409,419)
(410,418)(411,420)(412,423)(413,422)(414,421)(425,426)(427,428)(430,432);;
s3 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)
( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)( 35, 36)
( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)( 53, 54)
( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)( 65, 69)( 66, 68)( 71, 72)
( 73, 76)( 74, 78)( 75, 77)( 80, 81)( 82, 85)( 83, 87)( 84, 86)( 89, 90)
( 91, 94)( 92, 96)( 93, 95)( 98, 99)(100,103)(101,105)(102,104)(107,108)
(109,112)(110,114)(111,113)(116,117)(118,121)(119,123)(120,122)(125,126)
(127,130)(128,132)(129,131)(134,135)(136,139)(137,141)(138,140)(143,144)
(145,148)(146,150)(147,149)(152,153)(154,157)(155,159)(156,158)(161,162)
(163,166)(164,168)(165,167)(170,171)(172,175)(173,177)(174,176)(179,180)
(181,184)(182,186)(183,185)(188,189)(190,193)(191,195)(192,194)(197,198)
(199,202)(200,204)(201,203)(206,207)(208,211)(209,213)(210,212)(215,216)
(217,220)(218,222)(219,221)(224,225)(226,229)(227,231)(228,230)(233,234)
(235,238)(236,240)(237,239)(242,243)(244,247)(245,249)(246,248)(251,252)
(253,256)(254,258)(255,257)(260,261)(262,265)(263,267)(264,266)(269,270)
(271,274)(272,276)(273,275)(278,279)(280,283)(281,285)(282,284)(287,288)
(289,292)(290,294)(291,293)(296,297)(298,301)(299,303)(300,302)(305,306)
(307,310)(308,312)(309,311)(314,315)(316,319)(317,321)(318,320)(323,324)
(325,328)(326,330)(327,329)(332,333)(334,337)(335,339)(336,338)(341,342)
(343,346)(344,348)(345,347)(350,351)(352,355)(353,357)(354,356)(359,360)
(361,364)(362,366)(363,365)(368,369)(370,373)(371,375)(372,374)(377,378)
(379,382)(380,384)(381,383)(386,387)(388,391)(389,393)(390,392)(395,396)
(397,400)(398,402)(399,401)(404,405)(406,409)(407,411)(408,410)(413,414)
(415,418)(416,420)(417,419)(422,423)(424,427)(425,429)(426,428)(431,432);;
s4 := ( 1,217)( 2,219)( 3,218)( 4,223)( 5,225)( 6,224)( 7,220)( 8,222)
( 9,221)( 10,226)( 11,228)( 12,227)( 13,232)( 14,234)( 15,233)( 16,229)
( 17,231)( 18,230)( 19,235)( 20,237)( 21,236)( 22,241)( 23,243)( 24,242)
( 25,238)( 26,240)( 27,239)( 28,244)( 29,246)( 30,245)( 31,250)( 32,252)
( 33,251)( 34,247)( 35,249)( 36,248)( 37,253)( 38,255)( 39,254)( 40,259)
( 41,261)( 42,260)( 43,256)( 44,258)( 45,257)( 46,262)( 47,264)( 48,263)
( 49,268)( 50,270)( 51,269)( 52,265)( 53,267)( 54,266)( 55,271)( 56,273)
( 57,272)( 58,277)( 59,279)( 60,278)( 61,274)( 62,276)( 63,275)( 64,280)
( 65,282)( 66,281)( 67,286)( 68,288)( 69,287)( 70,283)( 71,285)( 72,284)
( 73,289)( 74,291)( 75,290)( 76,295)( 77,297)( 78,296)( 79,292)( 80,294)
( 81,293)( 82,298)( 83,300)( 84,299)( 85,304)( 86,306)( 87,305)( 88,301)
( 89,303)( 90,302)( 91,307)( 92,309)( 93,308)( 94,313)( 95,315)( 96,314)
( 97,310)( 98,312)( 99,311)(100,316)(101,318)(102,317)(103,322)(104,324)
(105,323)(106,319)(107,321)(108,320)(109,325)(110,327)(111,326)(112,331)
(113,333)(114,332)(115,328)(116,330)(117,329)(118,334)(119,336)(120,335)
(121,340)(122,342)(123,341)(124,337)(125,339)(126,338)(127,343)(128,345)
(129,344)(130,349)(131,351)(132,350)(133,346)(134,348)(135,347)(136,352)
(137,354)(138,353)(139,358)(140,360)(141,359)(142,355)(143,357)(144,356)
(145,361)(146,363)(147,362)(148,367)(149,369)(150,368)(151,364)(152,366)
(153,365)(154,370)(155,372)(156,371)(157,376)(158,378)(159,377)(160,373)
(161,375)(162,374)(163,379)(164,381)(165,380)(166,385)(167,387)(168,386)
(169,382)(170,384)(171,383)(172,388)(173,390)(174,389)(175,394)(176,396)
(177,395)(178,391)(179,393)(180,392)(181,397)(182,399)(183,398)(184,403)
(185,405)(186,404)(187,400)(188,402)(189,401)(190,406)(191,408)(192,407)
(193,412)(194,414)(195,413)(196,409)(197,411)(198,410)(199,415)(200,417)
(201,416)(202,421)(203,423)(204,422)(205,418)(206,420)(207,419)(208,424)
(209,426)(210,425)(211,430)(212,432)(213,431)(214,427)(215,429)(216,428);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1,109)( 2,110)( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)
( 8,116)( 9,117)( 10,118)( 11,119)( 12,120)( 13,121)( 14,122)( 15,123)
( 16,124)( 17,125)( 18,126)( 19,127)( 20,128)( 21,129)( 22,130)( 23,131)
( 24,132)( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)
( 32,140)( 33,141)( 34,142)( 35,143)( 36,144)( 37,145)( 38,146)( 39,147)
( 40,148)( 41,149)( 42,150)( 43,151)( 44,152)( 45,153)( 46,154)( 47,155)
( 48,156)( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,190)
( 56,191)( 57,192)( 58,193)( 59,194)( 60,195)( 61,196)( 62,197)( 63,198)
( 64,199)( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)
( 72,207)( 73,208)( 74,209)( 75,210)( 76,211)( 77,212)( 78,213)( 79,214)
( 80,215)( 81,216)( 82,163)( 83,164)( 84,165)( 85,166)( 86,167)( 87,168)
( 88,169)( 89,170)( 90,171)( 91,172)( 92,173)( 93,174)( 94,175)( 95,176)
( 96,177)( 97,178)( 98,179)( 99,180)(100,181)(101,182)(102,183)(103,184)
(104,185)(105,186)(106,187)(107,188)(108,189)(217,325)(218,326)(219,327)
(220,328)(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)
(228,336)(229,337)(230,338)(231,339)(232,340)(233,341)(234,342)(235,343)
(236,344)(237,345)(238,346)(239,347)(240,348)(241,349)(242,350)(243,351)
(244,352)(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)
(252,360)(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)
(260,368)(261,369)(262,370)(263,371)(264,372)(265,373)(266,374)(267,375)
(268,376)(269,377)(270,378)(271,406)(272,407)(273,408)(274,409)(275,410)
(276,411)(277,412)(278,413)(279,414)(280,415)(281,416)(282,417)(283,418)
(284,419)(285,420)(286,421)(287,422)(288,423)(289,424)(290,425)(291,426)
(292,427)(293,428)(294,429)(295,430)(296,431)(297,432)(298,379)(299,380)
(300,381)(301,382)(302,383)(303,384)(304,385)(305,386)(306,387)(307,388)
(308,389)(309,390)(310,391)(311,392)(312,393)(313,394)(314,395)(315,396)
(316,397)(317,398)(318,399)(319,400)(320,401)(321,402)(322,403)(323,404)
(324,405);
s1 := Sym(432)!( 1, 55)( 2, 57)( 3, 56)( 4, 58)( 5, 60)( 6, 59)( 7, 61)
( 8, 63)( 9, 62)( 10, 73)( 11, 75)( 12, 74)( 13, 76)( 14, 78)( 15, 77)
( 16, 79)( 17, 81)( 18, 80)( 19, 64)( 20, 66)( 21, 65)( 22, 67)( 23, 69)
( 24, 68)( 25, 70)( 26, 72)( 27, 71)( 28, 82)( 29, 84)( 30, 83)( 31, 85)
( 32, 87)( 33, 86)( 34, 88)( 35, 90)( 36, 89)( 37,100)( 38,102)( 39,101)
( 40,103)( 41,105)( 42,104)( 43,106)( 44,108)( 45,107)( 46, 91)( 47, 93)
( 48, 92)( 49, 94)( 50, 96)( 51, 95)( 52, 97)( 53, 99)( 54, 98)(109,163)
(110,165)(111,164)(112,166)(113,168)(114,167)(115,169)(116,171)(117,170)
(118,181)(119,183)(120,182)(121,184)(122,186)(123,185)(124,187)(125,189)
(126,188)(127,172)(128,174)(129,173)(130,175)(131,177)(132,176)(133,178)
(134,180)(135,179)(136,190)(137,192)(138,191)(139,193)(140,195)(141,194)
(142,196)(143,198)(144,197)(145,208)(146,210)(147,209)(148,211)(149,213)
(150,212)(151,214)(152,216)(153,215)(154,199)(155,201)(156,200)(157,202)
(158,204)(159,203)(160,205)(161,207)(162,206)(217,271)(218,273)(219,272)
(220,274)(221,276)(222,275)(223,277)(224,279)(225,278)(226,289)(227,291)
(228,290)(229,292)(230,294)(231,293)(232,295)(233,297)(234,296)(235,280)
(236,282)(237,281)(238,283)(239,285)(240,284)(241,286)(242,288)(243,287)
(244,298)(245,300)(246,299)(247,301)(248,303)(249,302)(250,304)(251,306)
(252,305)(253,316)(254,318)(255,317)(256,319)(257,321)(258,320)(259,322)
(260,324)(261,323)(262,307)(263,309)(264,308)(265,310)(266,312)(267,311)
(268,313)(269,315)(270,314)(325,379)(326,381)(327,380)(328,382)(329,384)
(330,383)(331,385)(332,387)(333,386)(334,397)(335,399)(336,398)(337,400)
(338,402)(339,401)(340,403)(341,405)(342,404)(343,388)(344,390)(345,389)
(346,391)(347,393)(348,392)(349,394)(350,396)(351,395)(352,406)(353,408)
(354,407)(355,409)(356,411)(357,410)(358,412)(359,414)(360,413)(361,424)
(362,426)(363,425)(364,427)(365,429)(366,428)(367,430)(368,432)(369,431)
(370,415)(371,417)(372,416)(373,418)(374,420)(375,419)(376,421)(377,423)
(378,422);
s2 := Sym(432)!( 1, 10)( 2, 12)( 3, 11)( 4, 14)( 5, 13)( 6, 15)( 7, 18)
( 8, 17)( 9, 16)( 20, 21)( 22, 23)( 25, 27)( 28, 37)( 29, 39)( 30, 38)
( 31, 41)( 32, 40)( 33, 42)( 34, 45)( 35, 44)( 36, 43)( 47, 48)( 49, 50)
( 52, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 68)( 59, 67)( 60, 69)( 61, 72)
( 62, 71)( 63, 70)( 74, 75)( 76, 77)( 79, 81)( 82, 91)( 83, 93)( 84, 92)
( 85, 95)( 86, 94)( 87, 96)( 88, 99)( 89, 98)( 90, 97)(101,102)(103,104)
(106,108)(109,118)(110,120)(111,119)(112,122)(113,121)(114,123)(115,126)
(116,125)(117,124)(128,129)(130,131)(133,135)(136,145)(137,147)(138,146)
(139,149)(140,148)(141,150)(142,153)(143,152)(144,151)(155,156)(157,158)
(160,162)(163,172)(164,174)(165,173)(166,176)(167,175)(168,177)(169,180)
(170,179)(171,178)(182,183)(184,185)(187,189)(190,199)(191,201)(192,200)
(193,203)(194,202)(195,204)(196,207)(197,206)(198,205)(209,210)(211,212)
(214,216)(217,226)(218,228)(219,227)(220,230)(221,229)(222,231)(223,234)
(224,233)(225,232)(236,237)(238,239)(241,243)(244,253)(245,255)(246,254)
(247,257)(248,256)(249,258)(250,261)(251,260)(252,259)(263,264)(265,266)
(268,270)(271,280)(272,282)(273,281)(274,284)(275,283)(276,285)(277,288)
(278,287)(279,286)(290,291)(292,293)(295,297)(298,307)(299,309)(300,308)
(301,311)(302,310)(303,312)(304,315)(305,314)(306,313)(317,318)(319,320)
(322,324)(325,334)(326,336)(327,335)(328,338)(329,337)(330,339)(331,342)
(332,341)(333,340)(344,345)(346,347)(349,351)(352,361)(353,363)(354,362)
(355,365)(356,364)(357,366)(358,369)(359,368)(360,367)(371,372)(373,374)
(376,378)(379,388)(380,390)(381,389)(382,392)(383,391)(384,393)(385,396)
(386,395)(387,394)(398,399)(400,401)(403,405)(406,415)(407,417)(408,416)
(409,419)(410,418)(411,420)(412,423)(413,422)(414,421)(425,426)(427,428)
(430,432);
s3 := Sym(432)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 13)( 11, 15)( 12, 14)
( 17, 18)( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)
( 35, 36)( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)
( 53, 54)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)( 65, 69)( 66, 68)
( 71, 72)( 73, 76)( 74, 78)( 75, 77)( 80, 81)( 82, 85)( 83, 87)( 84, 86)
( 89, 90)( 91, 94)( 92, 96)( 93, 95)( 98, 99)(100,103)(101,105)(102,104)
(107,108)(109,112)(110,114)(111,113)(116,117)(118,121)(119,123)(120,122)
(125,126)(127,130)(128,132)(129,131)(134,135)(136,139)(137,141)(138,140)
(143,144)(145,148)(146,150)(147,149)(152,153)(154,157)(155,159)(156,158)
(161,162)(163,166)(164,168)(165,167)(170,171)(172,175)(173,177)(174,176)
(179,180)(181,184)(182,186)(183,185)(188,189)(190,193)(191,195)(192,194)
(197,198)(199,202)(200,204)(201,203)(206,207)(208,211)(209,213)(210,212)
(215,216)(217,220)(218,222)(219,221)(224,225)(226,229)(227,231)(228,230)
(233,234)(235,238)(236,240)(237,239)(242,243)(244,247)(245,249)(246,248)
(251,252)(253,256)(254,258)(255,257)(260,261)(262,265)(263,267)(264,266)
(269,270)(271,274)(272,276)(273,275)(278,279)(280,283)(281,285)(282,284)
(287,288)(289,292)(290,294)(291,293)(296,297)(298,301)(299,303)(300,302)
(305,306)(307,310)(308,312)(309,311)(314,315)(316,319)(317,321)(318,320)
(323,324)(325,328)(326,330)(327,329)(332,333)(334,337)(335,339)(336,338)
(341,342)(343,346)(344,348)(345,347)(350,351)(352,355)(353,357)(354,356)
(359,360)(361,364)(362,366)(363,365)(368,369)(370,373)(371,375)(372,374)
(377,378)(379,382)(380,384)(381,383)(386,387)(388,391)(389,393)(390,392)
(395,396)(397,400)(398,402)(399,401)(404,405)(406,409)(407,411)(408,410)
(413,414)(415,418)(416,420)(417,419)(422,423)(424,427)(425,429)(426,428)
(431,432);
s4 := Sym(432)!( 1,217)( 2,219)( 3,218)( 4,223)( 5,225)( 6,224)( 7,220)
( 8,222)( 9,221)( 10,226)( 11,228)( 12,227)( 13,232)( 14,234)( 15,233)
( 16,229)( 17,231)( 18,230)( 19,235)( 20,237)( 21,236)( 22,241)( 23,243)
( 24,242)( 25,238)( 26,240)( 27,239)( 28,244)( 29,246)( 30,245)( 31,250)
( 32,252)( 33,251)( 34,247)( 35,249)( 36,248)( 37,253)( 38,255)( 39,254)
( 40,259)( 41,261)( 42,260)( 43,256)( 44,258)( 45,257)( 46,262)( 47,264)
( 48,263)( 49,268)( 50,270)( 51,269)( 52,265)( 53,267)( 54,266)( 55,271)
( 56,273)( 57,272)( 58,277)( 59,279)( 60,278)( 61,274)( 62,276)( 63,275)
( 64,280)( 65,282)( 66,281)( 67,286)( 68,288)( 69,287)( 70,283)( 71,285)
( 72,284)( 73,289)( 74,291)( 75,290)( 76,295)( 77,297)( 78,296)( 79,292)
( 80,294)( 81,293)( 82,298)( 83,300)( 84,299)( 85,304)( 86,306)( 87,305)
( 88,301)( 89,303)( 90,302)( 91,307)( 92,309)( 93,308)( 94,313)( 95,315)
( 96,314)( 97,310)( 98,312)( 99,311)(100,316)(101,318)(102,317)(103,322)
(104,324)(105,323)(106,319)(107,321)(108,320)(109,325)(110,327)(111,326)
(112,331)(113,333)(114,332)(115,328)(116,330)(117,329)(118,334)(119,336)
(120,335)(121,340)(122,342)(123,341)(124,337)(125,339)(126,338)(127,343)
(128,345)(129,344)(130,349)(131,351)(132,350)(133,346)(134,348)(135,347)
(136,352)(137,354)(138,353)(139,358)(140,360)(141,359)(142,355)(143,357)
(144,356)(145,361)(146,363)(147,362)(148,367)(149,369)(150,368)(151,364)
(152,366)(153,365)(154,370)(155,372)(156,371)(157,376)(158,378)(159,377)
(160,373)(161,375)(162,374)(163,379)(164,381)(165,380)(166,385)(167,387)
(168,386)(169,382)(170,384)(171,383)(172,388)(173,390)(174,389)(175,394)
(176,396)(177,395)(178,391)(179,393)(180,392)(181,397)(182,399)(183,398)
(184,403)(185,405)(186,404)(187,400)(188,402)(189,401)(190,406)(191,408)
(192,407)(193,412)(194,414)(195,413)(196,409)(197,411)(198,410)(199,415)
(200,417)(201,416)(202,421)(203,423)(204,422)(205,418)(206,420)(207,419)
(208,424)(209,426)(210,425)(211,430)(212,432)(213,431)(214,427)(215,429)
(216,428);
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope