Polytope of Type {12,6,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,3,4}*1728a
if this polytope has a name.
Group : SmallGroup(1728,30243)
Rank : 5
Schlafli Type : {12,6,3,4}
Number of vertices, edges, etc : 12, 36, 9, 6, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Universal
Non-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 : {6,6,3,4}*864a
3-fold quotients : {12,2,3,4}*576
4-fold quotients : {3,6,3,4}*432
6-fold quotients : {6,2,3,4}*288
9-fold quotients : {4,2,3,4}*192
12-fold quotients : {3,2,3,4}*144
18-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)
( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)
( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)
( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)
(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)
(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)
(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)
(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)
(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)
(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212)
(217,325)(218,326)(219,327)(220,328)(221,333)(222,334)(223,335)(224,336)
(225,329)(226,330)(227,331)(228,332)(229,349)(230,350)(231,351)(232,352)
(233,357)(234,358)(235,359)(236,360)(237,353)(238,354)(239,355)(240,356)
(241,337)(242,338)(243,339)(244,340)(245,345)(246,346)(247,347)(248,348)
(249,341)(250,342)(251,343)(252,344)(253,361)(254,362)(255,363)(256,364)
(257,369)(258,370)(259,371)(260,372)(261,365)(262,366)(263,367)(264,368)
(265,385)(266,386)(267,387)(268,388)(269,393)(270,394)(271,395)(272,396)
(273,389)(274,390)(275,391)(276,392)(277,373)(278,374)(279,375)(280,376)
(281,381)(282,382)(283,383)(284,384)(285,377)(286,378)(287,379)(288,380)
(289,397)(290,398)(291,399)(292,400)(293,405)(294,406)(295,407)(296,408)
(297,401)(298,402)(299,403)(300,404)(301,421)(302,422)(303,423)(304,424)
(305,429)(306,430)(307,431)(308,432)(309,425)(310,426)(311,427)(312,428)
(313,409)(314,410)(315,411)(316,412)(317,417)(318,418)(319,419)(320,420)
(321,413)(322,414)(323,415)(324,416);;
s1 := ( 1,229)( 2,230)( 3,231)( 4,232)( 5,237)( 6,238)( 7,239)( 8,240)
( 9,233)( 10,234)( 11,235)( 12,236)( 13,217)( 14,218)( 15,219)( 16,220)
( 17,225)( 18,226)( 19,227)( 20,228)( 21,221)( 22,222)( 23,223)( 24,224)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,249)( 30,250)( 31,251)( 32,252)
( 33,245)( 34,246)( 35,247)( 36,248)( 37,265)( 38,266)( 39,267)( 40,268)
( 41,273)( 42,274)( 43,275)( 44,276)( 45,269)( 46,270)( 47,271)( 48,272)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,261)( 54,262)( 55,263)( 56,264)
( 57,257)( 58,258)( 59,259)( 60,260)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,285)( 66,286)( 67,287)( 68,288)( 69,281)( 70,282)( 71,283)( 72,284)
( 73,301)( 74,302)( 75,303)( 76,304)( 77,309)( 78,310)( 79,311)( 80,312)
( 81,305)( 82,306)( 83,307)( 84,308)( 85,289)( 86,290)( 87,291)( 88,292)
( 89,297)( 90,298)( 91,299)( 92,300)( 93,293)( 94,294)( 95,295)( 96,296)
( 97,313)( 98,314)( 99,315)(100,316)(101,321)(102,322)(103,323)(104,324)
(105,317)(106,318)(107,319)(108,320)(109,337)(110,338)(111,339)(112,340)
(113,345)(114,346)(115,347)(116,348)(117,341)(118,342)(119,343)(120,344)
(121,325)(122,326)(123,327)(124,328)(125,333)(126,334)(127,335)(128,336)
(129,329)(130,330)(131,331)(132,332)(133,349)(134,350)(135,351)(136,352)
(137,357)(138,358)(139,359)(140,360)(141,353)(142,354)(143,355)(144,356)
(145,373)(146,374)(147,375)(148,376)(149,381)(150,382)(151,383)(152,384)
(153,377)(154,378)(155,379)(156,380)(157,361)(158,362)(159,363)(160,364)
(161,369)(162,370)(163,371)(164,372)(165,365)(166,366)(167,367)(168,368)
(169,385)(170,386)(171,387)(172,388)(173,393)(174,394)(175,395)(176,396)
(177,389)(178,390)(179,391)(180,392)(181,409)(182,410)(183,411)(184,412)
(185,417)(186,418)(187,419)(188,420)(189,413)(190,414)(191,415)(192,416)
(193,397)(194,398)(195,399)(196,400)(197,405)(198,406)(199,407)(200,408)
(201,401)(202,402)(203,403)(204,404)(205,421)(206,422)(207,423)(208,424)
(209,429)(210,430)(211,431)(212,432)(213,425)(214,426)(215,427)(216,428);;
s2 := ( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 45)( 6, 48)( 7, 47)( 8, 46)
( 9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 53)( 14, 56)( 15, 55)( 16, 54)
( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 57)( 22, 60)( 23, 59)( 24, 58)
( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)
( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 74, 76)( 77, 81)( 78, 84)( 79, 83)
( 80, 82)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 94, 96)( 97,105)( 98,108)
( 99,107)(100,106)(102,104)(109,145)(110,148)(111,147)(112,146)(113,153)
(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)(120,150)(121,161)
(122,164)(123,163)(124,162)(125,157)(126,160)(127,159)(128,158)(129,165)
(130,168)(131,167)(132,166)(133,177)(134,180)(135,179)(136,178)(137,173)
(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)(144,170)(182,184)
(185,189)(186,192)(187,191)(188,190)(193,197)(194,200)(195,199)(196,198)
(202,204)(205,213)(206,216)(207,215)(208,214)(210,212)(217,253)(218,256)
(219,255)(220,254)(221,261)(222,264)(223,263)(224,262)(225,257)(226,260)
(227,259)(228,258)(229,269)(230,272)(231,271)(232,270)(233,265)(234,268)
(235,267)(236,266)(237,273)(238,276)(239,275)(240,274)(241,285)(242,288)
(243,287)(244,286)(245,281)(246,284)(247,283)(248,282)(249,277)(250,280)
(251,279)(252,278)(290,292)(293,297)(294,300)(295,299)(296,298)(301,305)
(302,308)(303,307)(304,306)(310,312)(313,321)(314,324)(315,323)(316,322)
(318,320)(325,361)(326,364)(327,363)(328,362)(329,369)(330,372)(331,371)
(332,370)(333,365)(334,368)(335,367)(336,366)(337,377)(338,380)(339,379)
(340,378)(341,373)(342,376)(343,375)(344,374)(345,381)(346,384)(347,383)
(348,382)(349,393)(350,396)(351,395)(352,394)(353,389)(354,392)(355,391)
(356,390)(357,385)(358,388)(359,387)(360,386)(398,400)(401,405)(402,408)
(403,407)(404,406)(409,413)(410,416)(411,415)(412,414)(418,420)(421,429)
(422,432)(423,431)(424,430)(426,428);;
s3 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 73)
( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 77)
( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 93)
( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 97)
( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)
( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)(116,119)
(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)
(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)
(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)(158,194)
(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)(166,198)
(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)(174,214)
(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(219,220)(221,225)
(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)(236,239)
(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)(255,292)
(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)(263,296)
(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)(271,312)
(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)(279,316)
(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)(287,320)
(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)(341,345)
(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)(356,359)
(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)(368,407)
(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)(376,411)
(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)(384,415)
(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)(392,431)
(393,425)(394,426)(395,428)(396,427);;
s4 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432);;
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, s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s0*s1*s0*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)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 25)( 14, 26)( 15, 27)
( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)
( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)
( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)
( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)
( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)
(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)
(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)
(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)
(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)
(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)
(204,212)(217,325)(218,326)(219,327)(220,328)(221,333)(222,334)(223,335)
(224,336)(225,329)(226,330)(227,331)(228,332)(229,349)(230,350)(231,351)
(232,352)(233,357)(234,358)(235,359)(236,360)(237,353)(238,354)(239,355)
(240,356)(241,337)(242,338)(243,339)(244,340)(245,345)(246,346)(247,347)
(248,348)(249,341)(250,342)(251,343)(252,344)(253,361)(254,362)(255,363)
(256,364)(257,369)(258,370)(259,371)(260,372)(261,365)(262,366)(263,367)
(264,368)(265,385)(266,386)(267,387)(268,388)(269,393)(270,394)(271,395)
(272,396)(273,389)(274,390)(275,391)(276,392)(277,373)(278,374)(279,375)
(280,376)(281,381)(282,382)(283,383)(284,384)(285,377)(286,378)(287,379)
(288,380)(289,397)(290,398)(291,399)(292,400)(293,405)(294,406)(295,407)
(296,408)(297,401)(298,402)(299,403)(300,404)(301,421)(302,422)(303,423)
(304,424)(305,429)(306,430)(307,431)(308,432)(309,425)(310,426)(311,427)
(312,428)(313,409)(314,410)(315,411)(316,412)(317,417)(318,418)(319,419)
(320,420)(321,413)(322,414)(323,415)(324,416);
s1 := Sym(432)!( 1,229)( 2,230)( 3,231)( 4,232)( 5,237)( 6,238)( 7,239)
( 8,240)( 9,233)( 10,234)( 11,235)( 12,236)( 13,217)( 14,218)( 15,219)
( 16,220)( 17,225)( 18,226)( 19,227)( 20,228)( 21,221)( 22,222)( 23,223)
( 24,224)( 25,241)( 26,242)( 27,243)( 28,244)( 29,249)( 30,250)( 31,251)
( 32,252)( 33,245)( 34,246)( 35,247)( 36,248)( 37,265)( 38,266)( 39,267)
( 40,268)( 41,273)( 42,274)( 43,275)( 44,276)( 45,269)( 46,270)( 47,271)
( 48,272)( 49,253)( 50,254)( 51,255)( 52,256)( 53,261)( 54,262)( 55,263)
( 56,264)( 57,257)( 58,258)( 59,259)( 60,260)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,285)( 66,286)( 67,287)( 68,288)( 69,281)( 70,282)( 71,283)
( 72,284)( 73,301)( 74,302)( 75,303)( 76,304)( 77,309)( 78,310)( 79,311)
( 80,312)( 81,305)( 82,306)( 83,307)( 84,308)( 85,289)( 86,290)( 87,291)
( 88,292)( 89,297)( 90,298)( 91,299)( 92,300)( 93,293)( 94,294)( 95,295)
( 96,296)( 97,313)( 98,314)( 99,315)(100,316)(101,321)(102,322)(103,323)
(104,324)(105,317)(106,318)(107,319)(108,320)(109,337)(110,338)(111,339)
(112,340)(113,345)(114,346)(115,347)(116,348)(117,341)(118,342)(119,343)
(120,344)(121,325)(122,326)(123,327)(124,328)(125,333)(126,334)(127,335)
(128,336)(129,329)(130,330)(131,331)(132,332)(133,349)(134,350)(135,351)
(136,352)(137,357)(138,358)(139,359)(140,360)(141,353)(142,354)(143,355)
(144,356)(145,373)(146,374)(147,375)(148,376)(149,381)(150,382)(151,383)
(152,384)(153,377)(154,378)(155,379)(156,380)(157,361)(158,362)(159,363)
(160,364)(161,369)(162,370)(163,371)(164,372)(165,365)(166,366)(167,367)
(168,368)(169,385)(170,386)(171,387)(172,388)(173,393)(174,394)(175,395)
(176,396)(177,389)(178,390)(179,391)(180,392)(181,409)(182,410)(183,411)
(184,412)(185,417)(186,418)(187,419)(188,420)(189,413)(190,414)(191,415)
(192,416)(193,397)(194,398)(195,399)(196,400)(197,405)(198,406)(199,407)
(200,408)(201,401)(202,402)(203,403)(204,404)(205,421)(206,422)(207,423)
(208,424)(209,429)(210,430)(211,431)(212,432)(213,425)(214,426)(215,427)
(216,428);
s2 := Sym(432)!( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 45)( 6, 48)( 7, 47)
( 8, 46)( 9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 53)( 14, 56)( 15, 55)
( 16, 54)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 57)( 22, 60)( 23, 59)
( 24, 58)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)
( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 74, 76)( 77, 81)( 78, 84)
( 79, 83)( 80, 82)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 94, 96)( 97,105)
( 98,108)( 99,107)(100,106)(102,104)(109,145)(110,148)(111,147)(112,146)
(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)(120,150)
(121,161)(122,164)(123,163)(124,162)(125,157)(126,160)(127,159)(128,158)
(129,165)(130,168)(131,167)(132,166)(133,177)(134,180)(135,179)(136,178)
(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)(144,170)
(182,184)(185,189)(186,192)(187,191)(188,190)(193,197)(194,200)(195,199)
(196,198)(202,204)(205,213)(206,216)(207,215)(208,214)(210,212)(217,253)
(218,256)(219,255)(220,254)(221,261)(222,264)(223,263)(224,262)(225,257)
(226,260)(227,259)(228,258)(229,269)(230,272)(231,271)(232,270)(233,265)
(234,268)(235,267)(236,266)(237,273)(238,276)(239,275)(240,274)(241,285)
(242,288)(243,287)(244,286)(245,281)(246,284)(247,283)(248,282)(249,277)
(250,280)(251,279)(252,278)(290,292)(293,297)(294,300)(295,299)(296,298)
(301,305)(302,308)(303,307)(304,306)(310,312)(313,321)(314,324)(315,323)
(316,322)(318,320)(325,361)(326,364)(327,363)(328,362)(329,369)(330,372)
(331,371)(332,370)(333,365)(334,368)(335,367)(336,366)(337,377)(338,380)
(339,379)(340,378)(341,373)(342,376)(343,375)(344,374)(345,381)(346,384)
(347,383)(348,382)(349,393)(350,396)(351,395)(352,394)(353,389)(354,392)
(355,391)(356,390)(357,385)(358,388)(359,387)(360,386)(398,400)(401,405)
(402,408)(403,407)(404,406)(409,413)(410,416)(411,415)(412,414)(418,420)
(421,429)(422,432)(423,431)(424,430)(426,428);
s3 := Sym(432)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)
( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)
( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)
( 45, 77)( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)
( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)
( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)
( 69,101)( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)
(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)
(138,142)(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)
(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)
(158,194)(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)
(166,198)(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)
(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(219,220)
(221,225)(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)
(236,239)(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)
(255,292)(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)
(263,296)(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)
(271,312)(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)
(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)
(287,320)(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)
(341,345)(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)
(356,359)(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)
(368,407)(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)
(376,411)(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)
(384,415)(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)
(392,431)(393,425)(394,426)(395,428)(396,427);
s4 := Sym(432)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432);
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, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s4*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope