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