Polytope of Type {4,9,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,9,6,4}*1728
if this polytope has a name.
Group : SmallGroup(1728,30313)
Rank : 5
Schlafli Type : {4,9,6,4}
Number of vertices, edges, etc : 4, 18, 27, 12, 4
Order of s0s1s2s3s4 : 36
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 : {4,9,6,2}*864
3-fold quotients : {4,9,2,4}*576, {4,3,6,4}*576
6-fold quotients : {4,9,2,2}*288, {4,3,6,2}*288
9-fold quotients : {4,3,2,4}*192
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)( 13, 25)( 14, 26)( 15, 28)
( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)
( 24, 31)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)
( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49,105)( 50,106)( 51,108)
( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)( 59,100)
( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)( 67, 92)
( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)(111,112)(113,117)(114,118)
(115,120)(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)
(127,144)(128,143)(129,137)(130,138)(131,140)(132,139)(145,189)(146,190)
(147,192)(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)
(155,184)(156,183)(157,213)(158,214)(159,216)(160,215)(161,209)(162,210)
(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)(170,202)
(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)(178,194)
(179,196)(180,195)(219,220)(221,225)(222,226)(223,228)(224,227)(229,241)
(230,242)(231,244)(232,243)(233,249)(234,250)(235,252)(236,251)(237,245)
(238,246)(239,248)(240,247)(253,297)(254,298)(255,300)(256,299)(257,293)
(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)(264,291)(265,321)
(266,322)(267,324)(268,323)(269,317)(270,318)(271,320)(272,319)(273,313)
(274,314)(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)(281,305)
(282,306)(283,308)(284,307)(285,301)(286,302)(287,304)(288,303)(327,328)
(329,333)(330,334)(331,336)(332,335)(337,349)(338,350)(339,352)(340,351)
(341,357)(342,358)(343,360)(344,359)(345,353)(346,354)(347,356)(348,355)
(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)(368,403)
(369,397)(370,398)(371,400)(372,399)(373,429)(374,430)(375,432)(376,431)
(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)(384,423)
(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)
(393,409)(394,410)(395,412)(396,411);;
s2 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 57)( 6, 60)( 7, 59)( 8, 58)
( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 37)( 14, 40)( 15, 39)( 16, 38)
( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 41)( 22, 44)( 23, 43)( 24, 42)
( 25, 61)( 26, 64)( 27, 63)( 28, 62)( 29, 69)( 30, 72)( 31, 71)( 32, 70)
( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 73, 93)( 74, 96)( 75, 95)( 76, 94)
( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 85)( 82, 88)( 83, 87)( 84, 86)
( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,157)(110,160)(111,159)
(112,158)(113,165)(114,168)(115,167)(116,166)(117,161)(118,164)(119,163)
(120,162)(121,145)(122,148)(123,147)(124,146)(125,153)(126,156)(127,155)
(128,154)(129,149)(130,152)(131,151)(132,150)(133,169)(134,172)(135,171)
(136,170)(137,177)(138,180)(139,179)(140,178)(141,173)(142,176)(143,175)
(144,174)(181,201)(182,204)(183,203)(184,202)(185,197)(186,200)(187,199)
(188,198)(189,193)(190,196)(191,195)(192,194)(205,213)(206,216)(207,215)
(208,214)(210,212)(217,265)(218,268)(219,267)(220,266)(221,273)(222,276)
(223,275)(224,274)(225,269)(226,272)(227,271)(228,270)(229,253)(230,256)
(231,255)(232,254)(233,261)(234,264)(235,263)(236,262)(237,257)(238,260)
(239,259)(240,258)(241,277)(242,280)(243,279)(244,278)(245,285)(246,288)
(247,287)(248,286)(249,281)(250,284)(251,283)(252,282)(289,309)(290,312)
(291,311)(292,310)(293,305)(294,308)(295,307)(296,306)(297,301)(298,304)
(299,303)(300,302)(313,321)(314,324)(315,323)(316,322)(318,320)(325,373)
(326,376)(327,375)(328,374)(329,381)(330,384)(331,383)(332,382)(333,377)
(334,380)(335,379)(336,378)(337,361)(338,364)(339,363)(340,362)(341,369)
(342,372)(343,371)(344,370)(345,365)(346,368)(347,367)(348,366)(349,385)
(350,388)(351,387)(352,386)(353,393)(354,396)(355,395)(356,394)(357,389)
(358,392)(359,391)(360,390)(397,417)(398,420)(399,419)(400,418)(401,413)
(402,416)(403,415)(404,414)(405,409)(406,412)(407,411)(408,410)(421,429)
(422,432)(423,431)(424,430)(426,428);;
s3 := ( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)( 20, 32)
( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 49, 61)( 50, 62)( 51, 63)( 52, 64)
( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)( 60, 72)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)( 92,104)
( 93,105)( 94,106)( 95,107)( 96,108)(121,133)(122,134)(123,135)(124,136)
(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)
(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)
(165,177)(166,178)(167,179)(168,180)(193,205)(194,206)(195,207)(196,208)
(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)(204,216)
(217,325)(218,326)(219,327)(220,328)(221,329)(222,330)(223,331)(224,332)
(225,333)(226,334)(227,335)(228,336)(229,349)(230,350)(231,351)(232,352)
(233,353)(234,354)(235,355)(236,356)(237,357)(238,358)(239,359)(240,360)
(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)
(249,345)(250,346)(251,347)(252,348)(253,361)(254,362)(255,363)(256,364)
(257,365)(258,366)(259,367)(260,368)(261,369)(262,370)(263,371)(264,372)
(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)
(273,393)(274,394)(275,395)(276,396)(277,373)(278,374)(279,375)(280,376)
(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384)
(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)(296,404)
(297,405)(298,406)(299,407)(300,408)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)
(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,416)
(321,417)(322,418)(323,419)(324,420);;
s4 := ( 1,217)( 2,218)( 3,219)( 4,220)( 5,221)( 6,222)( 7,223)( 8,224)
( 9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)( 16,232)
( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)( 40,256)
( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)( 56,272)
( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)( 96,312)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)
(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)(120,336)
(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)(128,344)
(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,352)
(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)
(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)(152,368)
(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)
(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)(168,384)
(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)(176,392)
(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)(184,400)
(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)(192,408)
(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)(200,416)
(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)(208,424)
(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)(216,432);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*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(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)( 13, 25)( 14, 26)
( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)
( 23, 32)( 24, 31)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)
( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49,105)( 50,106)
( 51,108)( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)
( 59,100)( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)
( 67, 92)( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)(111,112)(113,117)
(114,118)(115,120)(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)
(126,142)(127,144)(128,143)(129,137)(130,138)(131,140)(132,139)(145,189)
(146,190)(147,192)(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)
(154,182)(155,184)(156,183)(157,213)(158,214)(159,216)(160,215)(161,209)
(162,210)(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)
(170,202)(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)
(178,194)(179,196)(180,195)(219,220)(221,225)(222,226)(223,228)(224,227)
(229,241)(230,242)(231,244)(232,243)(233,249)(234,250)(235,252)(236,251)
(237,245)(238,246)(239,248)(240,247)(253,297)(254,298)(255,300)(256,299)
(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)(264,291)
(265,321)(266,322)(267,324)(268,323)(269,317)(270,318)(271,320)(272,319)
(273,313)(274,314)(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)
(281,305)(282,306)(283,308)(284,307)(285,301)(286,302)(287,304)(288,303)
(327,328)(329,333)(330,334)(331,336)(332,335)(337,349)(338,350)(339,352)
(340,351)(341,357)(342,358)(343,360)(344,359)(345,353)(346,354)(347,356)
(348,355)(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)
(368,403)(369,397)(370,398)(371,400)(372,399)(373,429)(374,430)(375,432)
(376,431)(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)
(384,423)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)
(392,415)(393,409)(394,410)(395,412)(396,411);
s2 := Sym(432)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 57)( 6, 60)( 7, 59)
( 8, 58)( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 37)( 14, 40)( 15, 39)
( 16, 38)( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 41)( 22, 44)( 23, 43)
( 24, 42)( 25, 61)( 26, 64)( 27, 63)( 28, 62)( 29, 69)( 30, 72)( 31, 71)
( 32, 70)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 73, 93)( 74, 96)( 75, 95)
( 76, 94)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 85)( 82, 88)( 83, 87)
( 84, 86)( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,157)(110,160)
(111,159)(112,158)(113,165)(114,168)(115,167)(116,166)(117,161)(118,164)
(119,163)(120,162)(121,145)(122,148)(123,147)(124,146)(125,153)(126,156)
(127,155)(128,154)(129,149)(130,152)(131,151)(132,150)(133,169)(134,172)
(135,171)(136,170)(137,177)(138,180)(139,179)(140,178)(141,173)(142,176)
(143,175)(144,174)(181,201)(182,204)(183,203)(184,202)(185,197)(186,200)
(187,199)(188,198)(189,193)(190,196)(191,195)(192,194)(205,213)(206,216)
(207,215)(208,214)(210,212)(217,265)(218,268)(219,267)(220,266)(221,273)
(222,276)(223,275)(224,274)(225,269)(226,272)(227,271)(228,270)(229,253)
(230,256)(231,255)(232,254)(233,261)(234,264)(235,263)(236,262)(237,257)
(238,260)(239,259)(240,258)(241,277)(242,280)(243,279)(244,278)(245,285)
(246,288)(247,287)(248,286)(249,281)(250,284)(251,283)(252,282)(289,309)
(290,312)(291,311)(292,310)(293,305)(294,308)(295,307)(296,306)(297,301)
(298,304)(299,303)(300,302)(313,321)(314,324)(315,323)(316,322)(318,320)
(325,373)(326,376)(327,375)(328,374)(329,381)(330,384)(331,383)(332,382)
(333,377)(334,380)(335,379)(336,378)(337,361)(338,364)(339,363)(340,362)
(341,369)(342,372)(343,371)(344,370)(345,365)(346,368)(347,367)(348,366)
(349,385)(350,388)(351,387)(352,386)(353,393)(354,396)(355,395)(356,394)
(357,389)(358,392)(359,391)(360,390)(397,417)(398,420)(399,419)(400,418)
(401,413)(402,416)(403,415)(404,414)(405,409)(406,412)(407,411)(408,410)
(421,429)(422,432)(423,431)(424,430)(426,428);
s3 := Sym(432)!( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)
( 20, 32)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 49, 61)( 50, 62)( 51, 63)
( 52, 64)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)
( 60, 72)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)
( 92,104)( 93,105)( 94,106)( 95,107)( 96,108)(121,133)(122,134)(123,135)
(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)
(132,144)(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)
(164,176)(165,177)(166,178)(167,179)(168,180)(193,205)(194,206)(195,207)
(196,208)(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)
(204,216)(217,325)(218,326)(219,327)(220,328)(221,329)(222,330)(223,331)
(224,332)(225,333)(226,334)(227,335)(228,336)(229,349)(230,350)(231,351)
(232,352)(233,353)(234,354)(235,355)(236,356)(237,357)(238,358)(239,359)
(240,360)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)
(248,344)(249,345)(250,346)(251,347)(252,348)(253,361)(254,362)(255,363)
(256,364)(257,365)(258,366)(259,367)(260,368)(261,369)(262,370)(263,371)
(264,372)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)
(272,392)(273,393)(274,394)(275,395)(276,396)(277,373)(278,374)(279,375)
(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)
(288,384)(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)
(296,404)(297,405)(298,406)(299,407)(300,408)(301,421)(302,422)(303,423)
(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)
(312,432)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)
(320,416)(321,417)(322,418)(323,419)(324,420);
s4 := Sym(432)!( 1,217)( 2,218)( 3,219)( 4,220)( 5,221)( 6,222)( 7,223)
( 8,224)( 9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)
( 16,232)( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)
( 40,256)( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)
( 56,272)( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)
( 96,312)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)
(112,328)(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)
(120,336)(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)
(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)
(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)
(144,360)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)
(152,368)(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)
(160,376)(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)
(168,384)(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)
(176,392)(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)
(184,400)(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)
(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)
(200,416)(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)
(208,424)(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)
(216,432);
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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope