Polytope of Type {4,6,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,3,4}*1728a
Also Known As : {{4,6|2},{6,3}6,{3,4}3}. if this polytope has another name.
Group : SmallGroup(1728,30326)
Rank : 5
Schlafli Type : {4,6,3,4}
Number of vertices, edges, etc : 4, 36, 27, 18, 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 : {2,6,3,4}*864
3-fold quotients : {4,6,3,4}*576
6-fold quotients : {2,6,3,4}*288
9-fold quotients : {4,2,3,4}*192
18-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 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);;
s2 := ( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 17)( 6, 18)( 7, 20)( 8, 19)
( 9, 21)( 10, 22)( 11, 24)( 12, 23)( 27, 28)( 31, 32)( 35, 36)( 37, 85)
( 38, 86)( 39, 88)( 40, 87)( 41, 89)( 42, 90)( 43, 92)( 44, 91)( 45, 93)
( 46, 94)( 47, 96)( 48, 95)( 49, 73)( 50, 74)( 51, 76)( 52, 75)( 53, 77)
( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 82)( 59, 84)( 60, 83)( 61, 97)
( 62, 98)( 63,100)( 64, 99)( 65,101)( 66,102)( 67,104)( 68,103)( 69,105)
( 70,106)( 71,108)( 72,107)(109,121)(110,122)(111,124)(112,123)(113,125)
(114,126)(115,128)(116,127)(117,129)(118,130)(119,132)(120,131)(135,136)
(139,140)(143,144)(145,193)(146,194)(147,196)(148,195)(149,197)(150,198)
(151,200)(152,199)(153,201)(154,202)(155,204)(156,203)(157,181)(158,182)
(159,184)(160,183)(161,185)(162,186)(163,188)(164,187)(165,189)(166,190)
(167,192)(168,191)(169,205)(170,206)(171,208)(172,207)(173,209)(174,210)
(175,212)(176,211)(177,213)(178,214)(179,216)(180,215)(217,229)(218,230)
(219,232)(220,231)(221,233)(222,234)(223,236)(224,235)(225,237)(226,238)
(227,240)(228,239)(243,244)(247,248)(251,252)(253,301)(254,302)(255,304)
(256,303)(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)
(264,311)(265,289)(266,290)(267,292)(268,291)(269,293)(270,294)(271,296)
(272,295)(273,297)(274,298)(275,300)(276,299)(277,313)(278,314)(279,316)
(280,315)(281,317)(282,318)(283,320)(284,319)(285,321)(286,322)(287,324)
(288,323)(325,337)(326,338)(327,340)(328,339)(329,341)(330,342)(331,344)
(332,343)(333,345)(334,346)(335,348)(336,347)(351,352)(355,356)(359,360)
(361,409)(362,410)(363,412)(364,411)(365,413)(366,414)(367,416)(368,415)
(369,417)(370,418)(371,420)(372,419)(373,397)(374,398)(375,400)(376,399)
(377,401)(378,402)(379,404)(380,403)(381,405)(382,406)(383,408)(384,407)
(385,421)(386,422)(387,424)(388,423)(389,425)(390,426)(391,428)(392,427)
(393,429)(394,430)(395,432)(396,431);;
s3 := ( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 41)( 6, 44)( 7, 43)( 8, 42)
( 9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 69)( 14, 72)( 15, 71)( 16, 70)
( 17, 61)( 18, 64)( 19, 63)( 20, 62)( 21, 65)( 22, 68)( 23, 67)( 24, 66)
( 25, 53)( 26, 56)( 27, 55)( 28, 54)( 29, 57)( 30, 60)( 31, 59)( 32, 58)
( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 74, 76)( 78, 80)( 82, 84)( 85,105)
( 86,108)( 87,107)( 88,106)( 89, 97)( 90,100)( 91, 99)( 92, 98)( 93,101)
( 94,104)( 95,103)( 96,102)(109,145)(110,148)(111,147)(112,146)(113,149)
(114,152)(115,151)(116,150)(117,153)(118,156)(119,155)(120,154)(121,177)
(122,180)(123,179)(124,178)(125,169)(126,172)(127,171)(128,170)(129,173)
(130,176)(131,175)(132,174)(133,161)(134,164)(135,163)(136,162)(137,165)
(138,168)(139,167)(140,166)(141,157)(142,160)(143,159)(144,158)(182,184)
(186,188)(190,192)(193,213)(194,216)(195,215)(196,214)(197,205)(198,208)
(199,207)(200,206)(201,209)(202,212)(203,211)(204,210)(217,253)(218,256)
(219,255)(220,254)(221,257)(222,260)(223,259)(224,258)(225,261)(226,264)
(227,263)(228,262)(229,285)(230,288)(231,287)(232,286)(233,277)(234,280)
(235,279)(236,278)(237,281)(238,284)(239,283)(240,282)(241,269)(242,272)
(243,271)(244,270)(245,273)(246,276)(247,275)(248,274)(249,265)(250,268)
(251,267)(252,266)(290,292)(294,296)(298,300)(301,321)(302,324)(303,323)
(304,322)(305,313)(306,316)(307,315)(308,314)(309,317)(310,320)(311,319)
(312,318)(325,361)(326,364)(327,363)(328,362)(329,365)(330,368)(331,367)
(332,366)(333,369)(334,372)(335,371)(336,370)(337,393)(338,396)(339,395)
(340,394)(341,385)(342,388)(343,387)(344,386)(345,389)(346,392)(347,391)
(348,390)(349,377)(350,380)(351,379)(352,378)(353,381)(354,384)(355,383)
(356,382)(357,373)(358,376)(359,375)(360,374)(398,400)(402,404)(406,408)
(409,429)(410,432)(411,431)(412,430)(413,421)(414,424)(415,423)(416,422)
(417,425)(418,428)(419,427)(420,426);;
s4 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432);;
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,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := 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);
s2 := Sym(432)!( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 17)( 6, 18)( 7, 20)
( 8, 19)( 9, 21)( 10, 22)( 11, 24)( 12, 23)( 27, 28)( 31, 32)( 35, 36)
( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 89)( 42, 90)( 43, 92)( 44, 91)
( 45, 93)( 46, 94)( 47, 96)( 48, 95)( 49, 73)( 50, 74)( 51, 76)( 52, 75)
( 53, 77)( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 82)( 59, 84)( 60, 83)
( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,101)( 66,102)( 67,104)( 68,103)
( 69,105)( 70,106)( 71,108)( 72,107)(109,121)(110,122)(111,124)(112,123)
(113,125)(114,126)(115,128)(116,127)(117,129)(118,130)(119,132)(120,131)
(135,136)(139,140)(143,144)(145,193)(146,194)(147,196)(148,195)(149,197)
(150,198)(151,200)(152,199)(153,201)(154,202)(155,204)(156,203)(157,181)
(158,182)(159,184)(160,183)(161,185)(162,186)(163,188)(164,187)(165,189)
(166,190)(167,192)(168,191)(169,205)(170,206)(171,208)(172,207)(173,209)
(174,210)(175,212)(176,211)(177,213)(178,214)(179,216)(180,215)(217,229)
(218,230)(219,232)(220,231)(221,233)(222,234)(223,236)(224,235)(225,237)
(226,238)(227,240)(228,239)(243,244)(247,248)(251,252)(253,301)(254,302)
(255,304)(256,303)(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)
(263,312)(264,311)(265,289)(266,290)(267,292)(268,291)(269,293)(270,294)
(271,296)(272,295)(273,297)(274,298)(275,300)(276,299)(277,313)(278,314)
(279,316)(280,315)(281,317)(282,318)(283,320)(284,319)(285,321)(286,322)
(287,324)(288,323)(325,337)(326,338)(327,340)(328,339)(329,341)(330,342)
(331,344)(332,343)(333,345)(334,346)(335,348)(336,347)(351,352)(355,356)
(359,360)(361,409)(362,410)(363,412)(364,411)(365,413)(366,414)(367,416)
(368,415)(369,417)(370,418)(371,420)(372,419)(373,397)(374,398)(375,400)
(376,399)(377,401)(378,402)(379,404)(380,403)(381,405)(382,406)(383,408)
(384,407)(385,421)(386,422)(387,424)(388,423)(389,425)(390,426)(391,428)
(392,427)(393,429)(394,430)(395,432)(396,431);
s3 := Sym(432)!( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 41)( 6, 44)( 7, 43)
( 8, 42)( 9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 69)( 14, 72)( 15, 71)
( 16, 70)( 17, 61)( 18, 64)( 19, 63)( 20, 62)( 21, 65)( 22, 68)( 23, 67)
( 24, 66)( 25, 53)( 26, 56)( 27, 55)( 28, 54)( 29, 57)( 30, 60)( 31, 59)
( 32, 58)( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 74, 76)( 78, 80)( 82, 84)
( 85,105)( 86,108)( 87,107)( 88,106)( 89, 97)( 90,100)( 91, 99)( 92, 98)
( 93,101)( 94,104)( 95,103)( 96,102)(109,145)(110,148)(111,147)(112,146)
(113,149)(114,152)(115,151)(116,150)(117,153)(118,156)(119,155)(120,154)
(121,177)(122,180)(123,179)(124,178)(125,169)(126,172)(127,171)(128,170)
(129,173)(130,176)(131,175)(132,174)(133,161)(134,164)(135,163)(136,162)
(137,165)(138,168)(139,167)(140,166)(141,157)(142,160)(143,159)(144,158)
(182,184)(186,188)(190,192)(193,213)(194,216)(195,215)(196,214)(197,205)
(198,208)(199,207)(200,206)(201,209)(202,212)(203,211)(204,210)(217,253)
(218,256)(219,255)(220,254)(221,257)(222,260)(223,259)(224,258)(225,261)
(226,264)(227,263)(228,262)(229,285)(230,288)(231,287)(232,286)(233,277)
(234,280)(235,279)(236,278)(237,281)(238,284)(239,283)(240,282)(241,269)
(242,272)(243,271)(244,270)(245,273)(246,276)(247,275)(248,274)(249,265)
(250,268)(251,267)(252,266)(290,292)(294,296)(298,300)(301,321)(302,324)
(303,323)(304,322)(305,313)(306,316)(307,315)(308,314)(309,317)(310,320)
(311,319)(312,318)(325,361)(326,364)(327,363)(328,362)(329,365)(330,368)
(331,367)(332,366)(333,369)(334,372)(335,371)(336,370)(337,393)(338,396)
(339,395)(340,394)(341,385)(342,388)(343,387)(344,386)(345,389)(346,392)
(347,391)(348,390)(349,377)(350,380)(351,379)(352,378)(353,381)(354,384)
(355,383)(356,382)(357,373)(358,376)(359,375)(360,374)(398,400)(402,404)
(406,408)(409,429)(410,432)(411,431)(412,430)(413,421)(414,424)(415,423)
(416,422)(417,425)(418,428)(419,427)(420,426);
s4 := Sym(432)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432);
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 >;
References : None.
to this polytope