Polytope of Type {4,3,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,6,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 5
Schlafli Type : {4,3,6,6}
Number of vertices, edges, etc : 8, 12, 18, 18, 6
Order of s0s1s2s3s4 : 6
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 : {4,3,6,3}*864, {4,3,6,6}*864a
   3-fold quotients : {4,3,2,6}*576
   4-fold quotients : {4,3,6,3}*432, {2,3,6,6}*432a
   6-fold quotients : {4,3,2,3}*288, {4,3,2,6}*288
   8-fold quotients : {2,3,6,3}*216
   9-fold quotients : {4,3,2,2}*192
   12-fold quotients : {4,3,2,3}*144, {2,3,2,6}*144
   18-fold quotients : {4,3,2,2}*96
   24-fold quotients : {2,3,2,3}*72
   36-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1,219)(  2,220)(  3,217)(  4,218)(  5,223)(  6,224)(  7,221)(  8,222)
(  9,227)( 10,228)( 11,225)( 12,226)( 13,231)( 14,232)( 15,229)( 16,230)
( 17,235)( 18,236)( 19,233)( 20,234)( 21,239)( 22,240)( 23,237)( 24,238)
( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)( 32,246)
( 33,251)( 34,252)( 35,249)( 36,250)( 37,255)( 38,256)( 39,253)( 40,254)
( 41,259)( 42,260)( 43,257)( 44,258)( 45,263)( 46,264)( 47,261)( 48,262)
( 49,267)( 50,268)( 51,265)( 52,266)( 53,271)( 54,272)( 55,269)( 56,270)
( 57,275)( 58,276)( 59,273)( 60,274)( 61,279)( 62,280)( 63,277)( 64,278)
( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)( 72,286)
( 73,291)( 74,292)( 75,289)( 76,290)( 77,295)( 78,296)( 79,293)( 80,294)
( 81,299)( 82,300)( 83,297)( 84,298)( 85,303)( 86,304)( 87,301)( 88,302)
( 89,307)( 90,308)( 91,305)( 92,306)( 93,311)( 94,312)( 95,309)( 96,310)
( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)(104,318)
(105,323)(106,324)(107,321)(108,322)(109,327)(110,328)(111,325)(112,326)
(113,331)(114,332)(115,329)(116,330)(117,335)(118,336)(119,333)(120,334)
(121,339)(122,340)(123,337)(124,338)(125,343)(126,344)(127,341)(128,342)
(129,347)(130,348)(131,345)(132,346)(133,351)(134,352)(135,349)(136,350)
(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)(144,358)
(145,363)(146,364)(147,361)(148,362)(149,367)(150,368)(151,365)(152,366)
(153,371)(154,372)(155,369)(156,370)(157,375)(158,376)(159,373)(160,374)
(161,379)(162,380)(163,377)(164,378)(165,383)(166,384)(167,381)(168,382)
(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)(176,390)
(177,395)(178,396)(179,393)(180,394)(181,399)(182,400)(183,397)(184,398)
(185,403)(186,404)(187,401)(188,402)(189,407)(190,408)(191,405)(192,406)
(193,411)(194,412)(195,409)(196,410)(197,415)(198,416)(199,413)(200,414)
(201,419)(202,420)(203,417)(204,418)(205,423)(206,424)(207,421)(208,422)
(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)(216,430);;
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)
(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)(224,240)
(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)(248,252)
(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)(260,276)
(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)(284,288)
(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)(296,312)
(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)(320,324)
(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)(332,348)
(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)(356,360)
(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)(368,384)
(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)(392,396)
(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)(404,420)
(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)(428,432);;
s4 := (  1,109)(  2,110)(  3,111)(  4,112)(  5,117)(  6,118)(  7,119)(  8,120)
(  9,113)( 10,114)( 11,115)( 12,116)( 13,133)( 14,134)( 15,135)( 16,136)
( 17,141)( 18,142)( 19,143)( 20,144)( 21,137)( 22,138)( 23,139)( 24,140)
( 25,121)( 26,122)( 27,123)( 28,124)( 29,129)( 30,130)( 31,131)( 32,132)
( 33,125)( 34,126)( 35,127)( 36,128)( 37,145)( 38,146)( 39,147)( 40,148)
( 41,153)( 42,154)( 43,155)( 44,156)( 45,149)( 46,150)( 47,151)( 48,152)
( 49,169)( 50,170)( 51,171)( 52,172)( 53,177)( 54,178)( 55,179)( 56,180)
( 57,173)( 58,174)( 59,175)( 60,176)( 61,157)( 62,158)( 63,159)( 64,160)
( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)( 72,164)
( 73,181)( 74,182)( 75,183)( 76,184)( 77,189)( 78,190)( 79,191)( 80,192)
( 81,185)( 82,186)( 83,187)( 84,188)( 85,205)( 86,206)( 87,207)( 88,208)
( 89,213)( 90,214)( 91,215)( 92,216)( 93,209)( 94,210)( 95,211)( 96,212)
( 97,193)( 98,194)( 99,195)(100,196)(101,201)(102,202)(103,203)(104,204)
(105,197)(106,198)(107,199)(108,200)(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);;
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, 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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(432)!(  1,219)(  2,220)(  3,217)(  4,218)(  5,223)(  6,224)(  7,221)
(  8,222)(  9,227)( 10,228)( 11,225)( 12,226)( 13,231)( 14,232)( 15,229)
( 16,230)( 17,235)( 18,236)( 19,233)( 20,234)( 21,239)( 22,240)( 23,237)
( 24,238)( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)
( 32,246)( 33,251)( 34,252)( 35,249)( 36,250)( 37,255)( 38,256)( 39,253)
( 40,254)( 41,259)( 42,260)( 43,257)( 44,258)( 45,263)( 46,264)( 47,261)
( 48,262)( 49,267)( 50,268)( 51,265)( 52,266)( 53,271)( 54,272)( 55,269)
( 56,270)( 57,275)( 58,276)( 59,273)( 60,274)( 61,279)( 62,280)( 63,277)
( 64,278)( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)
( 72,286)( 73,291)( 74,292)( 75,289)( 76,290)( 77,295)( 78,296)( 79,293)
( 80,294)( 81,299)( 82,300)( 83,297)( 84,298)( 85,303)( 86,304)( 87,301)
( 88,302)( 89,307)( 90,308)( 91,305)( 92,306)( 93,311)( 94,312)( 95,309)
( 96,310)( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)
(104,318)(105,323)(106,324)(107,321)(108,322)(109,327)(110,328)(111,325)
(112,326)(113,331)(114,332)(115,329)(116,330)(117,335)(118,336)(119,333)
(120,334)(121,339)(122,340)(123,337)(124,338)(125,343)(126,344)(127,341)
(128,342)(129,347)(130,348)(131,345)(132,346)(133,351)(134,352)(135,349)
(136,350)(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)
(144,358)(145,363)(146,364)(147,361)(148,362)(149,367)(150,368)(151,365)
(152,366)(153,371)(154,372)(155,369)(156,370)(157,375)(158,376)(159,373)
(160,374)(161,379)(162,380)(163,377)(164,378)(165,383)(166,384)(167,381)
(168,382)(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)
(176,390)(177,395)(178,396)(179,393)(180,394)(181,399)(182,400)(183,397)
(184,398)(185,403)(186,404)(187,401)(188,402)(189,407)(190,408)(191,405)
(192,406)(193,411)(194,412)(195,409)(196,410)(197,415)(198,416)(199,413)
(200,414)(201,419)(202,420)(203,417)(204,418)(205,423)(206,424)(207,421)
(208,422)(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)
(216,430);
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)(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)
(224,240)(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)
(248,252)(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)
(260,276)(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)
(284,288)(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)
(296,312)(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)
(320,324)(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)
(332,348)(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)
(356,360)(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)
(368,384)(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)
(392,396)(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)
(404,420)(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)
(428,432);
s4 := Sym(432)!(  1,109)(  2,110)(  3,111)(  4,112)(  5,117)(  6,118)(  7,119)
(  8,120)(  9,113)( 10,114)( 11,115)( 12,116)( 13,133)( 14,134)( 15,135)
( 16,136)( 17,141)( 18,142)( 19,143)( 20,144)( 21,137)( 22,138)( 23,139)
( 24,140)( 25,121)( 26,122)( 27,123)( 28,124)( 29,129)( 30,130)( 31,131)
( 32,132)( 33,125)( 34,126)( 35,127)( 36,128)( 37,145)( 38,146)( 39,147)
( 40,148)( 41,153)( 42,154)( 43,155)( 44,156)( 45,149)( 46,150)( 47,151)
( 48,152)( 49,169)( 50,170)( 51,171)( 52,172)( 53,177)( 54,178)( 55,179)
( 56,180)( 57,173)( 58,174)( 59,175)( 60,176)( 61,157)( 62,158)( 63,159)
( 64,160)( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)
( 72,164)( 73,181)( 74,182)( 75,183)( 76,184)( 77,189)( 78,190)( 79,191)
( 80,192)( 81,185)( 82,186)( 83,187)( 84,188)( 85,205)( 86,206)( 87,207)
( 88,208)( 89,213)( 90,214)( 91,215)( 92,216)( 93,209)( 94,210)( 95,211)
( 96,212)( 97,193)( 98,194)( 99,195)(100,196)(101,201)(102,202)(103,203)
(104,204)(105,197)(106,198)(107,199)(108,200)(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);
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, 
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 >;
References : None.
to this polytope