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Polytope of Type {4,6,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,36}*1728b
if this polytope has a name.
Group : SmallGroup(1728,16621)
Rank : 4
Schlafli Type : {4,6,36}
Number of vertices, edges, etc : 4, 12, 108, 36
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 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 : {2,6,36}*864b, {4,6,18}*864b
   3-fold quotients : {4,2,36}*576, {4,6,12}*576b
   4-fold quotients : {4,6,9}*432, {2,6,18}*432b
   6-fold quotients : {2,2,36}*288, {4,2,18}*288, {2,6,12}*288b, {4,6,6}*288c
   8-fold quotients : {2,6,9}*216
   9-fold quotients : {4,2,12}*192
   12-fold quotients : {4,2,9}*144, {2,2,18}*144, {4,6,3}*144, {2,6,6}*144b
   18-fold quotients : {2,2,12}*96, {4,2,6}*96
   24-fold quotients : {2,2,9}*72, {2,6,3}*72
   27-fold quotients : {4,2,4}*64
   36-fold quotients : {4,2,3}*48, {2,2,6}*48
   54-fold quotients : {2,2,4}*32, {4,2,2}*32
   72-fold quotients : {2,2,3}*24
   108-fold quotients : {2,2,2}*16
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 := ( 10, 19)( 11, 20)( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)( 17, 26)
( 18, 27)( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)
( 44, 53)( 45, 54)( 64, 73)( 65, 74)( 66, 75)( 67, 76)( 68, 77)( 69, 78)
( 70, 79)( 71, 80)( 72, 81)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)
( 96,105)( 97,106)( 98,107)( 99,108)(118,127)(119,128)(120,129)(121,130)
(122,131)(123,132)(124,133)(125,134)(126,135)(145,154)(146,155)(147,156)
(148,157)(149,158)(150,159)(151,160)(152,161)(153,162)(172,181)(173,182)
(174,183)(175,184)(176,185)(177,186)(178,187)(179,188)(180,189)(199,208)
(200,209)(201,210)(202,211)(203,212)(204,213)(205,214)(206,215)(207,216)
(217,244)(218,245)(219,246)(220,247)(221,248)(222,249)(223,250)(224,251)
(225,252)(226,262)(227,263)(228,264)(229,265)(230,266)(231,267)(232,268)
(233,269)(234,270)(235,253)(236,254)(237,255)(238,256)(239,257)(240,258)
(241,259)(242,260)(243,261)(271,298)(272,299)(273,300)(274,301)(275,302)
(276,303)(277,304)(278,305)(279,306)(280,316)(281,317)(282,318)(283,319)
(284,320)(285,321)(286,322)(287,323)(288,324)(289,307)(290,308)(291,309)
(292,310)(293,311)(294,312)(295,313)(296,314)(297,315)(325,352)(326,353)
(327,354)(328,355)(329,356)(330,357)(331,358)(332,359)(333,360)(334,370)
(335,371)(336,372)(337,373)(338,374)(339,375)(340,376)(341,377)(342,378)
(343,361)(344,362)(345,363)(346,364)(347,365)(348,366)(349,367)(350,368)
(351,369)(379,406)(380,407)(381,408)(382,409)(383,410)(384,411)(385,412)
(386,413)(387,414)(388,424)(389,425)(390,426)(391,427)(392,428)(393,429)
(394,430)(395,431)(396,432)(397,415)(398,416)(399,417)(400,418)(401,419)
(402,420)(403,421)(404,422)(405,423);;
s2 := (  1, 10)(  2, 12)(  3, 11)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 37)( 29, 39)( 30, 38)
( 31, 45)( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 47, 48)( 49, 54)
( 50, 53)( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)( 60, 70)
( 61, 69)( 62, 68)( 63, 67)( 74, 75)( 76, 81)( 77, 80)( 78, 79)( 82, 91)
( 83, 93)( 84, 92)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)
(101,102)(103,108)(104,107)(105,106)(109,172)(110,174)(111,173)(112,180)
(113,179)(114,178)(115,177)(116,176)(117,175)(118,163)(119,165)(120,164)
(121,171)(122,170)(123,169)(124,168)(125,167)(126,166)(127,181)(128,183)
(129,182)(130,189)(131,188)(132,187)(133,186)(134,185)(135,184)(136,199)
(137,201)(138,200)(139,207)(140,206)(141,205)(142,204)(143,203)(144,202)
(145,190)(146,192)(147,191)(148,198)(149,197)(150,196)(151,195)(152,194)
(153,193)(154,208)(155,210)(156,209)(157,216)(158,215)(159,214)(160,213)
(161,212)(162,211)(217,226)(218,228)(219,227)(220,234)(221,233)(222,232)
(223,231)(224,230)(225,229)(236,237)(238,243)(239,242)(240,241)(244,253)
(245,255)(246,254)(247,261)(248,260)(249,259)(250,258)(251,257)(252,256)
(263,264)(265,270)(266,269)(267,268)(271,280)(272,282)(273,281)(274,288)
(275,287)(276,286)(277,285)(278,284)(279,283)(290,291)(292,297)(293,296)
(294,295)(298,307)(299,309)(300,308)(301,315)(302,314)(303,313)(304,312)
(305,311)(306,310)(317,318)(319,324)(320,323)(321,322)(325,388)(326,390)
(327,389)(328,396)(329,395)(330,394)(331,393)(332,392)(333,391)(334,379)
(335,381)(336,380)(337,387)(338,386)(339,385)(340,384)(341,383)(342,382)
(343,397)(344,399)(345,398)(346,405)(347,404)(348,403)(349,402)(350,401)
(351,400)(352,415)(353,417)(354,416)(355,423)(356,422)(357,421)(358,420)
(359,419)(360,418)(361,406)(362,408)(363,407)(364,414)(365,413)(366,412)
(367,411)(368,410)(369,409)(370,424)(371,426)(372,425)(373,432)(374,431)
(375,430)(376,429)(377,428)(378,427);;
s3 := (  1,112)(  2,114)(  3,113)(  4,109)(  5,111)(  6,110)(  7,117)(  8,116)
(  9,115)( 10,130)( 11,132)( 12,131)( 13,127)( 14,129)( 15,128)( 16,135)
( 17,134)( 18,133)( 19,121)( 20,123)( 21,122)( 22,118)( 23,120)( 24,119)
( 25,126)( 26,125)( 27,124)( 28,139)( 29,141)( 30,140)( 31,136)( 32,138)
( 33,137)( 34,144)( 35,143)( 36,142)( 37,157)( 38,159)( 39,158)( 40,154)
( 41,156)( 42,155)( 43,162)( 44,161)( 45,160)( 46,148)( 47,150)( 48,149)
( 49,145)( 50,147)( 51,146)( 52,153)( 53,152)( 54,151)( 55,166)( 56,168)
( 57,167)( 58,163)( 59,165)( 60,164)( 61,171)( 62,170)( 63,169)( 64,184)
( 65,186)( 66,185)( 67,181)( 68,183)( 69,182)( 70,189)( 71,188)( 72,187)
( 73,175)( 74,177)( 75,176)( 76,172)( 77,174)( 78,173)( 79,180)( 80,179)
( 81,178)( 82,193)( 83,195)( 84,194)( 85,190)( 86,192)( 87,191)( 88,198)
( 89,197)( 90,196)( 91,211)( 92,213)( 93,212)( 94,208)( 95,210)( 96,209)
( 97,216)( 98,215)( 99,214)(100,202)(101,204)(102,203)(103,199)(104,201)
(105,200)(106,207)(107,206)(108,205)(217,328)(218,330)(219,329)(220,325)
(221,327)(222,326)(223,333)(224,332)(225,331)(226,346)(227,348)(228,347)
(229,343)(230,345)(231,344)(232,351)(233,350)(234,349)(235,337)(236,339)
(237,338)(238,334)(239,336)(240,335)(241,342)(242,341)(243,340)(244,355)
(245,357)(246,356)(247,352)(248,354)(249,353)(250,360)(251,359)(252,358)
(253,373)(254,375)(255,374)(256,370)(257,372)(258,371)(259,378)(260,377)
(261,376)(262,364)(263,366)(264,365)(265,361)(266,363)(267,362)(268,369)
(269,368)(270,367)(271,382)(272,384)(273,383)(274,379)(275,381)(276,380)
(277,387)(278,386)(279,385)(280,400)(281,402)(282,401)(283,397)(284,399)
(285,398)(286,405)(287,404)(288,403)(289,391)(290,393)(291,392)(292,388)
(293,390)(294,389)(295,396)(296,395)(297,394)(298,409)(299,411)(300,410)
(301,406)(302,408)(303,407)(304,414)(305,413)(306,412)(307,427)(308,429)
(309,428)(310,424)(311,426)(312,425)(313,432)(314,431)(315,430)(316,418)
(317,420)(318,419)(319,415)(320,417)(321,416)(322,423)(323,422)(324,421);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!( 10, 19)( 11, 20)( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)
( 17, 26)( 18, 27)( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)
( 43, 52)( 44, 53)( 45, 54)( 64, 73)( 65, 74)( 66, 75)( 67, 76)( 68, 77)
( 69, 78)( 70, 79)( 71, 80)( 72, 81)( 91,100)( 92,101)( 93,102)( 94,103)
( 95,104)( 96,105)( 97,106)( 98,107)( 99,108)(118,127)(119,128)(120,129)
(121,130)(122,131)(123,132)(124,133)(125,134)(126,135)(145,154)(146,155)
(147,156)(148,157)(149,158)(150,159)(151,160)(152,161)(153,162)(172,181)
(173,182)(174,183)(175,184)(176,185)(177,186)(178,187)(179,188)(180,189)
(199,208)(200,209)(201,210)(202,211)(203,212)(204,213)(205,214)(206,215)
(207,216)(217,244)(218,245)(219,246)(220,247)(221,248)(222,249)(223,250)
(224,251)(225,252)(226,262)(227,263)(228,264)(229,265)(230,266)(231,267)
(232,268)(233,269)(234,270)(235,253)(236,254)(237,255)(238,256)(239,257)
(240,258)(241,259)(242,260)(243,261)(271,298)(272,299)(273,300)(274,301)
(275,302)(276,303)(277,304)(278,305)(279,306)(280,316)(281,317)(282,318)
(283,319)(284,320)(285,321)(286,322)(287,323)(288,324)(289,307)(290,308)
(291,309)(292,310)(293,311)(294,312)(295,313)(296,314)(297,315)(325,352)
(326,353)(327,354)(328,355)(329,356)(330,357)(331,358)(332,359)(333,360)
(334,370)(335,371)(336,372)(337,373)(338,374)(339,375)(340,376)(341,377)
(342,378)(343,361)(344,362)(345,363)(346,364)(347,365)(348,366)(349,367)
(350,368)(351,369)(379,406)(380,407)(381,408)(382,409)(383,410)(384,411)
(385,412)(386,413)(387,414)(388,424)(389,425)(390,426)(391,427)(392,428)
(393,429)(394,430)(395,431)(396,432)(397,415)(398,416)(399,417)(400,418)
(401,419)(402,420)(403,421)(404,422)(405,423);
s2 := Sym(432)!(  1, 10)(  2, 12)(  3, 11)(  4, 18)(  5, 17)(  6, 16)(  7, 15)
(  8, 14)(  9, 13)( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 37)( 29, 39)
( 30, 38)( 31, 45)( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 47, 48)
( 49, 54)( 50, 53)( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)
( 60, 70)( 61, 69)( 62, 68)( 63, 67)( 74, 75)( 76, 81)( 77, 80)( 78, 79)
( 82, 91)( 83, 93)( 84, 92)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)
( 90, 94)(101,102)(103,108)(104,107)(105,106)(109,172)(110,174)(111,173)
(112,180)(113,179)(114,178)(115,177)(116,176)(117,175)(118,163)(119,165)
(120,164)(121,171)(122,170)(123,169)(124,168)(125,167)(126,166)(127,181)
(128,183)(129,182)(130,189)(131,188)(132,187)(133,186)(134,185)(135,184)
(136,199)(137,201)(138,200)(139,207)(140,206)(141,205)(142,204)(143,203)
(144,202)(145,190)(146,192)(147,191)(148,198)(149,197)(150,196)(151,195)
(152,194)(153,193)(154,208)(155,210)(156,209)(157,216)(158,215)(159,214)
(160,213)(161,212)(162,211)(217,226)(218,228)(219,227)(220,234)(221,233)
(222,232)(223,231)(224,230)(225,229)(236,237)(238,243)(239,242)(240,241)
(244,253)(245,255)(246,254)(247,261)(248,260)(249,259)(250,258)(251,257)
(252,256)(263,264)(265,270)(266,269)(267,268)(271,280)(272,282)(273,281)
(274,288)(275,287)(276,286)(277,285)(278,284)(279,283)(290,291)(292,297)
(293,296)(294,295)(298,307)(299,309)(300,308)(301,315)(302,314)(303,313)
(304,312)(305,311)(306,310)(317,318)(319,324)(320,323)(321,322)(325,388)
(326,390)(327,389)(328,396)(329,395)(330,394)(331,393)(332,392)(333,391)
(334,379)(335,381)(336,380)(337,387)(338,386)(339,385)(340,384)(341,383)
(342,382)(343,397)(344,399)(345,398)(346,405)(347,404)(348,403)(349,402)
(350,401)(351,400)(352,415)(353,417)(354,416)(355,423)(356,422)(357,421)
(358,420)(359,419)(360,418)(361,406)(362,408)(363,407)(364,414)(365,413)
(366,412)(367,411)(368,410)(369,409)(370,424)(371,426)(372,425)(373,432)
(374,431)(375,430)(376,429)(377,428)(378,427);
s3 := Sym(432)!(  1,112)(  2,114)(  3,113)(  4,109)(  5,111)(  6,110)(  7,117)
(  8,116)(  9,115)( 10,130)( 11,132)( 12,131)( 13,127)( 14,129)( 15,128)
( 16,135)( 17,134)( 18,133)( 19,121)( 20,123)( 21,122)( 22,118)( 23,120)
( 24,119)( 25,126)( 26,125)( 27,124)( 28,139)( 29,141)( 30,140)( 31,136)
( 32,138)( 33,137)( 34,144)( 35,143)( 36,142)( 37,157)( 38,159)( 39,158)
( 40,154)( 41,156)( 42,155)( 43,162)( 44,161)( 45,160)( 46,148)( 47,150)
( 48,149)( 49,145)( 50,147)( 51,146)( 52,153)( 53,152)( 54,151)( 55,166)
( 56,168)( 57,167)( 58,163)( 59,165)( 60,164)( 61,171)( 62,170)( 63,169)
( 64,184)( 65,186)( 66,185)( 67,181)( 68,183)( 69,182)( 70,189)( 71,188)
( 72,187)( 73,175)( 74,177)( 75,176)( 76,172)( 77,174)( 78,173)( 79,180)
( 80,179)( 81,178)( 82,193)( 83,195)( 84,194)( 85,190)( 86,192)( 87,191)
( 88,198)( 89,197)( 90,196)( 91,211)( 92,213)( 93,212)( 94,208)( 95,210)
( 96,209)( 97,216)( 98,215)( 99,214)(100,202)(101,204)(102,203)(103,199)
(104,201)(105,200)(106,207)(107,206)(108,205)(217,328)(218,330)(219,329)
(220,325)(221,327)(222,326)(223,333)(224,332)(225,331)(226,346)(227,348)
(228,347)(229,343)(230,345)(231,344)(232,351)(233,350)(234,349)(235,337)
(236,339)(237,338)(238,334)(239,336)(240,335)(241,342)(242,341)(243,340)
(244,355)(245,357)(246,356)(247,352)(248,354)(249,353)(250,360)(251,359)
(252,358)(253,373)(254,375)(255,374)(256,370)(257,372)(258,371)(259,378)
(260,377)(261,376)(262,364)(263,366)(264,365)(265,361)(266,363)(267,362)
(268,369)(269,368)(270,367)(271,382)(272,384)(273,383)(274,379)(275,381)
(276,380)(277,387)(278,386)(279,385)(280,400)(281,402)(282,401)(283,397)
(284,399)(285,398)(286,405)(287,404)(288,403)(289,391)(290,393)(291,392)
(292,388)(293,390)(294,389)(295,396)(296,395)(297,394)(298,409)(299,411)
(300,410)(301,406)(302,408)(303,407)(304,414)(305,413)(306,412)(307,427)
(308,429)(309,428)(310,424)(311,426)(312,425)(313,432)(314,431)(315,430)
(316,418)(317,420)(318,419)(319,415)(320,417)(321,416)(322,423)(323,422)
(324,421);
poly := sub<Sym(432)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope