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Polytope of Type {4,12,9}

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