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Polytope of Type {9,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,4,12}*1728
if this polytope has a name.
Group : SmallGroup(1728,30229)
Rank : 4
Schlafli Type : {9,4,12}
Number of vertices, edges, etc : 18, 36, 48, 12
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 : {9,4,6}*864
   3-fold quotients : {9,4,4}*576b, {3,4,12}*576
   4-fold quotients : {9,2,12}*432
   6-fold quotients : {9,4,2}*288, {3,4,6}*288
   8-fold quotients : {9,2,6}*216
   9-fold quotients : {3,4,4}*192b
   12-fold quotients : {9,2,4}*144, {9,4,2}*144, {3,2,12}*144
   16-fold quotients : {9,2,3}*108
   18-fold quotients : {3,4,2}*96
   24-fold quotients : {9,2,2}*72, {3,2,6}*72
   36-fold quotients : {3,2,4}*48, {3,4,2}*48
   48-fold quotients : {3,2,3}*36
   72-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  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, 81)
( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 73)
( 46, 74)( 47, 76)( 48, 75)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)
( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61,105)
( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)( 68,103)( 69, 97)
( 70, 98)( 71,100)( 72, 99)(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)(145,189)(146,190)(147,192)(148,191)(149,185)(150,186)
(151,188)(152,187)(153,181)(154,182)(155,184)(156,183)(157,201)(158,202)
(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)(166,194)
(167,196)(168,195)(169,213)(170,214)(171,216)(172,215)(173,209)(174,210)
(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(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)(253,297)(254,298)(255,300)
(256,299)(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)
(264,291)(265,309)(266,310)(267,312)(268,311)(269,305)(270,306)(271,308)
(272,307)(273,301)(274,302)(275,304)(276,303)(277,321)(278,322)(279,324)
(280,323)(281,317)(282,318)(283,320)(284,319)(285,313)(286,314)(287,316)
(288,315)(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)
(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)(368,403)
(369,397)(370,398)(371,400)(372,399)(373,417)(374,418)(375,420)(376,419)
(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)(384,411)
(385,429)(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)(392,427)
(393,421)(394,422)(395,424)(396,423);;
s1 := (  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, 49)( 14, 52)( 15, 51)( 16, 50)
( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 21, 53)( 22, 56)( 23, 55)( 24, 54)
( 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, 81)( 74, 84)( 75, 83)( 76, 82)
( 78, 80)( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92)( 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)(121,157)
(122,160)(123,159)(124,158)(125,165)(126,168)(127,167)(128,166)(129,161)
(130,164)(131,163)(132,162)(133,169)(134,172)(135,171)(136,170)(137,177)
(138,180)(139,179)(140,178)(141,173)(142,176)(143,175)(144,174)(181,189)
(182,192)(183,191)(184,190)(186,188)(193,201)(194,204)(195,203)(196,202)
(198,200)(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)(229,265)(230,268)(231,267)(232,266)(233,273)(234,276)
(235,275)(236,274)(237,269)(238,272)(239,271)(240,270)(241,277)(242,280)
(243,279)(244,278)(245,285)(246,288)(247,287)(248,286)(249,281)(250,284)
(251,283)(252,282)(289,297)(290,300)(291,299)(292,298)(294,296)(301,309)
(302,312)(303,311)(304,310)(306,308)(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)(337,373)(338,376)(339,375)
(340,374)(341,381)(342,384)(343,383)(344,382)(345,377)(346,380)(347,379)
(348,378)(349,385)(350,388)(351,387)(352,386)(353,393)(354,396)(355,395)
(356,394)(357,389)(358,392)(359,391)(360,390)(397,405)(398,408)(399,407)
(400,406)(402,404)(409,417)(410,420)(411,419)(412,418)(414,416)(421,429)
(422,432)(423,431)(424,430)(426,428);;
s2 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 26)( 14, 25)
( 15, 28)( 16, 27)( 17, 30)( 18, 29)( 19, 32)( 20, 31)( 21, 34)( 22, 33)
( 23, 36)( 24, 35)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 66)( 54, 65)( 55, 68)( 56, 67)
( 57, 70)( 58, 69)( 59, 72)( 60, 71)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89,102)( 90,101)
( 91,104)( 92,103)( 93,106)( 94,105)( 95,108)( 96,107)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,134)(122,133)(123,136)(124,135)
(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)(132,143)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,170)(158,169)
(159,172)(160,171)(161,174)(162,173)(163,176)(164,175)(165,178)(166,177)
(167,180)(168,179)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,206)(194,205)(195,208)(196,207)(197,210)(198,209)(199,212)(200,211)
(201,214)(202,213)(203,216)(204,215)(217,326)(218,325)(219,328)(220,327)
(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)(228,335)
(229,350)(230,349)(231,352)(232,351)(233,354)(234,353)(235,356)(236,355)
(237,358)(238,357)(239,360)(240,359)(241,338)(242,337)(243,340)(244,339)
(245,342)(246,341)(247,344)(248,343)(249,346)(250,345)(251,348)(252,347)
(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)(260,367)
(261,370)(262,369)(263,372)(264,371)(265,386)(266,385)(267,388)(268,387)
(269,390)(270,389)(271,392)(272,391)(273,394)(274,393)(275,396)(276,395)
(277,374)(278,373)(279,376)(280,375)(281,378)(282,377)(283,380)(284,379)
(285,382)(286,381)(287,384)(288,383)(289,398)(290,397)(291,400)(292,399)
(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)(300,407)
(301,422)(302,421)(303,424)(304,423)(305,426)(306,425)(307,428)(308,427)
(309,430)(310,429)(311,432)(312,431)(313,410)(314,409)(315,412)(316,411)
(317,414)(318,413)(319,416)(320,415)(321,418)(322,417)(323,420)(324,419);;
s3 := (  1,229)(  2,230)(  3,231)(  4,232)(  5,233)(  6,234)(  7,235)(  8,236)
(  9,237)( 10,238)( 11,239)( 12,240)( 13,217)( 14,218)( 15,219)( 16,220)
( 17,221)( 18,222)( 19,223)( 20,224)( 21,225)( 22,226)( 23,227)( 24,228)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,249)( 34,250)( 35,251)( 36,252)( 37,265)( 38,266)( 39,267)( 40,268)
( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)( 48,276)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)( 56,260)
( 57,261)( 58,262)( 59,263)( 60,264)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,301)( 74,302)( 75,303)( 76,304)( 77,305)( 78,306)( 79,307)( 80,308)
( 81,309)( 82,310)( 83,311)( 84,312)( 85,289)( 86,290)( 87,291)( 88,292)
( 89,293)( 90,294)( 91,295)( 92,296)( 93,297)( 94,298)( 95,299)( 96,300)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,337)(110,338)(111,339)(112,340)
(113,341)(114,342)(115,343)(116,344)(117,345)(118,346)(119,347)(120,348)
(121,325)(122,326)(123,327)(124,328)(125,329)(126,330)(127,331)(128,332)
(129,333)(130,334)(131,335)(132,336)(133,349)(134,350)(135,351)(136,352)
(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)
(145,373)(146,374)(147,375)(148,376)(149,377)(150,378)(151,379)(152,380)
(153,381)(154,382)(155,383)(156,384)(157,361)(158,362)(159,363)(160,364)
(161,365)(162,366)(163,367)(164,368)(165,369)(166,370)(167,371)(168,372)
(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)(176,392)
(177,393)(178,394)(179,395)(180,396)(181,409)(182,410)(183,411)(184,412)
(185,413)(186,414)(187,415)(188,416)(189,417)(190,418)(191,419)(192,420)
(193,397)(194,398)(195,399)(196,400)(197,401)(198,402)(199,403)(200,404)
(201,405)(202,406)(203,407)(204,408)(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]);;
 
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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)!(  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, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)( 44, 79)
( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 93)( 50, 94)( 51, 96)( 52, 95)
( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)
( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)( 68,103)
( 69, 97)( 70, 98)( 71,100)( 72, 99)(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)(145,189)(146,190)(147,192)(148,191)(149,185)
(150,186)(151,188)(152,187)(153,181)(154,182)(155,184)(156,183)(157,201)
(158,202)(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)
(166,194)(167,196)(168,195)(169,213)(170,214)(171,216)(172,215)(173,209)
(174,210)(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(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)(253,297)(254,298)
(255,300)(256,299)(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)
(263,292)(264,291)(265,309)(266,310)(267,312)(268,311)(269,305)(270,306)
(271,308)(272,307)(273,301)(274,302)(275,304)(276,303)(277,321)(278,322)
(279,324)(280,323)(281,317)(282,318)(283,320)(284,319)(285,313)(286,314)
(287,316)(288,315)(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)(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)
(368,403)(369,397)(370,398)(371,400)(372,399)(373,417)(374,418)(375,420)
(376,419)(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)
(384,411)(385,429)(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)
(392,427)(393,421)(394,422)(395,424)(396,423);
s1 := 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, 49)( 14, 52)( 15, 51)
( 16, 50)( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 21, 53)( 22, 56)( 23, 55)
( 24, 54)( 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, 81)( 74, 84)( 75, 83)
( 76, 82)( 78, 80)( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92)( 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)
(121,157)(122,160)(123,159)(124,158)(125,165)(126,168)(127,167)(128,166)
(129,161)(130,164)(131,163)(132,162)(133,169)(134,172)(135,171)(136,170)
(137,177)(138,180)(139,179)(140,178)(141,173)(142,176)(143,175)(144,174)
(181,189)(182,192)(183,191)(184,190)(186,188)(193,201)(194,204)(195,203)
(196,202)(198,200)(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)(229,265)(230,268)(231,267)(232,266)(233,273)
(234,276)(235,275)(236,274)(237,269)(238,272)(239,271)(240,270)(241,277)
(242,280)(243,279)(244,278)(245,285)(246,288)(247,287)(248,286)(249,281)
(250,284)(251,283)(252,282)(289,297)(290,300)(291,299)(292,298)(294,296)
(301,309)(302,312)(303,311)(304,310)(306,308)(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)(337,373)(338,376)
(339,375)(340,374)(341,381)(342,384)(343,383)(344,382)(345,377)(346,380)
(347,379)(348,378)(349,385)(350,388)(351,387)(352,386)(353,393)(354,396)
(355,395)(356,394)(357,389)(358,392)(359,391)(360,390)(397,405)(398,408)
(399,407)(400,406)(402,404)(409,417)(410,420)(411,419)(412,418)(414,416)
(421,429)(422,432)(423,431)(424,430)(426,428);
s2 := Sym(432)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 26)
( 14, 25)( 15, 28)( 16, 27)( 17, 30)( 18, 29)( 19, 32)( 20, 31)( 21, 34)
( 22, 33)( 23, 36)( 24, 35)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 66)( 54, 65)( 55, 68)
( 56, 67)( 57, 70)( 58, 69)( 59, 72)( 60, 71)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89,102)
( 90,101)( 91,104)( 92,103)( 93,106)( 94,105)( 95,108)( 96,107)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,134)(122,133)(123,136)
(124,135)(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)
(132,143)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,170)
(158,169)(159,172)(160,171)(161,174)(162,173)(163,176)(164,175)(165,178)
(166,177)(167,180)(168,179)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,206)(194,205)(195,208)(196,207)(197,210)(198,209)(199,212)
(200,211)(201,214)(202,213)(203,216)(204,215)(217,326)(218,325)(219,328)
(220,327)(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)
(228,335)(229,350)(230,349)(231,352)(232,351)(233,354)(234,353)(235,356)
(236,355)(237,358)(238,357)(239,360)(240,359)(241,338)(242,337)(243,340)
(244,339)(245,342)(246,341)(247,344)(248,343)(249,346)(250,345)(251,348)
(252,347)(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)
(260,367)(261,370)(262,369)(263,372)(264,371)(265,386)(266,385)(267,388)
(268,387)(269,390)(270,389)(271,392)(272,391)(273,394)(274,393)(275,396)
(276,395)(277,374)(278,373)(279,376)(280,375)(281,378)(282,377)(283,380)
(284,379)(285,382)(286,381)(287,384)(288,383)(289,398)(290,397)(291,400)
(292,399)(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)
(300,407)(301,422)(302,421)(303,424)(304,423)(305,426)(306,425)(307,428)
(308,427)(309,430)(310,429)(311,432)(312,431)(313,410)(314,409)(315,412)
(316,411)(317,414)(318,413)(319,416)(320,415)(321,418)(322,417)(323,420)
(324,419);
s3 := Sym(432)!(  1,229)(  2,230)(  3,231)(  4,232)(  5,233)(  6,234)(  7,235)
(  8,236)(  9,237)( 10,238)( 11,239)( 12,240)( 13,217)( 14,218)( 15,219)
( 16,220)( 17,221)( 18,222)( 19,223)( 20,224)( 21,225)( 22,226)( 23,227)
( 24,228)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,249)( 34,250)( 35,251)( 36,252)( 37,265)( 38,266)( 39,267)
( 40,268)( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)
( 48,276)( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)
( 56,260)( 57,261)( 58,262)( 59,263)( 60,264)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,301)( 74,302)( 75,303)( 76,304)( 77,305)( 78,306)( 79,307)
( 80,308)( 81,309)( 82,310)( 83,311)( 84,312)( 85,289)( 86,290)( 87,291)
( 88,292)( 89,293)( 90,294)( 91,295)( 92,296)( 93,297)( 94,298)( 95,299)
( 96,300)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,337)(110,338)(111,339)
(112,340)(113,341)(114,342)(115,343)(116,344)(117,345)(118,346)(119,347)
(120,348)(121,325)(122,326)(123,327)(124,328)(125,329)(126,330)(127,331)
(128,332)(129,333)(130,334)(131,335)(132,336)(133,349)(134,350)(135,351)
(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)
(144,360)(145,373)(146,374)(147,375)(148,376)(149,377)(150,378)(151,379)
(152,380)(153,381)(154,382)(155,383)(156,384)(157,361)(158,362)(159,363)
(160,364)(161,365)(162,366)(163,367)(164,368)(165,369)(166,370)(167,371)
(168,372)(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)
(176,392)(177,393)(178,394)(179,395)(180,396)(181,409)(182,410)(183,411)
(184,412)(185,413)(186,414)(187,415)(188,416)(189,417)(190,418)(191,419)
(192,420)(193,397)(194,398)(195,399)(196,400)(197,401)(198,402)(199,403)
(200,404)(201,405)(202,406)(203,407)(204,408)(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>;
 
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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