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Polytope of Type {9,6,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,6,16}*1728
if this polytope has a name.
Group : SmallGroup(1728,5288)
Rank : 4
Schlafli Type : {9,6,16}
Number of vertices, edges, etc : 9, 27, 48, 16
Order of s0s1s2s3 : 144
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 : {9,6,8}*864
   3-fold quotients : {9,2,16}*576, {3,6,16}*576
   4-fold quotients : {9,6,4}*432
   6-fold quotients : {9,2,8}*288, {3,6,8}*288
   8-fold quotients : {9,6,2}*216
   9-fold quotients : {3,2,16}*192
   12-fold quotients : {9,2,4}*144, {3,6,4}*144
   18-fold quotients : {3,2,8}*96
   24-fold quotients : {9,2,2}*72, {3,6,2}*72
   36-fold quotients : {3,2,4}*48
   72-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 10, 21)( 11, 20)( 12, 19)( 13, 27)
( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)( 43, 51)
( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)( 65, 74)
( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 83, 84)
( 85, 88)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,100)( 94,108)( 95,107)
( 96,106)( 97,105)( 98,104)( 99,103)(110,111)(112,115)(113,117)(114,116)
(118,129)(119,128)(120,127)(121,135)(122,134)(123,133)(124,132)(125,131)
(126,130)(137,138)(139,142)(140,144)(141,143)(145,156)(146,155)(147,154)
(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(164,165)(166,169)
(167,171)(168,170)(172,183)(173,182)(174,181)(175,189)(176,188)(177,187)
(178,186)(179,185)(180,184)(191,192)(193,196)(194,198)(195,197)(199,210)
(200,209)(201,208)(202,216)(203,215)(204,214)(205,213)(206,212)(207,211)
(218,219)(220,223)(221,225)(222,224)(226,237)(227,236)(228,235)(229,243)
(230,242)(231,241)(232,240)(233,239)(234,238)(245,246)(247,250)(248,252)
(249,251)(253,264)(254,263)(255,262)(256,270)(257,269)(258,268)(259,267)
(260,266)(261,265)(272,273)(274,277)(275,279)(276,278)(280,291)(281,290)
(282,289)(283,297)(284,296)(285,295)(286,294)(287,293)(288,292)(299,300)
(301,304)(302,306)(303,305)(307,318)(308,317)(309,316)(310,324)(311,323)
(312,322)(313,321)(314,320)(315,319)(326,327)(328,331)(329,333)(330,332)
(334,345)(335,344)(336,343)(337,351)(338,350)(339,349)(340,348)(341,347)
(342,346)(353,354)(355,358)(356,360)(357,359)(361,372)(362,371)(363,370)
(364,378)(365,377)(366,376)(367,375)(368,374)(369,373)(380,381)(382,385)
(383,387)(384,386)(388,399)(389,398)(390,397)(391,405)(392,404)(393,403)
(394,402)(395,401)(396,400)(407,408)(409,412)(410,414)(411,413)(415,426)
(416,425)(417,424)(418,432)(419,431)(420,430)(421,429)(422,428)(423,427);;
s1 := (  1, 13)(  2, 15)(  3, 14)(  4, 10)(  5, 12)(  6, 11)(  7, 16)(  8, 18)
(  9, 17)( 19, 24)( 20, 23)( 21, 22)( 25, 27)( 28, 40)( 29, 42)( 30, 41)
( 31, 37)( 32, 39)( 33, 38)( 34, 43)( 35, 45)( 36, 44)( 46, 51)( 47, 50)
( 48, 49)( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)
( 61, 70)( 62, 72)( 63, 71)( 73, 78)( 74, 77)( 75, 76)( 79, 81)( 82, 94)
( 83, 96)( 84, 95)( 85, 91)( 86, 93)( 87, 92)( 88, 97)( 89, 99)( 90, 98)
(100,105)(101,104)(102,103)(106,108)(109,121)(110,123)(111,122)(112,118)
(113,120)(114,119)(115,124)(116,126)(117,125)(127,132)(128,131)(129,130)
(133,135)(136,148)(137,150)(138,149)(139,145)(140,147)(141,146)(142,151)
(143,153)(144,152)(154,159)(155,158)(156,157)(160,162)(163,175)(164,177)
(165,176)(166,172)(167,174)(168,173)(169,178)(170,180)(171,179)(181,186)
(182,185)(183,184)(187,189)(190,202)(191,204)(192,203)(193,199)(194,201)
(195,200)(196,205)(197,207)(198,206)(208,213)(209,212)(210,211)(214,216)
(217,229)(218,231)(219,230)(220,226)(221,228)(222,227)(223,232)(224,234)
(225,233)(235,240)(236,239)(237,238)(241,243)(244,256)(245,258)(246,257)
(247,253)(248,255)(249,254)(250,259)(251,261)(252,260)(262,267)(263,266)
(264,265)(268,270)(271,283)(272,285)(273,284)(274,280)(275,282)(276,281)
(277,286)(278,288)(279,287)(289,294)(290,293)(291,292)(295,297)(298,310)
(299,312)(300,311)(301,307)(302,309)(303,308)(304,313)(305,315)(306,314)
(316,321)(317,320)(318,319)(322,324)(325,337)(326,339)(327,338)(328,334)
(329,336)(330,335)(331,340)(332,342)(333,341)(343,348)(344,347)(345,346)
(349,351)(352,364)(353,366)(354,365)(355,361)(356,363)(357,362)(358,367)
(359,369)(360,368)(370,375)(371,374)(372,373)(376,378)(379,391)(380,393)
(381,392)(382,388)(383,390)(384,389)(385,394)(386,396)(387,395)(397,402)
(398,401)(399,400)(403,405)(406,418)(407,420)(408,419)(409,415)(410,417)
(411,416)(412,421)(413,423)(414,422)(424,429)(425,428)(426,427)(430,432);;
s2 := (  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)
( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)
( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)( 60, 90)
( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)( 68, 98)
( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)( 76,106)
( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(109,163)(110,164)(111,165)
(112,169)(113,170)(114,171)(115,166)(116,167)(117,168)(118,172)(119,173)
(120,174)(121,178)(122,179)(123,180)(124,175)(125,176)(126,177)(127,181)
(128,182)(129,183)(130,187)(131,188)(132,189)(133,184)(134,185)(135,186)
(136,190)(137,191)(138,192)(139,196)(140,197)(141,198)(142,193)(143,194)
(144,195)(145,199)(146,200)(147,201)(148,205)(149,206)(150,207)(151,202)
(152,203)(153,204)(154,208)(155,209)(156,210)(157,214)(158,215)(159,216)
(160,211)(161,212)(162,213)(217,325)(218,326)(219,327)(220,331)(221,332)
(222,333)(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)(229,340)
(230,341)(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)(237,345)
(238,349)(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)(245,353)
(246,354)(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)(253,361)
(254,362)(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)(261,366)
(262,370)(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)(269,374)
(270,375)(271,406)(272,407)(273,408)(274,412)(275,413)(276,414)(277,409)
(278,410)(279,411)(280,415)(281,416)(282,417)(283,421)(284,422)(285,423)
(286,418)(287,419)(288,420)(289,424)(290,425)(291,426)(292,430)(293,431)
(294,432)(295,427)(296,428)(297,429)(298,379)(299,380)(300,381)(301,385)
(302,386)(303,387)(304,382)(305,383)(306,384)(307,388)(308,389)(309,390)
(310,394)(311,395)(312,396)(313,391)(314,392)(315,393)(316,397)(317,398)
(318,399)(319,403)(320,404)(321,405)(322,400)(323,401)(324,402);;
s3 := (  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)( 55,298)( 56,299)
( 57,300)( 58,301)( 59,302)( 60,303)( 61,304)( 62,305)( 63,306)( 64,307)
( 65,308)( 66,309)( 67,310)( 68,311)( 69,312)( 70,313)( 71,314)( 72,315)
( 73,316)( 74,317)( 75,318)( 76,319)( 77,320)( 78,321)( 79,322)( 80,323)
( 81,324)( 82,271)( 83,272)( 84,273)( 85,274)( 86,275)( 87,276)( 88,277)
( 89,278)( 90,279)( 91,280)( 92,281)( 93,282)( 94,283)( 95,284)( 96,285)
( 97,286)( 98,287)( 99,288)(100,289)(101,290)(102,291)(103,292)(104,293)
(105,294)(106,295)(107,296)(108,297)(109,379)(110,380)(111,381)(112,382)
(113,383)(114,384)(115,385)(116,386)(117,387)(118,388)(119,389)(120,390)
(121,391)(122,392)(123,393)(124,394)(125,395)(126,396)(127,397)(128,398)
(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)
(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)(144,414)
(145,415)(146,416)(147,417)(148,418)(149,419)(150,420)(151,421)(152,422)
(153,423)(154,424)(155,425)(156,426)(157,427)(158,428)(159,429)(160,430)
(161,431)(162,432)(163,325)(164,326)(165,327)(166,328)(167,329)(168,330)
(169,331)(170,332)(171,333)(172,334)(173,335)(174,336)(175,337)(176,338)
(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,345)(184,346)
(185,347)(186,348)(187,349)(188,350)(189,351)(190,352)(191,353)(192,354)
(193,355)(194,356)(195,357)(196,358)(197,359)(198,360)(199,361)(200,362)
(201,363)(202,364)(203,365)(204,366)(205,367)(206,368)(207,369)(208,370)
(209,371)(210,372)(211,373)(212,374)(213,375)(214,376)(215,377)(216,378);;
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*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 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*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(432)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 10, 21)( 11, 20)( 12, 19)
( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)
( 32, 36)( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)
( 43, 51)( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)
( 65, 74)( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)
( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,100)( 94,108)
( 95,107)( 96,106)( 97,105)( 98,104)( 99,103)(110,111)(112,115)(113,117)
(114,116)(118,129)(119,128)(120,127)(121,135)(122,134)(123,133)(124,132)
(125,131)(126,130)(137,138)(139,142)(140,144)(141,143)(145,156)(146,155)
(147,154)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(164,165)
(166,169)(167,171)(168,170)(172,183)(173,182)(174,181)(175,189)(176,188)
(177,187)(178,186)(179,185)(180,184)(191,192)(193,196)(194,198)(195,197)
(199,210)(200,209)(201,208)(202,216)(203,215)(204,214)(205,213)(206,212)
(207,211)(218,219)(220,223)(221,225)(222,224)(226,237)(227,236)(228,235)
(229,243)(230,242)(231,241)(232,240)(233,239)(234,238)(245,246)(247,250)
(248,252)(249,251)(253,264)(254,263)(255,262)(256,270)(257,269)(258,268)
(259,267)(260,266)(261,265)(272,273)(274,277)(275,279)(276,278)(280,291)
(281,290)(282,289)(283,297)(284,296)(285,295)(286,294)(287,293)(288,292)
(299,300)(301,304)(302,306)(303,305)(307,318)(308,317)(309,316)(310,324)
(311,323)(312,322)(313,321)(314,320)(315,319)(326,327)(328,331)(329,333)
(330,332)(334,345)(335,344)(336,343)(337,351)(338,350)(339,349)(340,348)
(341,347)(342,346)(353,354)(355,358)(356,360)(357,359)(361,372)(362,371)
(363,370)(364,378)(365,377)(366,376)(367,375)(368,374)(369,373)(380,381)
(382,385)(383,387)(384,386)(388,399)(389,398)(390,397)(391,405)(392,404)
(393,403)(394,402)(395,401)(396,400)(407,408)(409,412)(410,414)(411,413)
(415,426)(416,425)(417,424)(418,432)(419,431)(420,430)(421,429)(422,428)
(423,427);
s1 := Sym(432)!(  1, 13)(  2, 15)(  3, 14)(  4, 10)(  5, 12)(  6, 11)(  7, 16)
(  8, 18)(  9, 17)( 19, 24)( 20, 23)( 21, 22)( 25, 27)( 28, 40)( 29, 42)
( 30, 41)( 31, 37)( 32, 39)( 33, 38)( 34, 43)( 35, 45)( 36, 44)( 46, 51)
( 47, 50)( 48, 49)( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)
( 60, 65)( 61, 70)( 62, 72)( 63, 71)( 73, 78)( 74, 77)( 75, 76)( 79, 81)
( 82, 94)( 83, 96)( 84, 95)( 85, 91)( 86, 93)( 87, 92)( 88, 97)( 89, 99)
( 90, 98)(100,105)(101,104)(102,103)(106,108)(109,121)(110,123)(111,122)
(112,118)(113,120)(114,119)(115,124)(116,126)(117,125)(127,132)(128,131)
(129,130)(133,135)(136,148)(137,150)(138,149)(139,145)(140,147)(141,146)
(142,151)(143,153)(144,152)(154,159)(155,158)(156,157)(160,162)(163,175)
(164,177)(165,176)(166,172)(167,174)(168,173)(169,178)(170,180)(171,179)
(181,186)(182,185)(183,184)(187,189)(190,202)(191,204)(192,203)(193,199)
(194,201)(195,200)(196,205)(197,207)(198,206)(208,213)(209,212)(210,211)
(214,216)(217,229)(218,231)(219,230)(220,226)(221,228)(222,227)(223,232)
(224,234)(225,233)(235,240)(236,239)(237,238)(241,243)(244,256)(245,258)
(246,257)(247,253)(248,255)(249,254)(250,259)(251,261)(252,260)(262,267)
(263,266)(264,265)(268,270)(271,283)(272,285)(273,284)(274,280)(275,282)
(276,281)(277,286)(278,288)(279,287)(289,294)(290,293)(291,292)(295,297)
(298,310)(299,312)(300,311)(301,307)(302,309)(303,308)(304,313)(305,315)
(306,314)(316,321)(317,320)(318,319)(322,324)(325,337)(326,339)(327,338)
(328,334)(329,336)(330,335)(331,340)(332,342)(333,341)(343,348)(344,347)
(345,346)(349,351)(352,364)(353,366)(354,365)(355,361)(356,363)(357,362)
(358,367)(359,369)(360,368)(370,375)(371,374)(372,373)(376,378)(379,391)
(380,393)(381,392)(382,388)(383,390)(384,389)(385,394)(386,396)(387,395)
(397,402)(398,401)(399,400)(403,405)(406,418)(407,420)(408,419)(409,415)
(410,417)(411,416)(412,421)(413,423)(414,422)(424,429)(425,428)(426,427)
(430,432);
s2 := Sym(432)!(  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)
( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)
( 49, 52)( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)
( 60, 90)( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)
( 68, 98)( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)
( 76,106)( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(109,163)(110,164)
(111,165)(112,169)(113,170)(114,171)(115,166)(116,167)(117,168)(118,172)
(119,173)(120,174)(121,178)(122,179)(123,180)(124,175)(125,176)(126,177)
(127,181)(128,182)(129,183)(130,187)(131,188)(132,189)(133,184)(134,185)
(135,186)(136,190)(137,191)(138,192)(139,196)(140,197)(141,198)(142,193)
(143,194)(144,195)(145,199)(146,200)(147,201)(148,205)(149,206)(150,207)
(151,202)(152,203)(153,204)(154,208)(155,209)(156,210)(157,214)(158,215)
(159,216)(160,211)(161,212)(162,213)(217,325)(218,326)(219,327)(220,331)
(221,332)(222,333)(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)
(229,340)(230,341)(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)
(237,345)(238,349)(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)
(245,353)(246,354)(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)
(253,361)(254,362)(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)
(261,366)(262,370)(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)
(269,374)(270,375)(271,406)(272,407)(273,408)(274,412)(275,413)(276,414)
(277,409)(278,410)(279,411)(280,415)(281,416)(282,417)(283,421)(284,422)
(285,423)(286,418)(287,419)(288,420)(289,424)(290,425)(291,426)(292,430)
(293,431)(294,432)(295,427)(296,428)(297,429)(298,379)(299,380)(300,381)
(301,385)(302,386)(303,387)(304,382)(305,383)(306,384)(307,388)(308,389)
(309,390)(310,394)(311,395)(312,396)(313,391)(314,392)(315,393)(316,397)
(317,398)(318,399)(319,403)(320,404)(321,405)(322,400)(323,401)(324,402);
s3 := 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)( 55,298)
( 56,299)( 57,300)( 58,301)( 59,302)( 60,303)( 61,304)( 62,305)( 63,306)
( 64,307)( 65,308)( 66,309)( 67,310)( 68,311)( 69,312)( 70,313)( 71,314)
( 72,315)( 73,316)( 74,317)( 75,318)( 76,319)( 77,320)( 78,321)( 79,322)
( 80,323)( 81,324)( 82,271)( 83,272)( 84,273)( 85,274)( 86,275)( 87,276)
( 88,277)( 89,278)( 90,279)( 91,280)( 92,281)( 93,282)( 94,283)( 95,284)
( 96,285)( 97,286)( 98,287)( 99,288)(100,289)(101,290)(102,291)(103,292)
(104,293)(105,294)(106,295)(107,296)(108,297)(109,379)(110,380)(111,381)
(112,382)(113,383)(114,384)(115,385)(116,386)(117,387)(118,388)(119,389)
(120,390)(121,391)(122,392)(123,393)(124,394)(125,395)(126,396)(127,397)
(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)
(136,406)(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)
(144,414)(145,415)(146,416)(147,417)(148,418)(149,419)(150,420)(151,421)
(152,422)(153,423)(154,424)(155,425)(156,426)(157,427)(158,428)(159,429)
(160,430)(161,431)(162,432)(163,325)(164,326)(165,327)(166,328)(167,329)
(168,330)(169,331)(170,332)(171,333)(172,334)(173,335)(174,336)(175,337)
(176,338)(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,345)
(184,346)(185,347)(186,348)(187,349)(188,350)(189,351)(190,352)(191,353)
(192,354)(193,355)(194,356)(195,357)(196,358)(197,359)(198,360)(199,361)
(200,362)(201,363)(202,364)(203,365)(204,366)(205,367)(206,368)(207,369)
(208,370)(209,371)(210,372)(211,373)(212,374)(213,375)(214,376)(215,377)
(216,378);
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*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
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*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope