Polytope of Type {27,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {27,4,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,11358)
Rank : 4
Schlafli Type : {27,4,4}
Number of vertices, edges, etc : 54, 108, 16, 4
Order of s0s1s2s3 : 108
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 : {27,4,2}*864
3-fold quotients : {9,4,4}*576b
4-fold quotients : {27,2,4}*432, {27,4,2}*432
6-fold quotients : {9,4,2}*288
8-fold quotients : {27,2,2}*216
9-fold quotients : {3,4,4}*192b
12-fold quotients : {9,2,4}*144, {9,4,2}*144
18-fold quotients : {3,4,2}*96
24-fold quotients : {9,2,2}*72
36-fold quotients : {3,2,4}*48, {3,4,2}*48
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)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)
( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 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, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)
( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)(114,118)
(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)(146,214)
(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)(154,206)
(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)
(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)(170,190)
(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)(178,182)
(179,184)(180,183)(219,220)(221,225)(222,226)(223,228)(224,227)(229,249)
(230,250)(231,252)(232,251)(233,245)(234,246)(235,248)(236,247)(237,241)
(238,242)(239,244)(240,243)(253,321)(254,322)(255,324)(256,323)(257,317)
(258,318)(259,320)(260,319)(261,313)(262,314)(263,316)(264,315)(265,309)
(266,310)(267,312)(268,311)(269,305)(270,306)(271,308)(272,307)(273,301)
(274,302)(275,304)(276,303)(277,297)(278,298)(279,300)(280,299)(281,293)
(282,294)(283,296)(284,295)(285,289)(286,290)(287,292)(288,291)(327,328)
(329,333)(330,334)(331,336)(332,335)(337,357)(338,358)(339,360)(340,359)
(341,353)(342,354)(343,356)(344,355)(345,349)(346,350)(347,352)(348,351)
(361,429)(362,430)(363,432)(364,431)(365,425)(366,426)(367,428)(368,427)
(369,421)(370,422)(371,424)(372,423)(373,417)(374,418)(375,420)(376,419)
(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)(384,411)
(385,405)(386,406)(387,408)(388,407)(389,401)(390,402)(391,404)(392,403)
(393,397)(394,398)(395,400)(396,399);;
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, 69)( 14, 72)( 15, 71)( 16, 70)
( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 61)( 22, 64)( 23, 63)( 24, 62)
( 25, 57)( 26, 60)( 27, 59)( 28, 58)( 29, 53)( 30, 56)( 31, 55)( 32, 54)
( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 73,105)( 74,108)( 75,107)( 76,106)
( 77,101)( 78,104)( 79,103)( 80,102)( 81, 97)( 82,100)( 83, 99)( 84, 98)
( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92)(109,145)(110,148)(111,147)
(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)
(120,150)(121,177)(122,180)(123,179)(124,178)(125,173)(126,176)(127,175)
(128,174)(129,169)(130,172)(131,171)(132,170)(133,165)(134,168)(135,167)
(136,166)(137,161)(138,164)(139,163)(140,162)(141,157)(142,160)(143,159)
(144,158)(181,213)(182,216)(183,215)(184,214)(185,209)(186,212)(187,211)
(188,210)(189,205)(190,208)(191,207)(192,206)(193,201)(194,204)(195,203)
(196,202)(198,200)(217,253)(218,256)(219,255)(220,254)(221,261)(222,264)
(223,263)(224,262)(225,257)(226,260)(227,259)(228,258)(229,285)(230,288)
(231,287)(232,286)(233,281)(234,284)(235,283)(236,282)(237,277)(238,280)
(239,279)(240,278)(241,273)(242,276)(243,275)(244,274)(245,269)(246,272)
(247,271)(248,270)(249,265)(250,268)(251,267)(252,266)(289,321)(290,324)
(291,323)(292,322)(293,317)(294,320)(295,319)(296,318)(297,313)(298,316)
(299,315)(300,314)(301,309)(302,312)(303,311)(304,310)(306,308)(325,361)
(326,364)(327,363)(328,362)(329,369)(330,372)(331,371)(332,370)(333,365)
(334,368)(335,367)(336,366)(337,393)(338,396)(339,395)(340,394)(341,389)
(342,392)(343,391)(344,390)(345,385)(346,388)(347,387)(348,386)(349,381)
(350,384)(351,383)(352,382)(353,377)(354,380)(355,379)(356,378)(357,373)
(358,376)(359,375)(360,374)(397,429)(398,432)(399,431)(400,430)(401,425)
(402,428)(403,427)(404,426)(405,421)(406,424)(407,423)(408,422)(409,417)
(410,420)(411,419)(412,418)(414,416);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,326)(218,325)(219,328)(220,327)
(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)(228,335)
(229,338)(230,337)(231,340)(232,339)(233,342)(234,341)(235,344)(236,343)
(237,346)(238,345)(239,348)(240,347)(241,350)(242,349)(243,352)(244,351)
(245,354)(246,353)(247,356)(248,355)(249,358)(250,357)(251,360)(252,359)
(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)(260,367)
(261,370)(262,369)(263,372)(264,371)(265,374)(266,373)(267,376)(268,375)
(269,378)(270,377)(271,380)(272,379)(273,382)(274,381)(275,384)(276,383)
(277,386)(278,385)(279,388)(280,387)(281,390)(282,389)(283,392)(284,391)
(285,394)(286,393)(287,396)(288,395)(289,398)(290,397)(291,400)(292,399)
(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)(300,407)
(301,410)(302,409)(303,412)(304,411)(305,414)(306,413)(307,416)(308,415)
(309,418)(310,417)(311,420)(312,419)(313,422)(314,421)(315,424)(316,423)
(317,426)(318,425)(319,428)(320,427)(321,430)(322,429)(323,432)(324,431);;
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)( 55,271)( 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);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)
( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 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, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)
(114,118)(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)
(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)
(146,214)(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)
(154,206)(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)
(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)
(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)
(178,182)(179,184)(180,183)(219,220)(221,225)(222,226)(223,228)(224,227)
(229,249)(230,250)(231,252)(232,251)(233,245)(234,246)(235,248)(236,247)
(237,241)(238,242)(239,244)(240,243)(253,321)(254,322)(255,324)(256,323)
(257,317)(258,318)(259,320)(260,319)(261,313)(262,314)(263,316)(264,315)
(265,309)(266,310)(267,312)(268,311)(269,305)(270,306)(271,308)(272,307)
(273,301)(274,302)(275,304)(276,303)(277,297)(278,298)(279,300)(280,299)
(281,293)(282,294)(283,296)(284,295)(285,289)(286,290)(287,292)(288,291)
(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)(338,358)(339,360)
(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)(346,350)(347,352)
(348,351)(361,429)(362,430)(363,432)(364,431)(365,425)(366,426)(367,428)
(368,427)(369,421)(370,422)(371,424)(372,423)(373,417)(374,418)(375,420)
(376,419)(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)
(384,411)(385,405)(386,406)(387,408)(388,407)(389,401)(390,402)(391,404)
(392,403)(393,397)(394,398)(395,400)(396,399);
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, 69)( 14, 72)( 15, 71)
( 16, 70)( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 61)( 22, 64)( 23, 63)
( 24, 62)( 25, 57)( 26, 60)( 27, 59)( 28, 58)( 29, 53)( 30, 56)( 31, 55)
( 32, 54)( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 73,105)( 74,108)( 75,107)
( 76,106)( 77,101)( 78,104)( 79,103)( 80,102)( 81, 97)( 82,100)( 83, 99)
( 84, 98)( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92)(109,145)(110,148)
(111,147)(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)
(119,151)(120,150)(121,177)(122,180)(123,179)(124,178)(125,173)(126,176)
(127,175)(128,174)(129,169)(130,172)(131,171)(132,170)(133,165)(134,168)
(135,167)(136,166)(137,161)(138,164)(139,163)(140,162)(141,157)(142,160)
(143,159)(144,158)(181,213)(182,216)(183,215)(184,214)(185,209)(186,212)
(187,211)(188,210)(189,205)(190,208)(191,207)(192,206)(193,201)(194,204)
(195,203)(196,202)(198,200)(217,253)(218,256)(219,255)(220,254)(221,261)
(222,264)(223,263)(224,262)(225,257)(226,260)(227,259)(228,258)(229,285)
(230,288)(231,287)(232,286)(233,281)(234,284)(235,283)(236,282)(237,277)
(238,280)(239,279)(240,278)(241,273)(242,276)(243,275)(244,274)(245,269)
(246,272)(247,271)(248,270)(249,265)(250,268)(251,267)(252,266)(289,321)
(290,324)(291,323)(292,322)(293,317)(294,320)(295,319)(296,318)(297,313)
(298,316)(299,315)(300,314)(301,309)(302,312)(303,311)(304,310)(306,308)
(325,361)(326,364)(327,363)(328,362)(329,369)(330,372)(331,371)(332,370)
(333,365)(334,368)(335,367)(336,366)(337,393)(338,396)(339,395)(340,394)
(341,389)(342,392)(343,391)(344,390)(345,385)(346,388)(347,387)(348,386)
(349,381)(350,384)(351,383)(352,382)(353,377)(354,380)(355,379)(356,378)
(357,373)(358,376)(359,375)(360,374)(397,429)(398,432)(399,431)(400,430)
(401,425)(402,428)(403,427)(404,426)(405,421)(406,424)(407,423)(408,422)
(409,417)(410,420)(411,419)(412,418)(414,416);
s2 := Sym(432)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,326)(218,325)(219,328)
(220,327)(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)
(228,335)(229,338)(230,337)(231,340)(232,339)(233,342)(234,341)(235,344)
(236,343)(237,346)(238,345)(239,348)(240,347)(241,350)(242,349)(243,352)
(244,351)(245,354)(246,353)(247,356)(248,355)(249,358)(250,357)(251,360)
(252,359)(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)
(260,367)(261,370)(262,369)(263,372)(264,371)(265,374)(266,373)(267,376)
(268,375)(269,378)(270,377)(271,380)(272,379)(273,382)(274,381)(275,384)
(276,383)(277,386)(278,385)(279,388)(280,387)(281,390)(282,389)(283,392)
(284,391)(285,394)(286,393)(287,396)(288,395)(289,398)(290,397)(291,400)
(292,399)(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)
(300,407)(301,410)(302,409)(303,412)(304,411)(305,414)(306,413)(307,416)
(308,415)(309,418)(310,417)(311,420)(312,419)(313,422)(314,421)(315,424)
(316,423)(317,426)(318,425)(319,428)(320,427)(321,430)(322,429)(323,432)
(324,431);
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)( 55,271)
( 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);
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,
s2*s3*s2*s3*s2*s3*s2*s3, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope