Polytope of Type {3,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,4}*1728a
Also Known As : {{3,12}6,{12,4|2}}. if this polytope has another name.
Group : SmallGroup(1728,30326)
Rank : 4
Schlafli Type : {3,12,4}
Number of vertices, edges, etc : 18, 108, 144, 4
Order of s0s1s2s3 : 12
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 : {3,12,2}*864
3-fold quotients : {3,12,4}*576
4-fold quotients : {3,6,4}*432a
6-fold quotients : {3,12,2}*288
8-fold quotients : {3,6,2}*216
9-fold quotients : {3,4,4}*192b
12-fold quotients : {3,6,4}*144
18-fold quotients : {3,4,2}*96
24-fold quotients : {3,6,2}*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)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)
( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 37, 73)
( 38, 74)( 39, 76)( 40, 75)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 81)
( 46, 82)( 47, 84)( 48, 83)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)
( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)( 60,107)( 61, 85)
( 62, 86)( 63, 88)( 64, 87)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 93)
( 70, 94)( 71, 96)( 72, 95)(111,112)(115,116)(119,120)(121,133)(122,134)
(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)(129,141)(130,142)
(131,144)(132,143)(145,181)(146,182)(147,184)(148,183)(149,185)(150,186)
(151,188)(152,187)(153,189)(154,190)(155,192)(156,191)(157,205)(158,206)
(159,208)(160,207)(161,209)(162,210)(163,212)(164,211)(165,213)(166,214)
(167,216)(168,215)(169,193)(170,194)(171,196)(172,195)(173,197)(174,198)
(175,200)(176,199)(177,201)(178,202)(179,204)(180,203)(219,220)(223,224)
(227,228)(229,241)(230,242)(231,244)(232,243)(233,245)(234,246)(235,248)
(236,247)(237,249)(238,250)(239,252)(240,251)(253,289)(254,290)(255,292)
(256,291)(257,293)(258,294)(259,296)(260,295)(261,297)(262,298)(263,300)
(264,299)(265,313)(266,314)(267,316)(268,315)(269,317)(270,318)(271,320)
(272,319)(273,321)(274,322)(275,324)(276,323)(277,301)(278,302)(279,304)
(280,303)(281,305)(282,306)(283,308)(284,307)(285,309)(286,310)(287,312)
(288,311)(327,328)(331,332)(335,336)(337,349)(338,350)(339,352)(340,351)
(341,353)(342,354)(343,356)(344,355)(345,357)(346,358)(347,360)(348,359)
(361,397)(362,398)(363,400)(364,399)(365,401)(366,402)(367,404)(368,403)
(369,405)(370,406)(371,408)(372,407)(373,421)(374,422)(375,424)(376,423)
(377,425)(378,426)(379,428)(380,427)(381,429)(382,430)(383,432)(384,431)
(385,409)(386,410)(387,412)(388,411)(389,413)(390,414)(391,416)(392,415)
(393,417)(394,418)(395,420)(396,419);;
s1 := ( 1, 89)( 2, 91)( 3, 90)( 4, 92)( 5, 93)( 6, 95)( 7, 94)( 8, 96)
( 9, 85)( 10, 87)( 11, 86)( 12, 88)( 13, 81)( 14, 83)( 15, 82)( 16, 84)
( 17, 73)( 18, 75)( 19, 74)( 20, 76)( 21, 77)( 22, 79)( 23, 78)( 24, 80)
( 25, 97)( 26, 99)( 27, 98)( 28,100)( 29,101)( 30,103)( 31,102)( 32,104)
( 33,105)( 34,107)( 35,106)( 36,108)( 37, 53)( 38, 55)( 39, 54)( 40, 56)
( 41, 57)( 42, 59)( 43, 58)( 44, 60)( 45, 49)( 46, 51)( 47, 50)( 48, 52)
( 62, 63)( 66, 67)( 70, 71)(109,197)(110,199)(111,198)(112,200)(113,201)
(114,203)(115,202)(116,204)(117,193)(118,195)(119,194)(120,196)(121,189)
(122,191)(123,190)(124,192)(125,181)(126,183)(127,182)(128,184)(129,185)
(130,187)(131,186)(132,188)(133,205)(134,207)(135,206)(136,208)(137,209)
(138,211)(139,210)(140,212)(141,213)(142,215)(143,214)(144,216)(145,161)
(146,163)(147,162)(148,164)(149,165)(150,167)(151,166)(152,168)(153,157)
(154,159)(155,158)(156,160)(170,171)(174,175)(178,179)(217,305)(218,307)
(219,306)(220,308)(221,309)(222,311)(223,310)(224,312)(225,301)(226,303)
(227,302)(228,304)(229,297)(230,299)(231,298)(232,300)(233,289)(234,291)
(235,290)(236,292)(237,293)(238,295)(239,294)(240,296)(241,313)(242,315)
(243,314)(244,316)(245,317)(246,319)(247,318)(248,320)(249,321)(250,323)
(251,322)(252,324)(253,269)(254,271)(255,270)(256,272)(257,273)(258,275)
(259,274)(260,276)(261,265)(262,267)(263,266)(264,268)(278,279)(282,283)
(286,287)(325,413)(326,415)(327,414)(328,416)(329,417)(330,419)(331,418)
(332,420)(333,409)(334,411)(335,410)(336,412)(337,405)(338,407)(339,406)
(340,408)(341,397)(342,399)(343,398)(344,400)(345,401)(346,403)(347,402)
(348,404)(349,421)(350,423)(351,422)(352,424)(353,425)(354,427)(355,426)
(356,428)(357,429)(358,431)(359,430)(360,432)(361,377)(362,379)(363,378)
(364,380)(365,381)(366,383)(367,382)(368,384)(369,373)(370,375)(371,374)
(372,376)(386,387)(390,391)(394,395);;
s2 := ( 1, 2)( 3, 4)( 5, 10)( 6, 9)( 7, 12)( 8, 11)( 13, 26)( 14, 25)
( 15, 28)( 16, 27)( 17, 34)( 18, 33)( 19, 36)( 20, 35)( 21, 30)( 22, 29)
( 23, 32)( 24, 31)( 37, 38)( 39, 40)( 41, 46)( 42, 45)( 43, 48)( 44, 47)
( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 70)( 54, 69)( 55, 72)( 56, 71)
( 57, 66)( 58, 65)( 59, 68)( 60, 67)( 73, 74)( 75, 76)( 77, 82)( 78, 81)
( 79, 84)( 80, 83)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89,106)( 90,105)
( 91,108)( 92,107)( 93,102)( 94,101)( 95,104)( 96,103)(109,110)(111,112)
(113,118)(114,117)(115,120)(116,119)(121,134)(122,133)(123,136)(124,135)
(125,142)(126,141)(127,144)(128,143)(129,138)(130,137)(131,140)(132,139)
(145,146)(147,148)(149,154)(150,153)(151,156)(152,155)(157,170)(158,169)
(159,172)(160,171)(161,178)(162,177)(163,180)(164,179)(165,174)(166,173)
(167,176)(168,175)(181,182)(183,184)(185,190)(186,189)(187,192)(188,191)
(193,206)(194,205)(195,208)(196,207)(197,214)(198,213)(199,216)(200,215)
(201,210)(202,209)(203,212)(204,211)(217,326)(218,325)(219,328)(220,327)
(221,334)(222,333)(223,336)(224,335)(225,330)(226,329)(227,332)(228,331)
(229,350)(230,349)(231,352)(232,351)(233,358)(234,357)(235,360)(236,359)
(237,354)(238,353)(239,356)(240,355)(241,338)(242,337)(243,340)(244,339)
(245,346)(246,345)(247,348)(248,347)(249,342)(250,341)(251,344)(252,343)
(253,362)(254,361)(255,364)(256,363)(257,370)(258,369)(259,372)(260,371)
(261,366)(262,365)(263,368)(264,367)(265,386)(266,385)(267,388)(268,387)
(269,394)(270,393)(271,396)(272,395)(273,390)(274,389)(275,392)(276,391)
(277,374)(278,373)(279,376)(280,375)(281,382)(282,381)(283,384)(284,383)
(285,378)(286,377)(287,380)(288,379)(289,398)(290,397)(291,400)(292,399)
(293,406)(294,405)(295,408)(296,407)(297,402)(298,401)(299,404)(300,403)
(301,422)(302,421)(303,424)(304,423)(305,430)(306,429)(307,432)(308,431)
(309,426)(310,425)(311,428)(312,427)(313,410)(314,409)(315,412)(316,411)
(317,418)(318,417)(319,420)(320,419)(321,414)(322,413)(323,416)(324,415);;
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, s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)
( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 77)( 42, 78)( 43, 80)( 44, 79)
( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 97)( 50, 98)( 51,100)( 52, 99)
( 53,101)( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)( 60,107)
( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 89)( 66, 90)( 67, 92)( 68, 91)
( 69, 93)( 70, 94)( 71, 96)( 72, 95)(111,112)(115,116)(119,120)(121,133)
(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)(129,141)
(130,142)(131,144)(132,143)(145,181)(146,182)(147,184)(148,183)(149,185)
(150,186)(151,188)(152,187)(153,189)(154,190)(155,192)(156,191)(157,205)
(158,206)(159,208)(160,207)(161,209)(162,210)(163,212)(164,211)(165,213)
(166,214)(167,216)(168,215)(169,193)(170,194)(171,196)(172,195)(173,197)
(174,198)(175,200)(176,199)(177,201)(178,202)(179,204)(180,203)(219,220)
(223,224)(227,228)(229,241)(230,242)(231,244)(232,243)(233,245)(234,246)
(235,248)(236,247)(237,249)(238,250)(239,252)(240,251)(253,289)(254,290)
(255,292)(256,291)(257,293)(258,294)(259,296)(260,295)(261,297)(262,298)
(263,300)(264,299)(265,313)(266,314)(267,316)(268,315)(269,317)(270,318)
(271,320)(272,319)(273,321)(274,322)(275,324)(276,323)(277,301)(278,302)
(279,304)(280,303)(281,305)(282,306)(283,308)(284,307)(285,309)(286,310)
(287,312)(288,311)(327,328)(331,332)(335,336)(337,349)(338,350)(339,352)
(340,351)(341,353)(342,354)(343,356)(344,355)(345,357)(346,358)(347,360)
(348,359)(361,397)(362,398)(363,400)(364,399)(365,401)(366,402)(367,404)
(368,403)(369,405)(370,406)(371,408)(372,407)(373,421)(374,422)(375,424)
(376,423)(377,425)(378,426)(379,428)(380,427)(381,429)(382,430)(383,432)
(384,431)(385,409)(386,410)(387,412)(388,411)(389,413)(390,414)(391,416)
(392,415)(393,417)(394,418)(395,420)(396,419);
s1 := Sym(432)!( 1, 89)( 2, 91)( 3, 90)( 4, 92)( 5, 93)( 6, 95)( 7, 94)
( 8, 96)( 9, 85)( 10, 87)( 11, 86)( 12, 88)( 13, 81)( 14, 83)( 15, 82)
( 16, 84)( 17, 73)( 18, 75)( 19, 74)( 20, 76)( 21, 77)( 22, 79)( 23, 78)
( 24, 80)( 25, 97)( 26, 99)( 27, 98)( 28,100)( 29,101)( 30,103)( 31,102)
( 32,104)( 33,105)( 34,107)( 35,106)( 36,108)( 37, 53)( 38, 55)( 39, 54)
( 40, 56)( 41, 57)( 42, 59)( 43, 58)( 44, 60)( 45, 49)( 46, 51)( 47, 50)
( 48, 52)( 62, 63)( 66, 67)( 70, 71)(109,197)(110,199)(111,198)(112,200)
(113,201)(114,203)(115,202)(116,204)(117,193)(118,195)(119,194)(120,196)
(121,189)(122,191)(123,190)(124,192)(125,181)(126,183)(127,182)(128,184)
(129,185)(130,187)(131,186)(132,188)(133,205)(134,207)(135,206)(136,208)
(137,209)(138,211)(139,210)(140,212)(141,213)(142,215)(143,214)(144,216)
(145,161)(146,163)(147,162)(148,164)(149,165)(150,167)(151,166)(152,168)
(153,157)(154,159)(155,158)(156,160)(170,171)(174,175)(178,179)(217,305)
(218,307)(219,306)(220,308)(221,309)(222,311)(223,310)(224,312)(225,301)
(226,303)(227,302)(228,304)(229,297)(230,299)(231,298)(232,300)(233,289)
(234,291)(235,290)(236,292)(237,293)(238,295)(239,294)(240,296)(241,313)
(242,315)(243,314)(244,316)(245,317)(246,319)(247,318)(248,320)(249,321)
(250,323)(251,322)(252,324)(253,269)(254,271)(255,270)(256,272)(257,273)
(258,275)(259,274)(260,276)(261,265)(262,267)(263,266)(264,268)(278,279)
(282,283)(286,287)(325,413)(326,415)(327,414)(328,416)(329,417)(330,419)
(331,418)(332,420)(333,409)(334,411)(335,410)(336,412)(337,405)(338,407)
(339,406)(340,408)(341,397)(342,399)(343,398)(344,400)(345,401)(346,403)
(347,402)(348,404)(349,421)(350,423)(351,422)(352,424)(353,425)(354,427)
(355,426)(356,428)(357,429)(358,431)(359,430)(360,432)(361,377)(362,379)
(363,378)(364,380)(365,381)(366,383)(367,382)(368,384)(369,373)(370,375)
(371,374)(372,376)(386,387)(390,391)(394,395);
s2 := Sym(432)!( 1, 2)( 3, 4)( 5, 10)( 6, 9)( 7, 12)( 8, 11)( 13, 26)
( 14, 25)( 15, 28)( 16, 27)( 17, 34)( 18, 33)( 19, 36)( 20, 35)( 21, 30)
( 22, 29)( 23, 32)( 24, 31)( 37, 38)( 39, 40)( 41, 46)( 42, 45)( 43, 48)
( 44, 47)( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 70)( 54, 69)( 55, 72)
( 56, 71)( 57, 66)( 58, 65)( 59, 68)( 60, 67)( 73, 74)( 75, 76)( 77, 82)
( 78, 81)( 79, 84)( 80, 83)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89,106)
( 90,105)( 91,108)( 92,107)( 93,102)( 94,101)( 95,104)( 96,103)(109,110)
(111,112)(113,118)(114,117)(115,120)(116,119)(121,134)(122,133)(123,136)
(124,135)(125,142)(126,141)(127,144)(128,143)(129,138)(130,137)(131,140)
(132,139)(145,146)(147,148)(149,154)(150,153)(151,156)(152,155)(157,170)
(158,169)(159,172)(160,171)(161,178)(162,177)(163,180)(164,179)(165,174)
(166,173)(167,176)(168,175)(181,182)(183,184)(185,190)(186,189)(187,192)
(188,191)(193,206)(194,205)(195,208)(196,207)(197,214)(198,213)(199,216)
(200,215)(201,210)(202,209)(203,212)(204,211)(217,326)(218,325)(219,328)
(220,327)(221,334)(222,333)(223,336)(224,335)(225,330)(226,329)(227,332)
(228,331)(229,350)(230,349)(231,352)(232,351)(233,358)(234,357)(235,360)
(236,359)(237,354)(238,353)(239,356)(240,355)(241,338)(242,337)(243,340)
(244,339)(245,346)(246,345)(247,348)(248,347)(249,342)(250,341)(251,344)
(252,343)(253,362)(254,361)(255,364)(256,363)(257,370)(258,369)(259,372)
(260,371)(261,366)(262,365)(263,368)(264,367)(265,386)(266,385)(267,388)
(268,387)(269,394)(270,393)(271,396)(272,395)(273,390)(274,389)(275,392)
(276,391)(277,374)(278,373)(279,376)(280,375)(281,382)(282,381)(283,384)
(284,383)(285,378)(286,377)(287,380)(288,379)(289,398)(290,397)(291,400)
(292,399)(293,406)(294,405)(295,408)(296,407)(297,402)(298,401)(299,404)
(300,403)(301,422)(302,421)(303,424)(304,423)(305,430)(306,429)(307,432)
(308,431)(309,426)(310,425)(311,428)(312,427)(313,410)(314,409)(315,412)
(316,411)(317,418)(318,417)(319,420)(320,419)(321,414)(322,413)(323,416)
(324,415);
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,
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope