Polytope of Type {12,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,3}*1728a
if this polytope has a name.
Group : SmallGroup(1728,30243)
Rank : 4
Schlafli Type : {12,12,3}
Number of vertices, edges, etc : 12, 144, 36, 6
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 6
Special Properties :
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 : {6,12,3}*864a
3-fold quotients : {12,4,3}*576
4-fold quotients : {12,6,3}*432a
6-fold quotients : {6,4,3}*288
8-fold quotients : {6,6,3}*216a
9-fold quotients : {4,4,3}*192b
12-fold quotients : {12,2,3}*144
16-fold quotients : {3,6,3}*108
18-fold quotients : {2,4,3}*96
24-fold quotients : {6,2,3}*72
36-fold quotients : {4,2,3}*48, {2,4,3}*48
48-fold quotients : {3,2,3}*36
72-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)
( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)
( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)
( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)
(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)
(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)
(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)
(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)
(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)
(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212)
(217,325)(218,326)(219,327)(220,328)(221,333)(222,334)(223,335)(224,336)
(225,329)(226,330)(227,331)(228,332)(229,349)(230,350)(231,351)(232,352)
(233,357)(234,358)(235,359)(236,360)(237,353)(238,354)(239,355)(240,356)
(241,337)(242,338)(243,339)(244,340)(245,345)(246,346)(247,347)(248,348)
(249,341)(250,342)(251,343)(252,344)(253,361)(254,362)(255,363)(256,364)
(257,369)(258,370)(259,371)(260,372)(261,365)(262,366)(263,367)(264,368)
(265,385)(266,386)(267,387)(268,388)(269,393)(270,394)(271,395)(272,396)
(273,389)(274,390)(275,391)(276,392)(277,373)(278,374)(279,375)(280,376)
(281,381)(282,382)(283,383)(284,384)(285,377)(286,378)(287,379)(288,380)
(289,397)(290,398)(291,399)(292,400)(293,405)(294,406)(295,407)(296,408)
(297,401)(298,402)(299,403)(300,404)(301,421)(302,422)(303,423)(304,424)
(305,429)(306,430)(307,431)(308,432)(309,425)(310,426)(311,427)(312,428)
(313,409)(314,410)(315,411)(316,412)(317,417)(318,418)(319,419)(320,420)
(321,413)(322,414)(323,415)(324,416);;
s1 := ( 1,230)( 2,229)( 3,232)( 4,231)( 5,238)( 6,237)( 7,240)( 8,239)
( 9,234)( 10,233)( 11,236)( 12,235)( 13,218)( 14,217)( 15,220)( 16,219)
( 17,226)( 18,225)( 19,228)( 20,227)( 21,222)( 22,221)( 23,224)( 24,223)
( 25,242)( 26,241)( 27,244)( 28,243)( 29,250)( 30,249)( 31,252)( 32,251)
( 33,246)( 34,245)( 35,248)( 36,247)( 37,266)( 38,265)( 39,268)( 40,267)
( 41,274)( 42,273)( 43,276)( 44,275)( 45,270)( 46,269)( 47,272)( 48,271)
( 49,254)( 50,253)( 51,256)( 52,255)( 53,262)( 54,261)( 55,264)( 56,263)
( 57,258)( 58,257)( 59,260)( 60,259)( 61,278)( 62,277)( 63,280)( 64,279)
( 65,286)( 66,285)( 67,288)( 68,287)( 69,282)( 70,281)( 71,284)( 72,283)
( 73,302)( 74,301)( 75,304)( 76,303)( 77,310)( 78,309)( 79,312)( 80,311)
( 81,306)( 82,305)( 83,308)( 84,307)( 85,290)( 86,289)( 87,292)( 88,291)
( 89,298)( 90,297)( 91,300)( 92,299)( 93,294)( 94,293)( 95,296)( 96,295)
( 97,314)( 98,313)( 99,316)(100,315)(101,322)(102,321)(103,324)(104,323)
(105,318)(106,317)(107,320)(108,319)(109,338)(110,337)(111,340)(112,339)
(113,346)(114,345)(115,348)(116,347)(117,342)(118,341)(119,344)(120,343)
(121,326)(122,325)(123,328)(124,327)(125,334)(126,333)(127,336)(128,335)
(129,330)(130,329)(131,332)(132,331)(133,350)(134,349)(135,352)(136,351)
(137,358)(138,357)(139,360)(140,359)(141,354)(142,353)(143,356)(144,355)
(145,374)(146,373)(147,376)(148,375)(149,382)(150,381)(151,384)(152,383)
(153,378)(154,377)(155,380)(156,379)(157,362)(158,361)(159,364)(160,363)
(161,370)(162,369)(163,372)(164,371)(165,366)(166,365)(167,368)(168,367)
(169,386)(170,385)(171,388)(172,387)(173,394)(174,393)(175,396)(176,395)
(177,390)(178,389)(179,392)(180,391)(181,410)(182,409)(183,412)(184,411)
(185,418)(186,417)(187,420)(188,419)(189,414)(190,413)(191,416)(192,415)
(193,398)(194,397)(195,400)(196,399)(197,406)(198,405)(199,408)(200,407)
(201,402)(202,401)(203,404)(204,403)(205,422)(206,421)(207,424)(208,423)
(209,430)(210,429)(211,432)(212,431)(213,426)(214,425)(215,428)(216,427);;
s2 := ( 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, 53)( 14, 56)( 15, 55)( 16, 54)
( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 57)( 22, 60)( 23, 59)( 24, 58)
( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)
( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 74, 76)( 77, 81)( 78, 84)( 79, 83)
( 80, 82)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 94, 96)( 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)(121,161)
(122,164)(123,163)(124,162)(125,157)(126,160)(127,159)(128,158)(129,165)
(130,168)(131,167)(132,166)(133,177)(134,180)(135,179)(136,178)(137,173)
(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)(144,170)(182,184)
(185,189)(186,192)(187,191)(188,190)(193,197)(194,200)(195,199)(196,198)
(202,204)(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)(229,269)(230,272)(231,271)(232,270)(233,265)(234,268)
(235,267)(236,266)(237,273)(238,276)(239,275)(240,274)(241,285)(242,288)
(243,287)(244,286)(245,281)(246,284)(247,283)(248,282)(249,277)(250,280)
(251,279)(252,278)(290,292)(293,297)(294,300)(295,299)(296,298)(301,305)
(302,308)(303,307)(304,306)(310,312)(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)(337,377)(338,380)(339,379)
(340,378)(341,373)(342,376)(343,375)(344,374)(345,381)(346,384)(347,383)
(348,382)(349,393)(350,396)(351,395)(352,394)(353,389)(354,392)(355,391)
(356,390)(357,385)(358,388)(359,387)(360,386)(398,400)(401,405)(402,408)
(403,407)(404,406)(409,413)(410,416)(411,415)(412,414)(418,420)(421,429)
(422,432)(423,431)(424,430)(426,428);;
s3 := ( 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, 73)
( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 77)
( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 93)
( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 97)
( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)
( 70,102)( 71,104)( 72,103)(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)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)
(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)(158,194)
(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)(166,198)
(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)(174,214)
(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(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)(253,289)(254,290)(255,292)
(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)(263,296)
(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)(271,312)
(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)(279,316)
(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)(287,320)
(288,319)(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)
(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)(368,407)
(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)(376,411)
(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)(384,415)
(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)(392,431)
(393,425)(394,426)(395,428)(396,427);;
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, s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s3*s1*s2*s1*s0*s1*s2*s3*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 25)( 14, 26)( 15, 27)
( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)
( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)
( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)
( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)
( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)
(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)
(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)
(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)
(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)
(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)
(204,212)(217,325)(218,326)(219,327)(220,328)(221,333)(222,334)(223,335)
(224,336)(225,329)(226,330)(227,331)(228,332)(229,349)(230,350)(231,351)
(232,352)(233,357)(234,358)(235,359)(236,360)(237,353)(238,354)(239,355)
(240,356)(241,337)(242,338)(243,339)(244,340)(245,345)(246,346)(247,347)
(248,348)(249,341)(250,342)(251,343)(252,344)(253,361)(254,362)(255,363)
(256,364)(257,369)(258,370)(259,371)(260,372)(261,365)(262,366)(263,367)
(264,368)(265,385)(266,386)(267,387)(268,388)(269,393)(270,394)(271,395)
(272,396)(273,389)(274,390)(275,391)(276,392)(277,373)(278,374)(279,375)
(280,376)(281,381)(282,382)(283,383)(284,384)(285,377)(286,378)(287,379)
(288,380)(289,397)(290,398)(291,399)(292,400)(293,405)(294,406)(295,407)
(296,408)(297,401)(298,402)(299,403)(300,404)(301,421)(302,422)(303,423)
(304,424)(305,429)(306,430)(307,431)(308,432)(309,425)(310,426)(311,427)
(312,428)(313,409)(314,410)(315,411)(316,412)(317,417)(318,418)(319,419)
(320,420)(321,413)(322,414)(323,415)(324,416);
s1 := Sym(432)!( 1,230)( 2,229)( 3,232)( 4,231)( 5,238)( 6,237)( 7,240)
( 8,239)( 9,234)( 10,233)( 11,236)( 12,235)( 13,218)( 14,217)( 15,220)
( 16,219)( 17,226)( 18,225)( 19,228)( 20,227)( 21,222)( 22,221)( 23,224)
( 24,223)( 25,242)( 26,241)( 27,244)( 28,243)( 29,250)( 30,249)( 31,252)
( 32,251)( 33,246)( 34,245)( 35,248)( 36,247)( 37,266)( 38,265)( 39,268)
( 40,267)( 41,274)( 42,273)( 43,276)( 44,275)( 45,270)( 46,269)( 47,272)
( 48,271)( 49,254)( 50,253)( 51,256)( 52,255)( 53,262)( 54,261)( 55,264)
( 56,263)( 57,258)( 58,257)( 59,260)( 60,259)( 61,278)( 62,277)( 63,280)
( 64,279)( 65,286)( 66,285)( 67,288)( 68,287)( 69,282)( 70,281)( 71,284)
( 72,283)( 73,302)( 74,301)( 75,304)( 76,303)( 77,310)( 78,309)( 79,312)
( 80,311)( 81,306)( 82,305)( 83,308)( 84,307)( 85,290)( 86,289)( 87,292)
( 88,291)( 89,298)( 90,297)( 91,300)( 92,299)( 93,294)( 94,293)( 95,296)
( 96,295)( 97,314)( 98,313)( 99,316)(100,315)(101,322)(102,321)(103,324)
(104,323)(105,318)(106,317)(107,320)(108,319)(109,338)(110,337)(111,340)
(112,339)(113,346)(114,345)(115,348)(116,347)(117,342)(118,341)(119,344)
(120,343)(121,326)(122,325)(123,328)(124,327)(125,334)(126,333)(127,336)
(128,335)(129,330)(130,329)(131,332)(132,331)(133,350)(134,349)(135,352)
(136,351)(137,358)(138,357)(139,360)(140,359)(141,354)(142,353)(143,356)
(144,355)(145,374)(146,373)(147,376)(148,375)(149,382)(150,381)(151,384)
(152,383)(153,378)(154,377)(155,380)(156,379)(157,362)(158,361)(159,364)
(160,363)(161,370)(162,369)(163,372)(164,371)(165,366)(166,365)(167,368)
(168,367)(169,386)(170,385)(171,388)(172,387)(173,394)(174,393)(175,396)
(176,395)(177,390)(178,389)(179,392)(180,391)(181,410)(182,409)(183,412)
(184,411)(185,418)(186,417)(187,420)(188,419)(189,414)(190,413)(191,416)
(192,415)(193,398)(194,397)(195,400)(196,399)(197,406)(198,405)(199,408)
(200,407)(201,402)(202,401)(203,404)(204,403)(205,422)(206,421)(207,424)
(208,423)(209,430)(210,429)(211,432)(212,431)(213,426)(214,425)(215,428)
(216,427);
s2 := 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, 53)( 14, 56)( 15, 55)
( 16, 54)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 57)( 22, 60)( 23, 59)
( 24, 58)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)
( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 74, 76)( 77, 81)( 78, 84)
( 79, 83)( 80, 82)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 94, 96)( 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)
(121,161)(122,164)(123,163)(124,162)(125,157)(126,160)(127,159)(128,158)
(129,165)(130,168)(131,167)(132,166)(133,177)(134,180)(135,179)(136,178)
(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)(144,170)
(182,184)(185,189)(186,192)(187,191)(188,190)(193,197)(194,200)(195,199)
(196,198)(202,204)(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)(229,269)(230,272)(231,271)(232,270)(233,265)
(234,268)(235,267)(236,266)(237,273)(238,276)(239,275)(240,274)(241,285)
(242,288)(243,287)(244,286)(245,281)(246,284)(247,283)(248,282)(249,277)
(250,280)(251,279)(252,278)(290,292)(293,297)(294,300)(295,299)(296,298)
(301,305)(302,308)(303,307)(304,306)(310,312)(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)(337,377)(338,380)
(339,379)(340,378)(341,373)(342,376)(343,375)(344,374)(345,381)(346,384)
(347,383)(348,382)(349,393)(350,396)(351,395)(352,394)(353,389)(354,392)
(355,391)(356,390)(357,385)(358,388)(359,387)(360,386)(398,400)(401,405)
(402,408)(403,407)(404,406)(409,413)(410,416)(411,415)(412,414)(418,420)
(421,429)(422,432)(423,431)(424,430)(426,428);
s3 := 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, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)
( 45, 77)( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)
( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)
( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)
( 69,101)( 70,102)( 71,104)( 72,103)(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)(145,181)(146,182)(147,184)(148,183)(149,189)
(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)
(158,194)(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)
(166,198)(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)
(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(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)(253,289)(254,290)
(255,292)(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)
(263,296)(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)
(271,312)(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)
(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)
(287,320)(288,319)(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)(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)
(368,407)(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)
(376,411)(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)
(384,415)(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)
(392,431)(393,425)(394,426)(395,428)(396,427);
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,
s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s3*s1*s2*s1*s0*s1*s2*s3*s1*s2*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 >;
References : None.
to this polytope