Polytope of Type {48,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6,3}*1728a
if this polytope has a name.
Group : SmallGroup(1728,3073)
Rank : 4
Schlafli Type : {48,6,3}
Number of vertices, edges, etc : 48, 144, 9, 3
Order of s0s1s2s3 : 48
Order of s0s1s2s3s2s1 : 6
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 : {24,6,3}*864a
3-fold quotients : {48,2,3}*576
4-fold quotients : {12,6,3}*432a
6-fold quotients : {24,2,3}*288
8-fold quotients : {6,6,3}*216a
9-fold quotients : {16,2,3}*192
12-fold quotients : {12,2,3}*144
16-fold quotients : {3,6,3}*108
18-fold quotients : {8,2,3}*96
24-fold quotients : {6,2,3}*72
36-fold quotients : {4,2,3}*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 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)
( 55, 82)( 56, 84)( 57, 83)( 58, 88)( 59, 90)( 60, 89)( 61, 85)( 62, 87)
( 63, 86)( 64, 91)( 65, 93)( 66, 92)( 67, 97)( 68, 99)( 69, 98)( 70, 94)
( 71, 96)( 72, 95)( 73,100)( 74,102)( 75,101)( 76,106)( 77,108)( 78,107)
( 79,103)( 80,105)( 81,104)(109,163)(110,165)(111,164)(112,169)(113,171)
(114,170)(115,166)(116,168)(117,167)(118,172)(119,174)(120,173)(121,178)
(122,180)(123,179)(124,175)(125,177)(126,176)(127,181)(128,183)(129,182)
(130,187)(131,189)(132,188)(133,184)(134,186)(135,185)(136,190)(137,192)
(138,191)(139,196)(140,198)(141,197)(142,193)(143,195)(144,194)(145,199)
(146,201)(147,200)(148,205)(149,207)(150,206)(151,202)(152,204)(153,203)
(154,208)(155,210)(156,209)(157,214)(158,216)(159,215)(160,211)(161,213)
(162,212)(217,325)(218,327)(219,326)(220,331)(221,333)(222,332)(223,328)
(224,330)(225,329)(226,334)(227,336)(228,335)(229,340)(230,342)(231,341)
(232,337)(233,339)(234,338)(235,343)(236,345)(237,344)(238,349)(239,351)
(240,350)(241,346)(242,348)(243,347)(244,352)(245,354)(246,353)(247,358)
(248,360)(249,359)(250,355)(251,357)(252,356)(253,361)(254,363)(255,362)
(256,367)(257,369)(258,368)(259,364)(260,366)(261,365)(262,370)(263,372)
(264,371)(265,376)(266,378)(267,377)(268,373)(269,375)(270,374)(271,406)
(272,408)(273,407)(274,412)(275,414)(276,413)(277,409)(278,411)(279,410)
(280,415)(281,417)(282,416)(283,421)(284,423)(285,422)(286,418)(287,420)
(288,419)(289,424)(290,426)(291,425)(292,430)(293,432)(294,431)(295,427)
(296,429)(297,428)(298,379)(299,381)(300,380)(301,385)(302,387)(303,386)
(304,382)(305,384)(306,383)(307,388)(308,390)(309,389)(310,394)(311,396)
(312,395)(313,391)(314,393)(315,392)(316,397)(317,399)(318,398)(319,403)
(320,405)(321,404)(322,400)(323,402)(324,401);;
s1 := ( 1,220)( 2,222)( 3,221)( 4,217)( 5,219)( 6,218)( 7,223)( 8,225)
( 9,224)( 10,229)( 11,231)( 12,230)( 13,226)( 14,228)( 15,227)( 16,232)
( 17,234)( 18,233)( 19,238)( 20,240)( 21,239)( 22,235)( 23,237)( 24,236)
( 25,241)( 26,243)( 27,242)( 28,247)( 29,249)( 30,248)( 31,244)( 32,246)
( 33,245)( 34,250)( 35,252)( 36,251)( 37,256)( 38,258)( 39,257)( 40,253)
( 41,255)( 42,254)( 43,259)( 44,261)( 45,260)( 46,265)( 47,267)( 48,266)
( 49,262)( 50,264)( 51,263)( 52,268)( 53,270)( 54,269)( 55,301)( 56,303)
( 57,302)( 58,298)( 59,300)( 60,299)( 61,304)( 62,306)( 63,305)( 64,310)
( 65,312)( 66,311)( 67,307)( 68,309)( 69,308)( 70,313)( 71,315)( 72,314)
( 73,319)( 74,321)( 75,320)( 76,316)( 77,318)( 78,317)( 79,322)( 80,324)
( 81,323)( 82,274)( 83,276)( 84,275)( 85,271)( 86,273)( 87,272)( 88,277)
( 89,279)( 90,278)( 91,283)( 92,285)( 93,284)( 94,280)( 95,282)( 96,281)
( 97,286)( 98,288)( 99,287)(100,292)(101,294)(102,293)(103,289)(104,291)
(105,290)(106,295)(107,297)(108,296)(109,382)(110,384)(111,383)(112,379)
(113,381)(114,380)(115,385)(116,387)(117,386)(118,391)(119,393)(120,392)
(121,388)(122,390)(123,389)(124,394)(125,396)(126,395)(127,400)(128,402)
(129,401)(130,397)(131,399)(132,398)(133,403)(134,405)(135,404)(136,409)
(137,411)(138,410)(139,406)(140,408)(141,407)(142,412)(143,414)(144,413)
(145,418)(146,420)(147,419)(148,415)(149,417)(150,416)(151,421)(152,423)
(153,422)(154,427)(155,429)(156,428)(157,424)(158,426)(159,425)(160,430)
(161,432)(162,431)(163,328)(164,330)(165,329)(166,325)(167,327)(168,326)
(169,331)(170,333)(171,332)(172,337)(173,339)(174,338)(175,334)(176,336)
(177,335)(178,340)(179,342)(180,341)(181,346)(182,348)(183,347)(184,343)
(185,345)(186,344)(187,349)(188,351)(189,350)(190,355)(191,357)(192,356)
(193,352)(194,354)(195,353)(196,358)(197,360)(198,359)(199,364)(200,366)
(201,365)(202,361)(203,363)(204,362)(205,367)(206,369)(207,368)(208,373)
(209,375)(210,374)(211,370)(212,372)(213,371)(214,376)(215,378)(216,377);;
s2 := ( 1, 10)( 2, 12)( 3, 11)( 4, 14)( 5, 13)( 6, 15)( 7, 18)( 8, 17)
( 9, 16)( 20, 21)( 22, 23)( 25, 27)( 28, 37)( 29, 39)( 30, 38)( 31, 41)
( 32, 40)( 33, 42)( 34, 45)( 35, 44)( 36, 43)( 47, 48)( 49, 50)( 52, 54)
( 55, 64)( 56, 66)( 57, 65)( 58, 68)( 59, 67)( 60, 69)( 61, 72)( 62, 71)
( 63, 70)( 74, 75)( 76, 77)( 79, 81)( 82, 91)( 83, 93)( 84, 92)( 85, 95)
( 86, 94)( 87, 96)( 88, 99)( 89, 98)( 90, 97)(101,102)(103,104)(106,108)
(109,118)(110,120)(111,119)(112,122)(113,121)(114,123)(115,126)(116,125)
(117,124)(128,129)(130,131)(133,135)(136,145)(137,147)(138,146)(139,149)
(140,148)(141,150)(142,153)(143,152)(144,151)(155,156)(157,158)(160,162)
(163,172)(164,174)(165,173)(166,176)(167,175)(168,177)(169,180)(170,179)
(171,178)(182,183)(184,185)(187,189)(190,199)(191,201)(192,200)(193,203)
(194,202)(195,204)(196,207)(197,206)(198,205)(209,210)(211,212)(214,216)
(217,226)(218,228)(219,227)(220,230)(221,229)(222,231)(223,234)(224,233)
(225,232)(236,237)(238,239)(241,243)(244,253)(245,255)(246,254)(247,257)
(248,256)(249,258)(250,261)(251,260)(252,259)(263,264)(265,266)(268,270)
(271,280)(272,282)(273,281)(274,284)(275,283)(276,285)(277,288)(278,287)
(279,286)(290,291)(292,293)(295,297)(298,307)(299,309)(300,308)(301,311)
(302,310)(303,312)(304,315)(305,314)(306,313)(317,318)(319,320)(322,324)
(325,334)(326,336)(327,335)(328,338)(329,337)(330,339)(331,342)(332,341)
(333,340)(344,345)(346,347)(349,351)(352,361)(353,363)(354,362)(355,365)
(356,364)(357,366)(358,369)(359,368)(360,367)(371,372)(373,374)(376,378)
(379,388)(380,390)(381,389)(382,392)(383,391)(384,393)(385,396)(386,395)
(387,394)(398,399)(400,401)(403,405)(406,415)(407,417)(408,416)(409,419)
(410,418)(411,420)(412,423)(413,422)(414,421)(425,426)(427,428)(430,432);;
s3 := ( 2, 3)( 5, 6)( 8, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)
( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)( 37, 46)
( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)( 45, 53)
( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)( 68, 78)
( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)( 91,100)
( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)( 99,107)
(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)(122,132)
(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)(145,154)
(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)(153,161)
(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)(176,186)
(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)(199,208)
(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)(207,215)
(218,219)(221,222)(224,225)(226,235)(227,237)(228,236)(229,238)(230,240)
(231,239)(232,241)(233,243)(234,242)(245,246)(248,249)(251,252)(253,262)
(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)(261,269)
(272,273)(275,276)(278,279)(280,289)(281,291)(282,290)(283,292)(284,294)
(285,293)(286,295)(287,297)(288,296)(299,300)(302,303)(305,306)(307,316)
(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)(314,324)(315,323)
(326,327)(329,330)(332,333)(334,343)(335,345)(336,344)(337,346)(338,348)
(339,347)(340,349)(341,351)(342,350)(353,354)(356,357)(359,360)(361,370)
(362,372)(363,371)(364,373)(365,375)(366,374)(367,376)(368,378)(369,377)
(380,381)(383,384)(386,387)(388,397)(389,399)(390,398)(391,400)(392,402)
(393,401)(394,403)(395,405)(396,404)(407,408)(410,411)(413,414)(415,424)
(416,426)(417,425)(418,427)(419,429)(420,428)(421,430)(422,432)(423,431);;
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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
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*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)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)
( 51, 53)( 55, 82)( 56, 84)( 57, 83)( 58, 88)( 59, 90)( 60, 89)( 61, 85)
( 62, 87)( 63, 86)( 64, 91)( 65, 93)( 66, 92)( 67, 97)( 68, 99)( 69, 98)
( 70, 94)( 71, 96)( 72, 95)( 73,100)( 74,102)( 75,101)( 76,106)( 77,108)
( 78,107)( 79,103)( 80,105)( 81,104)(109,163)(110,165)(111,164)(112,169)
(113,171)(114,170)(115,166)(116,168)(117,167)(118,172)(119,174)(120,173)
(121,178)(122,180)(123,179)(124,175)(125,177)(126,176)(127,181)(128,183)
(129,182)(130,187)(131,189)(132,188)(133,184)(134,186)(135,185)(136,190)
(137,192)(138,191)(139,196)(140,198)(141,197)(142,193)(143,195)(144,194)
(145,199)(146,201)(147,200)(148,205)(149,207)(150,206)(151,202)(152,204)
(153,203)(154,208)(155,210)(156,209)(157,214)(158,216)(159,215)(160,211)
(161,213)(162,212)(217,325)(218,327)(219,326)(220,331)(221,333)(222,332)
(223,328)(224,330)(225,329)(226,334)(227,336)(228,335)(229,340)(230,342)
(231,341)(232,337)(233,339)(234,338)(235,343)(236,345)(237,344)(238,349)
(239,351)(240,350)(241,346)(242,348)(243,347)(244,352)(245,354)(246,353)
(247,358)(248,360)(249,359)(250,355)(251,357)(252,356)(253,361)(254,363)
(255,362)(256,367)(257,369)(258,368)(259,364)(260,366)(261,365)(262,370)
(263,372)(264,371)(265,376)(266,378)(267,377)(268,373)(269,375)(270,374)
(271,406)(272,408)(273,407)(274,412)(275,414)(276,413)(277,409)(278,411)
(279,410)(280,415)(281,417)(282,416)(283,421)(284,423)(285,422)(286,418)
(287,420)(288,419)(289,424)(290,426)(291,425)(292,430)(293,432)(294,431)
(295,427)(296,429)(297,428)(298,379)(299,381)(300,380)(301,385)(302,387)
(303,386)(304,382)(305,384)(306,383)(307,388)(308,390)(309,389)(310,394)
(311,396)(312,395)(313,391)(314,393)(315,392)(316,397)(317,399)(318,398)
(319,403)(320,405)(321,404)(322,400)(323,402)(324,401);
s1 := Sym(432)!( 1,220)( 2,222)( 3,221)( 4,217)( 5,219)( 6,218)( 7,223)
( 8,225)( 9,224)( 10,229)( 11,231)( 12,230)( 13,226)( 14,228)( 15,227)
( 16,232)( 17,234)( 18,233)( 19,238)( 20,240)( 21,239)( 22,235)( 23,237)
( 24,236)( 25,241)( 26,243)( 27,242)( 28,247)( 29,249)( 30,248)( 31,244)
( 32,246)( 33,245)( 34,250)( 35,252)( 36,251)( 37,256)( 38,258)( 39,257)
( 40,253)( 41,255)( 42,254)( 43,259)( 44,261)( 45,260)( 46,265)( 47,267)
( 48,266)( 49,262)( 50,264)( 51,263)( 52,268)( 53,270)( 54,269)( 55,301)
( 56,303)( 57,302)( 58,298)( 59,300)( 60,299)( 61,304)( 62,306)( 63,305)
( 64,310)( 65,312)( 66,311)( 67,307)( 68,309)( 69,308)( 70,313)( 71,315)
( 72,314)( 73,319)( 74,321)( 75,320)( 76,316)( 77,318)( 78,317)( 79,322)
( 80,324)( 81,323)( 82,274)( 83,276)( 84,275)( 85,271)( 86,273)( 87,272)
( 88,277)( 89,279)( 90,278)( 91,283)( 92,285)( 93,284)( 94,280)( 95,282)
( 96,281)( 97,286)( 98,288)( 99,287)(100,292)(101,294)(102,293)(103,289)
(104,291)(105,290)(106,295)(107,297)(108,296)(109,382)(110,384)(111,383)
(112,379)(113,381)(114,380)(115,385)(116,387)(117,386)(118,391)(119,393)
(120,392)(121,388)(122,390)(123,389)(124,394)(125,396)(126,395)(127,400)
(128,402)(129,401)(130,397)(131,399)(132,398)(133,403)(134,405)(135,404)
(136,409)(137,411)(138,410)(139,406)(140,408)(141,407)(142,412)(143,414)
(144,413)(145,418)(146,420)(147,419)(148,415)(149,417)(150,416)(151,421)
(152,423)(153,422)(154,427)(155,429)(156,428)(157,424)(158,426)(159,425)
(160,430)(161,432)(162,431)(163,328)(164,330)(165,329)(166,325)(167,327)
(168,326)(169,331)(170,333)(171,332)(172,337)(173,339)(174,338)(175,334)
(176,336)(177,335)(178,340)(179,342)(180,341)(181,346)(182,348)(183,347)
(184,343)(185,345)(186,344)(187,349)(188,351)(189,350)(190,355)(191,357)
(192,356)(193,352)(194,354)(195,353)(196,358)(197,360)(198,359)(199,364)
(200,366)(201,365)(202,361)(203,363)(204,362)(205,367)(206,369)(207,368)
(208,373)(209,375)(210,374)(211,370)(212,372)(213,371)(214,376)(215,378)
(216,377);
s2 := Sym(432)!( 1, 10)( 2, 12)( 3, 11)( 4, 14)( 5, 13)( 6, 15)( 7, 18)
( 8, 17)( 9, 16)( 20, 21)( 22, 23)( 25, 27)( 28, 37)( 29, 39)( 30, 38)
( 31, 41)( 32, 40)( 33, 42)( 34, 45)( 35, 44)( 36, 43)( 47, 48)( 49, 50)
( 52, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 68)( 59, 67)( 60, 69)( 61, 72)
( 62, 71)( 63, 70)( 74, 75)( 76, 77)( 79, 81)( 82, 91)( 83, 93)( 84, 92)
( 85, 95)( 86, 94)( 87, 96)( 88, 99)( 89, 98)( 90, 97)(101,102)(103,104)
(106,108)(109,118)(110,120)(111,119)(112,122)(113,121)(114,123)(115,126)
(116,125)(117,124)(128,129)(130,131)(133,135)(136,145)(137,147)(138,146)
(139,149)(140,148)(141,150)(142,153)(143,152)(144,151)(155,156)(157,158)
(160,162)(163,172)(164,174)(165,173)(166,176)(167,175)(168,177)(169,180)
(170,179)(171,178)(182,183)(184,185)(187,189)(190,199)(191,201)(192,200)
(193,203)(194,202)(195,204)(196,207)(197,206)(198,205)(209,210)(211,212)
(214,216)(217,226)(218,228)(219,227)(220,230)(221,229)(222,231)(223,234)
(224,233)(225,232)(236,237)(238,239)(241,243)(244,253)(245,255)(246,254)
(247,257)(248,256)(249,258)(250,261)(251,260)(252,259)(263,264)(265,266)
(268,270)(271,280)(272,282)(273,281)(274,284)(275,283)(276,285)(277,288)
(278,287)(279,286)(290,291)(292,293)(295,297)(298,307)(299,309)(300,308)
(301,311)(302,310)(303,312)(304,315)(305,314)(306,313)(317,318)(319,320)
(322,324)(325,334)(326,336)(327,335)(328,338)(329,337)(330,339)(331,342)
(332,341)(333,340)(344,345)(346,347)(349,351)(352,361)(353,363)(354,362)
(355,365)(356,364)(357,366)(358,369)(359,368)(360,367)(371,372)(373,374)
(376,378)(379,388)(380,390)(381,389)(382,392)(383,391)(384,393)(385,396)
(386,395)(387,394)(398,399)(400,401)(403,405)(406,415)(407,417)(408,416)
(409,419)(410,418)(411,420)(412,423)(413,422)(414,421)(425,426)(427,428)
(430,432);
s3 := Sym(432)!( 2, 3)( 5, 6)( 8, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)
( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)
( 37, 46)( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)
( 45, 53)( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)
( 68, 78)( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)
( 91,100)( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)
( 99,107)(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)
(122,132)(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)
(145,154)(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)
(153,161)(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)
(176,186)(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)
(199,208)(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)
(207,215)(218,219)(221,222)(224,225)(226,235)(227,237)(228,236)(229,238)
(230,240)(231,239)(232,241)(233,243)(234,242)(245,246)(248,249)(251,252)
(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)
(261,269)(272,273)(275,276)(278,279)(280,289)(281,291)(282,290)(283,292)
(284,294)(285,293)(286,295)(287,297)(288,296)(299,300)(302,303)(305,306)
(307,316)(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)(314,324)
(315,323)(326,327)(329,330)(332,333)(334,343)(335,345)(336,344)(337,346)
(338,348)(339,347)(340,349)(341,351)(342,350)(353,354)(356,357)(359,360)
(361,370)(362,372)(363,371)(364,373)(365,375)(366,374)(367,376)(368,378)
(369,377)(380,381)(383,384)(386,387)(388,397)(389,399)(390,398)(391,400)
(392,402)(393,401)(394,403)(395,405)(396,404)(407,408)(410,411)(413,414)
(415,424)(416,426)(417,425)(418,427)(419,429)(420,428)(421,430)(422,432)
(423,431);
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,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 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*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