Polytope of Type {4,6,9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,9}*1728a
if this polytope has a name.
Group : SmallGroup(1728,30216)
Rank : 4
Schlafli Type : {4,6,9}
Number of vertices, edges, etc : 4, 48, 108, 36
Order of s0s1s2s3 : 36
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 : {2,6,9}*864
3-fold quotients : {4,6,3}*576a
4-fold quotients : {4,6,9}*432
6-fold quotients : {2,6,3}*288
8-fold quotients : {2,6,9}*216
9-fold quotients : {4,6,3}*192
12-fold quotients : {4,2,9}*144, {4,6,3}*144
18-fold quotients : {2,6,3}*96
24-fold quotients : {2,2,9}*72, {2,6,3}*72
36-fold quotients : {4,2,3}*48, {2,3,3}*48
72-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 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, 85)( 50, 86)( 51, 88)
( 52, 87)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 93)( 58, 94)( 59, 96)
( 60, 95)( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,101)( 66,102)( 67,104)
( 68,103)( 69,105)( 70,106)( 71,108)( 72,107)(111,112)(115,116)(119,120)
(123,124)(127,128)(131,132)(135,136)(139,140)(143,144)(145,181)(146,182)
(147,184)(148,183)(149,185)(150,186)(151,188)(152,187)(153,189)(154,190)
(155,192)(156,191)(157,193)(158,194)(159,196)(160,195)(161,197)(162,198)
(163,200)(164,199)(165,201)(166,202)(167,204)(168,203)(169,205)(170,206)
(171,208)(172,207)(173,209)(174,210)(175,212)(176,211)(177,213)(178,214)
(179,216)(180,215)(217,325)(218,326)(219,328)(220,327)(221,329)(222,330)
(223,332)(224,331)(225,333)(226,334)(227,336)(228,335)(229,337)(230,338)
(231,340)(232,339)(233,341)(234,342)(235,344)(236,343)(237,345)(238,346)
(239,348)(240,347)(241,349)(242,350)(243,352)(244,351)(245,353)(246,354)
(247,356)(248,355)(249,357)(250,358)(251,360)(252,359)(253,397)(254,398)
(255,400)(256,399)(257,401)(258,402)(259,404)(260,403)(261,405)(262,406)
(263,408)(264,407)(265,409)(266,410)(267,412)(268,411)(269,413)(270,414)
(271,416)(272,415)(273,417)(274,418)(275,420)(276,419)(277,421)(278,422)
(279,424)(280,423)(281,425)(282,426)(283,428)(284,427)(285,429)(286,430)
(287,432)(288,431)(289,361)(290,362)(291,364)(292,363)(293,365)(294,366)
(295,368)(296,367)(297,369)(298,370)(299,372)(300,371)(301,373)(302,374)
(303,376)(304,375)(305,377)(306,378)(307,380)(308,379)(309,381)(310,382)
(311,384)(312,383)(313,385)(314,386)(315,388)(316,387)(317,389)(318,390)
(319,392)(320,391)(321,393)(322,394)(323,396)(324,395);;
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, 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)( 74, 76)( 77, 81)( 78, 84)( 79, 83)
( 80, 82)( 85,105)( 86,108)( 87,107)( 88,106)( 89,101)( 90,104)( 91,103)
( 92,102)( 93, 97)( 94,100)( 95, 99)( 96, 98)(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)(182,184)(185,189)(186,192)(187,191)(188,190)(193,213)(194,216)
(195,215)(196,214)(197,209)(198,212)(199,211)(200,210)(201,205)(202,208)
(203,207)(204,206)(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)(290,292)(293,297)
(294,300)(295,299)(296,298)(301,321)(302,324)(303,323)(304,322)(305,317)
(306,320)(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)(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)(398,400)(401,405)(402,408)(403,407)(404,406)
(409,429)(410,432)(411,431)(412,430)(413,425)(414,428)(415,427)(416,426)
(417,421)(418,424)(419,423)(420,422);;
s3 := ( 1, 14)( 2, 13)( 3, 15)( 4, 16)( 5, 22)( 6, 21)( 7, 23)( 8, 24)
( 9, 18)( 10, 17)( 11, 19)( 12, 20)( 25, 34)( 26, 33)( 27, 35)( 28, 36)
( 29, 30)( 37, 86)( 38, 85)( 39, 87)( 40, 88)( 41, 94)( 42, 93)( 43, 95)
( 44, 96)( 45, 90)( 46, 89)( 47, 91)( 48, 92)( 49, 74)( 50, 73)( 51, 75)
( 52, 76)( 53, 82)( 54, 81)( 55, 83)( 56, 84)( 57, 78)( 58, 77)( 59, 79)
( 60, 80)( 61,106)( 62,105)( 63,107)( 64,108)( 65,102)( 66,101)( 67,103)
( 68,104)( 69, 98)( 70, 97)( 71, 99)( 72,100)(109,122)(110,121)(111,123)
(112,124)(113,130)(114,129)(115,131)(116,132)(117,126)(118,125)(119,127)
(120,128)(133,142)(134,141)(135,143)(136,144)(137,138)(145,194)(146,193)
(147,195)(148,196)(149,202)(150,201)(151,203)(152,204)(153,198)(154,197)
(155,199)(156,200)(157,182)(158,181)(159,183)(160,184)(161,190)(162,189)
(163,191)(164,192)(165,186)(166,185)(167,187)(168,188)(169,214)(170,213)
(171,215)(172,216)(173,210)(174,209)(175,211)(176,212)(177,206)(178,205)
(179,207)(180,208)(217,230)(218,229)(219,231)(220,232)(221,238)(222,237)
(223,239)(224,240)(225,234)(226,233)(227,235)(228,236)(241,250)(242,249)
(243,251)(244,252)(245,246)(253,302)(254,301)(255,303)(256,304)(257,310)
(258,309)(259,311)(260,312)(261,306)(262,305)(263,307)(264,308)(265,290)
(266,289)(267,291)(268,292)(269,298)(270,297)(271,299)(272,300)(273,294)
(274,293)(275,295)(276,296)(277,322)(278,321)(279,323)(280,324)(281,318)
(282,317)(283,319)(284,320)(285,314)(286,313)(287,315)(288,316)(325,338)
(326,337)(327,339)(328,340)(329,346)(330,345)(331,347)(332,348)(333,342)
(334,341)(335,343)(336,344)(349,358)(350,357)(351,359)(352,360)(353,354)
(361,410)(362,409)(363,411)(364,412)(365,418)(366,417)(367,419)(368,420)
(369,414)(370,413)(371,415)(372,416)(373,398)(374,397)(375,399)(376,400)
(377,406)(378,405)(379,407)(380,408)(381,402)(382,401)(383,403)(384,404)
(385,430)(386,429)(387,431)(388,432)(389,426)(390,425)(391,427)(392,428)
(393,422)(394,421)(395,423)(396,424);;
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*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(432)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 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, 85)( 50, 86)
( 51, 88)( 52, 87)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 93)( 58, 94)
( 59, 96)( 60, 95)( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,101)( 66,102)
( 67,104)( 68,103)( 69,105)( 70,106)( 71,108)( 72,107)(111,112)(115,116)
(119,120)(123,124)(127,128)(131,132)(135,136)(139,140)(143,144)(145,181)
(146,182)(147,184)(148,183)(149,185)(150,186)(151,188)(152,187)(153,189)
(154,190)(155,192)(156,191)(157,193)(158,194)(159,196)(160,195)(161,197)
(162,198)(163,200)(164,199)(165,201)(166,202)(167,204)(168,203)(169,205)
(170,206)(171,208)(172,207)(173,209)(174,210)(175,212)(176,211)(177,213)
(178,214)(179,216)(180,215)(217,325)(218,326)(219,328)(220,327)(221,329)
(222,330)(223,332)(224,331)(225,333)(226,334)(227,336)(228,335)(229,337)
(230,338)(231,340)(232,339)(233,341)(234,342)(235,344)(236,343)(237,345)
(238,346)(239,348)(240,347)(241,349)(242,350)(243,352)(244,351)(245,353)
(246,354)(247,356)(248,355)(249,357)(250,358)(251,360)(252,359)(253,397)
(254,398)(255,400)(256,399)(257,401)(258,402)(259,404)(260,403)(261,405)
(262,406)(263,408)(264,407)(265,409)(266,410)(267,412)(268,411)(269,413)
(270,414)(271,416)(272,415)(273,417)(274,418)(275,420)(276,419)(277,421)
(278,422)(279,424)(280,423)(281,425)(282,426)(283,428)(284,427)(285,429)
(286,430)(287,432)(288,431)(289,361)(290,362)(291,364)(292,363)(293,365)
(294,366)(295,368)(296,367)(297,369)(298,370)(299,372)(300,371)(301,373)
(302,374)(303,376)(304,375)(305,377)(306,378)(307,380)(308,379)(309,381)
(310,382)(311,384)(312,383)(313,385)(314,386)(315,388)(316,387)(317,389)
(318,390)(319,392)(320,391)(321,393)(322,394)(323,396)(324,395);
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, 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)( 74, 76)( 77, 81)( 78, 84)
( 79, 83)( 80, 82)( 85,105)( 86,108)( 87,107)( 88,106)( 89,101)( 90,104)
( 91,103)( 92,102)( 93, 97)( 94,100)( 95, 99)( 96, 98)(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)(182,184)(185,189)(186,192)(187,191)(188,190)(193,213)
(194,216)(195,215)(196,214)(197,209)(198,212)(199,211)(200,210)(201,205)
(202,208)(203,207)(204,206)(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)(290,292)
(293,297)(294,300)(295,299)(296,298)(301,321)(302,324)(303,323)(304,322)
(305,317)(306,320)(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)
(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)(398,400)(401,405)(402,408)(403,407)
(404,406)(409,429)(410,432)(411,431)(412,430)(413,425)(414,428)(415,427)
(416,426)(417,421)(418,424)(419,423)(420,422);
s3 := Sym(432)!( 1, 14)( 2, 13)( 3, 15)( 4, 16)( 5, 22)( 6, 21)( 7, 23)
( 8, 24)( 9, 18)( 10, 17)( 11, 19)( 12, 20)( 25, 34)( 26, 33)( 27, 35)
( 28, 36)( 29, 30)( 37, 86)( 38, 85)( 39, 87)( 40, 88)( 41, 94)( 42, 93)
( 43, 95)( 44, 96)( 45, 90)( 46, 89)( 47, 91)( 48, 92)( 49, 74)( 50, 73)
( 51, 75)( 52, 76)( 53, 82)( 54, 81)( 55, 83)( 56, 84)( 57, 78)( 58, 77)
( 59, 79)( 60, 80)( 61,106)( 62,105)( 63,107)( 64,108)( 65,102)( 66,101)
( 67,103)( 68,104)( 69, 98)( 70, 97)( 71, 99)( 72,100)(109,122)(110,121)
(111,123)(112,124)(113,130)(114,129)(115,131)(116,132)(117,126)(118,125)
(119,127)(120,128)(133,142)(134,141)(135,143)(136,144)(137,138)(145,194)
(146,193)(147,195)(148,196)(149,202)(150,201)(151,203)(152,204)(153,198)
(154,197)(155,199)(156,200)(157,182)(158,181)(159,183)(160,184)(161,190)
(162,189)(163,191)(164,192)(165,186)(166,185)(167,187)(168,188)(169,214)
(170,213)(171,215)(172,216)(173,210)(174,209)(175,211)(176,212)(177,206)
(178,205)(179,207)(180,208)(217,230)(218,229)(219,231)(220,232)(221,238)
(222,237)(223,239)(224,240)(225,234)(226,233)(227,235)(228,236)(241,250)
(242,249)(243,251)(244,252)(245,246)(253,302)(254,301)(255,303)(256,304)
(257,310)(258,309)(259,311)(260,312)(261,306)(262,305)(263,307)(264,308)
(265,290)(266,289)(267,291)(268,292)(269,298)(270,297)(271,299)(272,300)
(273,294)(274,293)(275,295)(276,296)(277,322)(278,321)(279,323)(280,324)
(281,318)(282,317)(283,319)(284,320)(285,314)(286,313)(287,315)(288,316)
(325,338)(326,337)(327,339)(328,340)(329,346)(330,345)(331,347)(332,348)
(333,342)(334,341)(335,343)(336,344)(349,358)(350,357)(351,359)(352,360)
(353,354)(361,410)(362,409)(363,411)(364,412)(365,418)(366,417)(367,419)
(368,420)(369,414)(370,413)(371,415)(372,416)(373,398)(374,397)(375,399)
(376,400)(377,406)(378,405)(379,407)(380,408)(381,402)(382,401)(383,403)
(384,404)(385,430)(386,429)(387,431)(388,432)(389,426)(390,425)(391,427)
(392,428)(393,422)(394,421)(395,423)(396,424);
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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;
References : None.
to this polytope