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Polytope of Type {4,6,3}

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