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Polytope of Type {12,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,4}*1728e
if this polytope has a name.
Group : SmallGroup(1728,30326)
Rank : 4
Schlafli Type : {12,6,4}
Number of vertices, edges, etc : 36, 108, 36, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Non-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 : {6,6,4}*864e
   3-fold quotients : {12,6,4}*576e
   4-fold quotients : {6,3,4}*432
   6-fold quotients : {6,6,4}*288e
   9-fold quotients : {4,6,4}*192b
   12-fold quotients : {6,3,4}*144
   18-fold quotients : {2,6,4}*96c
   36-fold quotients : {2,3,4}*48
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 := (  1,229)(  2,230)(  3,232)(  4,231)(  5,233)(  6,234)(  7,236)(  8,235)
(  9,237)( 10,238)( 11,240)( 12,239)( 13,217)( 14,218)( 15,220)( 16,219)
( 17,221)( 18,222)( 19,224)( 20,223)( 21,225)( 22,226)( 23,228)( 24,227)
( 25,241)( 26,242)( 27,244)( 28,243)( 29,245)( 30,246)( 31,248)( 32,247)
( 33,249)( 34,250)( 35,252)( 36,251)( 37,301)( 38,302)( 39,304)( 40,303)
( 41,305)( 42,306)( 43,308)( 44,307)( 45,309)( 46,310)( 47,312)( 48,311)
( 49,289)( 50,290)( 51,292)( 52,291)( 53,293)( 54,294)( 55,296)( 56,295)
( 57,297)( 58,298)( 59,300)( 60,299)( 61,313)( 62,314)( 63,316)( 64,315)
( 65,317)( 66,318)( 67,320)( 68,319)( 69,321)( 70,322)( 71,324)( 72,323)
( 73,265)( 74,266)( 75,268)( 76,267)( 77,269)( 78,270)( 79,272)( 80,271)
( 81,273)( 82,274)( 83,276)( 84,275)( 85,253)( 86,254)( 87,256)( 88,255)
( 89,257)( 90,258)( 91,260)( 92,259)( 93,261)( 94,262)( 95,264)( 96,263)
( 97,277)( 98,278)( 99,280)(100,279)(101,281)(102,282)(103,284)(104,283)
(105,285)(106,286)(107,288)(108,287)(109,337)(110,338)(111,340)(112,339)
(113,341)(114,342)(115,344)(116,343)(117,345)(118,346)(119,348)(120,347)
(121,325)(122,326)(123,328)(124,327)(125,329)(126,330)(127,332)(128,331)
(129,333)(130,334)(131,336)(132,335)(133,349)(134,350)(135,352)(136,351)
(137,353)(138,354)(139,356)(140,355)(141,357)(142,358)(143,360)(144,359)
(145,409)(146,410)(147,412)(148,411)(149,413)(150,414)(151,416)(152,415)
(153,417)(154,418)(155,420)(156,419)(157,397)(158,398)(159,400)(160,399)
(161,401)(162,402)(163,404)(164,403)(165,405)(166,406)(167,408)(168,407)
(169,421)(170,422)(171,424)(172,423)(173,425)(174,426)(175,428)(176,427)
(177,429)(178,430)(179,432)(180,431)(181,373)(182,374)(183,376)(184,375)
(185,377)(186,378)(187,380)(188,379)(189,381)(190,382)(191,384)(192,383)
(193,361)(194,362)(195,364)(196,363)(197,365)(198,366)(199,368)(200,367)
(201,369)(202,370)(203,372)(204,371)(205,385)(206,386)(207,388)(208,387)
(209,389)(210,390)(211,392)(212,391)(213,393)(214,394)(215,396)(216,395);;
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,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432);;
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*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*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)!(  1,229)(  2,230)(  3,232)(  4,231)(  5,233)(  6,234)(  7,236)
(  8,235)(  9,237)( 10,238)( 11,240)( 12,239)( 13,217)( 14,218)( 15,220)
( 16,219)( 17,221)( 18,222)( 19,224)( 20,223)( 21,225)( 22,226)( 23,228)
( 24,227)( 25,241)( 26,242)( 27,244)( 28,243)( 29,245)( 30,246)( 31,248)
( 32,247)( 33,249)( 34,250)( 35,252)( 36,251)( 37,301)( 38,302)( 39,304)
( 40,303)( 41,305)( 42,306)( 43,308)( 44,307)( 45,309)( 46,310)( 47,312)
( 48,311)( 49,289)( 50,290)( 51,292)( 52,291)( 53,293)( 54,294)( 55,296)
( 56,295)( 57,297)( 58,298)( 59,300)( 60,299)( 61,313)( 62,314)( 63,316)
( 64,315)( 65,317)( 66,318)( 67,320)( 68,319)( 69,321)( 70,322)( 71,324)
( 72,323)( 73,265)( 74,266)( 75,268)( 76,267)( 77,269)( 78,270)( 79,272)
( 80,271)( 81,273)( 82,274)( 83,276)( 84,275)( 85,253)( 86,254)( 87,256)
( 88,255)( 89,257)( 90,258)( 91,260)( 92,259)( 93,261)( 94,262)( 95,264)
( 96,263)( 97,277)( 98,278)( 99,280)(100,279)(101,281)(102,282)(103,284)
(104,283)(105,285)(106,286)(107,288)(108,287)(109,337)(110,338)(111,340)
(112,339)(113,341)(114,342)(115,344)(116,343)(117,345)(118,346)(119,348)
(120,347)(121,325)(122,326)(123,328)(124,327)(125,329)(126,330)(127,332)
(128,331)(129,333)(130,334)(131,336)(132,335)(133,349)(134,350)(135,352)
(136,351)(137,353)(138,354)(139,356)(140,355)(141,357)(142,358)(143,360)
(144,359)(145,409)(146,410)(147,412)(148,411)(149,413)(150,414)(151,416)
(152,415)(153,417)(154,418)(155,420)(156,419)(157,397)(158,398)(159,400)
(160,399)(161,401)(162,402)(163,404)(164,403)(165,405)(166,406)(167,408)
(168,407)(169,421)(170,422)(171,424)(172,423)(173,425)(174,426)(175,428)
(176,427)(177,429)(178,430)(179,432)(180,431)(181,373)(182,374)(183,376)
(184,375)(185,377)(186,378)(187,380)(188,379)(189,381)(190,382)(191,384)
(192,383)(193,361)(194,362)(195,364)(196,363)(197,365)(198,366)(199,368)
(200,367)(201,369)(202,370)(203,372)(204,371)(205,385)(206,386)(207,388)
(208,387)(209,389)(210,390)(211,392)(212,391)(213,393)(214,394)(215,396)
(216,395);
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,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432);
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*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 >; 
 
References : None.
to this polytope