Polytope of Type {4,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,3}*1728a
Also Known As : {{4,12|2},{12,3}6}. if this polytope has another name.
Group : SmallGroup(1728,30326)
Rank : 4
Schlafli Type : {4,12,3}
Number of vertices, edges, etc : 4, 144, 108, 18
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 : {2,12,3}*864
   3-fold quotients : {4,12,3}*576
   4-fold quotients : {4,6,3}*432a
   6-fold quotients : {2,12,3}*288
   8-fold quotients : {2,6,3}*216
   9-fold quotients : {4,4,3}*192b
   12-fold quotients : {4,6,3}*144
   18-fold quotients : {2,4,3}*96
   24-fold quotients : {2,6,3}*72
   36-fold quotients : {4,2,3}*48, {2,4,3}*48
   72-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      12 facets:
         6 of {4,6}*48a
         6 of {4,12}*96a
      4 vertex figures:
         4 of 2-fold non-regular quotient of {12,3}*432
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2> of order 3.
      10 facets:
         6 of {4,4}*32
         4 of {4,12}*96a
      4 vertex figures:
         4 of 3-fold non-regular quotient of {12,3}*432
   P/N, where N=<s1*s2*s1*s2> of order 6.
      8 facets:
         6 of {4,2}*16
         2 of {4,12}*96a
      4 vertex figures:
         4 of 6-fold non-regular quotient of {12,3}*432
   P/N, where N=<s1*s3*s2*s1*s2*s1*s2*s1*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 6.
      6 facets:
         2 of {4,6}*48a
         3 of {4,4}*32
         1 of {4,12}*96a
      4 vertex figures:
         4 of 6-fold non-regular quotient of {12,3}*432

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