Polytope of Type {4,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 4
Schlafli Type : {4,6,6}
Number of vertices, edges, etc : 8, 72, 108, 18
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {4,3,6}*864, {4,6,6}*864d, {4,6,6}*864f
   3-fold quotients : {4,6,6}*576b
   4-fold quotients : {4,3,6}*432, {2,6,6}*432c
   6-fold quotients : {4,3,6}*288, {4,6,6}*288e, {4,6,6}*288f
   8-fold quotients : {2,3,6}*216
   9-fold quotients : {4,6,2}*192
   12-fold quotients : {4,3,6}*144, {2,6,6}*144c
   18-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
   24-fold quotients : {2,3,6}*72
   36-fold quotients : {4,3,2}*48, {2,6,2}*48
   72-fold quotients : {2,3,2}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1> of order 2.
      18 facets:
         18 of 2-fold non-regular quotient of {4,6}*96
      4 vertex figures:
         4 of {6,6}*216c
   P/N, where N=<s1*s2*s3*s2*s1*s2*s3*s2> of order 3.
      6 facets:
         6 of {4,6}*96
      8 vertex figures:
         8 of 3-fold non-regular quotient of {6,6}*216c
   P/N, where N=<s0*s1*s0*s1, s1*s2*s3*s2*s1*s3> of order 6.
      6 facets:
         6 of 2-fold non-regular quotient of {4,6}*96
      4 vertex figures:
         4 of 3-fold non-regular quotient of {6,6}*216c
   P/N, where N=<s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2> of order 6.
      6 facets:
         6 of 2-fold non-regular quotient of {4,6}*96
      4 vertex figures:
         4 of 3-fold non-regular quotient of {6,6}*216c

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