Polytope of Type {24,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,15888)
Rank : 4
Schlafli Type : {24,6,6}
Number of vertices, edges, etc : 24, 72, 18, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 6
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 : {24,6,3}*864a, {12,6,6}*864a
   3-fold quotients : {24,2,6}*576
   4-fold quotients : {12,6,3}*432a, {6,6,6}*432a
   6-fold quotients : {24,2,3}*288, {12,2,6}*288
   8-fold quotients : {3,6,6}*216a, {6,6,3}*216a
   9-fold quotients : {24,2,2}*192, {8,2,6}*192
   12-fold quotients : {12,2,3}*144, {6,2,6}*144
   16-fold quotients : {3,6,3}*108
   18-fold quotients : {8,2,3}*96, {12,2,2}*96, {4,2,6}*96
   24-fold quotients : {3,2,6}*72, {6,2,3}*72
   27-fold quotients : {8,2,2}*64
   36-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
   48-fold quotients : {3,2,3}*36
   54-fold quotients : {4,2,2}*32
   72-fold quotients : {2,2,3}*24, {3,2,2}*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):
   None.

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