Polytope of Type {4,6,6,3} with group SmallGroup(1728,46116)

Overview

Group: SmallGroup(1728,46116)
Rank: 5
Schläfli Type: {4,6,6,3}
Vertices, edges, …: 8, 24, 36, 9, 3
Order of s₀s₁s₂s₃s₄: 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

3-fold

{4,6,2,3}*576

4-fold

6-fold

8-fold

{2,3,6,3}*216

12-fold

24-fold

{2,3,2,3}*72

36-fold

{2,2,2,3}*48

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2> of order 2

3 facets

3 of 2-fold non-regular quotient of {4,6,6}*576b

4 vertex figures

4 of {6,6,3}*216a

Representations

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)(  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)(219,220)(221,225)(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)(236,239)(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)(255,292)(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)(263,296)(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)(271,312)(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)(287,320)(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)(341,345)(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)(356,359)(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)(368,407)(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)(376,411)(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)(384,415)(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)(392,431)(393,425)(394,426)(395,428)(396,427);;
s2 := (  1,145)(  2,148)(  3,147)(  4,146)(  5,153)(  6,156)(  7,155)(  8,154)(  9,149)( 10,152)( 11,151)( 12,150)( 13,161)( 14,164)( 15,163)( 16,162)( 17,157)( 18,160)( 19,159)( 20,158)( 21,165)( 22,168)( 23,167)( 24,166)( 25,177)( 26,180)( 27,179)( 28,178)( 29,173)( 30,176)( 31,175)( 32,174)( 33,169)( 34,172)( 35,171)( 36,170)( 37,109)( 38,112)( 39,111)( 40,110)( 41,117)( 42,120)( 43,119)( 44,118)( 45,113)( 46,116)( 47,115)( 48,114)( 49,125)( 50,128)( 51,127)( 52,126)( 53,121)( 54,124)( 55,123)( 56,122)( 57,129)( 58,132)( 59,131)( 60,130)( 61,141)( 62,144)( 63,143)( 64,142)( 65,137)( 66,140)( 67,139)( 68,138)( 69,133)( 70,136)( 71,135)( 72,134)( 73,181)( 74,184)( 75,183)( 76,182)( 77,189)( 78,192)( 79,191)( 80,190)( 81,185)( 82,188)( 83,187)( 84,186)( 85,197)( 86,200)( 87,199)( 88,198)( 89,193)( 90,196)( 91,195)( 92,194)( 93,201)( 94,204)( 95,203)( 96,202)( 97,213)( 98,216)( 99,215)(100,214)(101,209)(102,212)(103,211)(104,210)(105,205)(106,208)(107,207)(108,206)(217,361)(218,364)(219,363)(220,362)(221,369)(222,372)(223,371)(224,370)(225,365)(226,368)(227,367)(228,366)(229,377)(230,380)(231,379)(232,378)(233,373)(234,376)(235,375)(236,374)(237,381)(238,384)(239,383)(240,382)(241,393)(242,396)(243,395)(244,394)(245,389)(246,392)(247,391)(248,390)(249,385)(250,388)(251,387)(252,386)(253,325)(254,328)(255,327)(256,326)(257,333)(258,336)(259,335)(260,334)(261,329)(262,332)(263,331)(264,330)(265,341)(266,344)(267,343)(268,342)(269,337)(270,340)(271,339)(272,338)(273,345)(274,348)(275,347)(276,346)(277,357)(278,360)(279,359)(280,358)(281,353)(282,356)(283,355)(284,354)(285,349)(286,352)(287,351)(288,350)(289,397)(290,400)(291,399)(292,398)(293,405)(294,408)(295,407)(296,406)(297,401)(298,404)(299,403)(300,402)(301,413)(302,416)(303,415)(304,414)(305,409)(306,412)(307,411)(308,410)(309,417)(310,420)(311,419)(312,418)(313,429)(314,432)(315,431)(316,430)(317,425)(318,428)(319,427)(320,426)(321,421)(322,424)(323,423)(324,422);;
s3 := (  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5, 21)(  6, 22)(  7, 23)(  8, 24)(  9, 17)( 10, 18)( 11, 19)( 12, 20)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 89)( 82, 90)( 83, 91)( 84, 92)(101,105)(102,106)(103,107)(104,108)(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)(116,132)(117,125)(118,126)(119,127)(120,128)(137,141)(138,142)(139,143)(140,144)(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)(152,168)(153,161)(154,162)(155,163)(156,164)(173,177)(174,178)(175,179)(176,180)(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)(188,204)(189,197)(190,198)(191,199)(192,200)(209,213)(210,214)(211,215)(212,216)(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)(224,240)(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)(248,252)(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)(260,276)(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)(284,288)(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)(296,312)(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)(320,324)(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)(332,348)(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)(356,360)(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)(368,384)(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)(392,396)(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)(404,420)(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)(428,432);;
s4 := (  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,s4]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)(  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)(219,220)(221,225)(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)(236,239)(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)(255,292)(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)(263,296)(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)(271,312)(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)(287,320)(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)(341,345)(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)(356,359)(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)(368,407)(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)(376,411)(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)(384,415)(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)(392,431)(393,425)(394,426)(395,428)(396,427);
s2 := Sym(432)!(  1,145)(  2,148)(  3,147)(  4,146)(  5,153)(  6,156)(  7,155)(  8,154)(  9,149)( 10,152)( 11,151)( 12,150)( 13,161)( 14,164)( 15,163)( 16,162)( 17,157)( 18,160)( 19,159)( 20,158)( 21,165)( 22,168)( 23,167)( 24,166)( 25,177)( 26,180)( 27,179)( 28,178)( 29,173)( 30,176)( 31,175)( 32,174)( 33,169)( 34,172)( 35,171)( 36,170)( 37,109)( 38,112)( 39,111)( 40,110)( 41,117)( 42,120)( 43,119)( 44,118)( 45,113)( 46,116)( 47,115)( 48,114)( 49,125)( 50,128)( 51,127)( 52,126)( 53,121)( 54,124)( 55,123)( 56,122)( 57,129)( 58,132)( 59,131)( 60,130)( 61,141)( 62,144)( 63,143)( 64,142)( 65,137)( 66,140)( 67,139)( 68,138)( 69,133)( 70,136)( 71,135)( 72,134)( 73,181)( 74,184)( 75,183)( 76,182)( 77,189)( 78,192)( 79,191)( 80,190)( 81,185)( 82,188)( 83,187)( 84,186)( 85,197)( 86,200)( 87,199)( 88,198)( 89,193)( 90,196)( 91,195)( 92,194)( 93,201)( 94,204)( 95,203)( 96,202)( 97,213)( 98,216)( 99,215)(100,214)(101,209)(102,212)(103,211)(104,210)(105,205)(106,208)(107,207)(108,206)(217,361)(218,364)(219,363)(220,362)(221,369)(222,372)(223,371)(224,370)(225,365)(226,368)(227,367)(228,366)(229,377)(230,380)(231,379)(232,378)(233,373)(234,376)(235,375)(236,374)(237,381)(238,384)(239,383)(240,382)(241,393)(242,396)(243,395)(244,394)(245,389)(246,392)(247,391)(248,390)(249,385)(250,388)(251,387)(252,386)(253,325)(254,328)(255,327)(256,326)(257,333)(258,336)(259,335)(260,334)(261,329)(262,332)(263,331)(264,330)(265,341)(266,344)(267,343)(268,342)(269,337)(270,340)(271,339)(272,338)(273,345)(274,348)(275,347)(276,346)(277,357)(278,360)(279,359)(280,358)(281,353)(282,356)(283,355)(284,354)(285,349)(286,352)(287,351)(288,350)(289,397)(290,400)(291,399)(292,398)(293,405)(294,408)(295,407)(296,406)(297,401)(298,404)(299,403)(300,402)(301,413)(302,416)(303,415)(304,414)(305,409)(306,412)(307,411)(308,410)(309,417)(310,420)(311,419)(312,418)(313,429)(314,432)(315,431)(316,430)(317,425)(318,428)(319,427)(320,426)(321,421)(322,424)(323,423)(324,422);
s3 := Sym(432)!(  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5, 21)(  6, 22)(  7, 23)(  8, 24)(  9, 17)( 10, 18)( 11, 19)( 12, 20)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 89)( 82, 90)( 83, 91)( 84, 92)(101,105)(102,106)(103,107)(104,108)(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)(116,132)(117,125)(118,126)(119,127)(120,128)(137,141)(138,142)(139,143)(140,144)(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)(152,168)(153,161)(154,162)(155,163)(156,164)(173,177)(174,178)(175,179)(176,180)(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)(188,204)(189,197)(190,198)(191,199)(192,200)(209,213)(210,214)(211,215)(212,216)(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)(224,240)(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)(248,252)(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)(260,276)(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)(284,288)(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)(296,312)(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)(320,324)(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)(332,348)(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)(356,360)(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)(368,384)(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)(392,396)(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)(404,420)(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)(428,432);
s4 := 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,s4>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.