Polytope of Type {3,6,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,6,4}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 5
Schlafli Type : {3,6,6,4}
Number of vertices, edges, etc : 3, 9, 36, 24, 8
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 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 : {3,6,3,4}*864, {3,6,6,4}*864b, {3,6,6,4}*864c
3-fold quotients : {3,2,6,4}*576
4-fold quotients : {3,6,3,4}*432, {3,6,6,2}*432a
6-fold quotients : {3,2,3,4}*288, {3,2,6,4}*288b, {3,2,6,4}*288c
8-fold quotients : {3,6,3,2}*216
12-fold quotients : {3,2,3,4}*144, {3,2,6,2}*144
24-fold quotients : {3,2,3,2}*72
36-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s3*s4*s3*s4> of order 2.
4 facets:
4 of {3,6,6}*216a
3 vertex figures:
3 of 2-fold non-regular quotient of {6,6,4}*576b
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)(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);;
s1 := ( 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);;
s2 := ( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 45)( 6, 48)( 7, 47)( 8, 46)( 9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 57)( 22, 60)( 23, 59)( 24, 58)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 74, 76)( 77, 81)( 78, 84)( 79, 83)( 80, 82)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 94, 96)( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,145)(110,148)(111,147)(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)(120,150)(121,161)(122,164)(123,163)(124,162)(125,157)(126,160)(127,159)(128,158)(129,165)(130,168)(131,167)(132,166)(133,177)(134,180)(135,179)(136,178)(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)(144,170)(182,184)(185,189)(186,192)(187,191)(188,190)(193,197)(194,200)(195,199)(196,198)(202,204)(205,213)(206,216)(207,215)(208,214)(210,212)(217,253)(218,256)(219,255)(220,254)(221,261)(222,264)(223,263)(224,262)(225,257)(226,260)(227,259)(228,258)(229,269)(230,272)(231,271)(232,270)(233,265)(234,268)(235,267)(236,266)(237,273)(238,276)(239,275)(240,274)(241,285)(242,288)(243,287)(244,286)(245,281)(246,284)(247,283)(248,282)(249,277)(250,280)(251,279)(252,278)(290,292)(293,297)(294,300)(295,299)(296,298)(301,305)(302,308)(303,307)(304,306)(310,312)(313,321)(314,324)(315,323)(316,322)(318,320)(325,361)(326,364)(327,363)(328,362)(329,369)(330,372)(331,371)(332,370)(333,365)(334,368)(335,367)(336,366)(337,377)(338,380)(339,379)(340,378)(341,373)(342,376)(343,375)(344,374)(345,381)(346,384)(347,383)(348,382)(349,393)(350,396)(351,395)(352,394)(353,389)(354,392)(355,391)(356,390)(357,385)(358,388)(359,387)(360,386)(398,400)(401,405)(402,408)(403,407)(404,406)(409,413)(410,416)(411,415)(412,414)(418,420)(421,429)(422,432)(423,431)(424,430)(426,428);;
s3 := ( 1,217)( 2,218)( 3,220)( 4,219)( 5,225)( 6,226)( 7,228)( 8,227)( 9,221)( 10,222)( 11,224)( 12,223)( 13,229)( 14,230)( 15,232)( 16,231)( 17,237)( 18,238)( 19,240)( 20,239)( 21,233)( 22,234)( 23,236)( 24,235)( 25,241)( 26,242)( 27,244)( 28,243)( 29,249)( 30,250)( 31,252)( 32,251)( 33,245)( 34,246)( 35,248)( 36,247)( 37,289)( 38,290)( 39,292)( 40,291)( 41,297)( 42,298)( 43,300)( 44,299)( 45,293)( 46,294)( 47,296)( 48,295)( 49,301)( 50,302)( 51,304)( 52,303)( 53,309)( 54,310)( 55,312)( 56,311)( 57,305)( 58,306)( 59,308)( 60,307)( 61,313)( 62,314)( 63,316)( 64,315)( 65,321)( 66,322)( 67,324)( 68,323)( 69,317)( 70,318)( 71,320)( 72,319)( 73,253)( 74,254)( 75,256)( 76,255)( 77,261)( 78,262)( 79,264)( 80,263)( 81,257)( 82,258)( 83,260)( 84,259)( 85,265)( 86,266)( 87,268)( 88,267)( 89,273)( 90,274)( 91,276)( 92,275)( 93,269)( 94,270)( 95,272)( 96,271)( 97,277)( 98,278)( 99,280)(100,279)(101,285)(102,286)(103,288)(104,287)(105,281)(106,282)(107,284)(108,283)(109,325)(110,326)(111,328)(112,327)(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)(120,331)(121,337)(122,338)(123,340)(124,339)(125,345)(126,346)(127,348)(128,347)(129,341)(130,342)(131,344)(132,343)(133,349)(134,350)(135,352)(136,351)(137,357)(138,358)(139,360)(140,359)(141,353)(142,354)(143,356)(144,355)(145,397)(146,398)(147,400)(148,399)(149,405)(150,406)(151,408)(152,407)(153,401)(154,402)(155,404)(156,403)(157,409)(158,410)(159,412)(160,411)(161,417)(162,418)(163,420)(164,419)(165,413)(166,414)(167,416)(168,415)(169,421)(170,422)(171,424)(172,423)(173,429)(174,430)(175,432)(176,431)(177,425)(178,426)(179,428)(180,427)(181,361)(182,362)(183,364)(184,363)(185,369)(186,370)(187,372)(188,371)(189,365)(190,366)(191,368)(192,367)(193,373)(194,374)(195,376)(196,375)(197,381)(198,382)(199,384)(200,383)(201,377)(202,378)(203,380)(204,379)(205,385)(206,386)(207,388)(208,387)(209,393)(210,394)(211,396)(212,395)(213,389)(214,390)(215,392)(216,391);;
s4 := ( 1,111)( 2,112)( 3,109)( 4,110)( 5,115)( 6,116)( 7,113)( 8,114)( 9,119)( 10,120)( 11,117)( 12,118)( 13,123)( 14,124)( 15,121)( 16,122)( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)( 22,132)( 23,129)( 24,130)( 25,135)( 26,136)( 27,133)( 28,134)( 29,139)( 30,140)( 31,137)( 32,138)( 33,143)( 34,144)( 35,141)( 36,142)( 37,147)( 38,148)( 39,145)( 40,146)( 41,151)( 42,152)( 43,149)( 44,150)( 45,155)( 46,156)( 47,153)( 48,154)( 49,159)( 50,160)( 51,157)( 52,158)( 53,163)( 54,164)( 55,161)( 56,162)( 57,167)( 58,168)( 59,165)( 60,166)( 61,171)( 62,172)( 63,169)( 64,170)( 65,175)( 66,176)( 67,173)( 68,174)( 69,179)( 70,180)( 71,177)( 72,178)( 73,183)( 74,184)( 75,181)( 76,182)( 77,187)( 78,188)( 79,185)( 80,186)( 81,191)( 82,192)( 83,189)( 84,190)( 85,195)( 86,196)( 87,193)( 88,194)( 89,199)( 90,200)( 91,197)( 92,198)( 93,203)( 94,204)( 95,201)( 96,202)( 97,207)( 98,208)( 99,205)(100,206)(101,211)(102,212)(103,209)(104,210)(105,215)(106,216)(107,213)(108,214)(217,327)(218,328)(219,325)(220,326)(221,331)(222,332)(223,329)(224,330)(225,335)(226,336)(227,333)(228,334)(229,339)(230,340)(231,337)(232,338)(233,343)(234,344)(235,341)(236,342)(237,347)(238,348)(239,345)(240,346)(241,351)(242,352)(243,349)(244,350)(245,355)(246,356)(247,353)(248,354)(249,359)(250,360)(251,357)(252,358)(253,363)(254,364)(255,361)(256,362)(257,367)(258,368)(259,365)(260,366)(261,371)(262,372)(263,369)(264,370)(265,375)(266,376)(267,373)(268,374)(269,379)(270,380)(271,377)(272,378)(273,383)(274,384)(275,381)(276,382)(277,387)(278,388)(279,385)(280,386)(281,391)(282,392)(283,389)(284,390)(285,395)(286,396)(287,393)(288,394)(289,399)(290,400)(291,397)(292,398)(293,403)(294,404)(295,401)(296,402)(297,407)(298,408)(299,405)(300,406)(301,411)(302,412)(303,409)(304,410)(305,415)(306,416)(307,413)(308,414)(309,419)(310,420)(311,417)(312,418)(313,423)(314,424)(315,421)(316,422)(317,427)(318,428)(319,425)(320,426)(321,431)(322,432)(323,429)(324,430);;
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, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3 ];;
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)(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);
s1 := 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);
s2 := Sym(432)!( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 45)( 6, 48)( 7, 47)( 8, 46)( 9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 57)( 22, 60)( 23, 59)( 24, 58)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 74, 76)( 77, 81)( 78, 84)( 79, 83)( 80, 82)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 94, 96)( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,145)(110,148)(111,147)(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)(120,150)(121,161)(122,164)(123,163)(124,162)(125,157)(126,160)(127,159)(128,158)(129,165)(130,168)(131,167)(132,166)(133,177)(134,180)(135,179)(136,178)(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)(144,170)(182,184)(185,189)(186,192)(187,191)(188,190)(193,197)(194,200)(195,199)(196,198)(202,204)(205,213)(206,216)(207,215)(208,214)(210,212)(217,253)(218,256)(219,255)(220,254)(221,261)(222,264)(223,263)(224,262)(225,257)(226,260)(227,259)(228,258)(229,269)(230,272)(231,271)(232,270)(233,265)(234,268)(235,267)(236,266)(237,273)(238,276)(239,275)(240,274)(241,285)(242,288)(243,287)(244,286)(245,281)(246,284)(247,283)(248,282)(249,277)(250,280)(251,279)(252,278)(290,292)(293,297)(294,300)(295,299)(296,298)(301,305)(302,308)(303,307)(304,306)(310,312)(313,321)(314,324)(315,323)(316,322)(318,320)(325,361)(326,364)(327,363)(328,362)(329,369)(330,372)(331,371)(332,370)(333,365)(334,368)(335,367)(336,366)(337,377)(338,380)(339,379)(340,378)(341,373)(342,376)(343,375)(344,374)(345,381)(346,384)(347,383)(348,382)(349,393)(350,396)(351,395)(352,394)(353,389)(354,392)(355,391)(356,390)(357,385)(358,388)(359,387)(360,386)(398,400)(401,405)(402,408)(403,407)(404,406)(409,413)(410,416)(411,415)(412,414)(418,420)(421,429)(422,432)(423,431)(424,430)(426,428);
s3 := Sym(432)!( 1,217)( 2,218)( 3,220)( 4,219)( 5,225)( 6,226)( 7,228)( 8,227)( 9,221)( 10,222)( 11,224)( 12,223)( 13,229)( 14,230)( 15,232)( 16,231)( 17,237)( 18,238)( 19,240)( 20,239)( 21,233)( 22,234)( 23,236)( 24,235)( 25,241)( 26,242)( 27,244)( 28,243)( 29,249)( 30,250)( 31,252)( 32,251)( 33,245)( 34,246)( 35,248)( 36,247)( 37,289)( 38,290)( 39,292)( 40,291)( 41,297)( 42,298)( 43,300)( 44,299)( 45,293)( 46,294)( 47,296)( 48,295)( 49,301)( 50,302)( 51,304)( 52,303)( 53,309)( 54,310)( 55,312)( 56,311)( 57,305)( 58,306)( 59,308)( 60,307)( 61,313)( 62,314)( 63,316)( 64,315)( 65,321)( 66,322)( 67,324)( 68,323)( 69,317)( 70,318)( 71,320)( 72,319)( 73,253)( 74,254)( 75,256)( 76,255)( 77,261)( 78,262)( 79,264)( 80,263)( 81,257)( 82,258)( 83,260)( 84,259)( 85,265)( 86,266)( 87,268)( 88,267)( 89,273)( 90,274)( 91,276)( 92,275)( 93,269)( 94,270)( 95,272)( 96,271)( 97,277)( 98,278)( 99,280)(100,279)(101,285)(102,286)(103,288)(104,287)(105,281)(106,282)(107,284)(108,283)(109,325)(110,326)(111,328)(112,327)(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)(120,331)(121,337)(122,338)(123,340)(124,339)(125,345)(126,346)(127,348)(128,347)(129,341)(130,342)(131,344)(132,343)(133,349)(134,350)(135,352)(136,351)(137,357)(138,358)(139,360)(140,359)(141,353)(142,354)(143,356)(144,355)(145,397)(146,398)(147,400)(148,399)(149,405)(150,406)(151,408)(152,407)(153,401)(154,402)(155,404)(156,403)(157,409)(158,410)(159,412)(160,411)(161,417)(162,418)(163,420)(164,419)(165,413)(166,414)(167,416)(168,415)(169,421)(170,422)(171,424)(172,423)(173,429)(174,430)(175,432)(176,431)(177,425)(178,426)(179,428)(180,427)(181,361)(182,362)(183,364)(184,363)(185,369)(186,370)(187,372)(188,371)(189,365)(190,366)(191,368)(192,367)(193,373)(194,374)(195,376)(196,375)(197,381)(198,382)(199,384)(200,383)(201,377)(202,378)(203,380)(204,379)(205,385)(206,386)(207,388)(208,387)(209,393)(210,394)(211,396)(212,395)(213,389)(214,390)(215,392)(216,391);
s4 := Sym(432)!( 1,111)( 2,112)( 3,109)( 4,110)( 5,115)( 6,116)( 7,113)( 8,114)( 9,119)( 10,120)( 11,117)( 12,118)( 13,123)( 14,124)( 15,121)( 16,122)( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)( 22,132)( 23,129)( 24,130)( 25,135)( 26,136)( 27,133)( 28,134)( 29,139)( 30,140)( 31,137)( 32,138)( 33,143)( 34,144)( 35,141)( 36,142)( 37,147)( 38,148)( 39,145)( 40,146)( 41,151)( 42,152)( 43,149)( 44,150)( 45,155)( 46,156)( 47,153)( 48,154)( 49,159)( 50,160)( 51,157)( 52,158)( 53,163)( 54,164)( 55,161)( 56,162)( 57,167)( 58,168)( 59,165)( 60,166)( 61,171)( 62,172)( 63,169)( 64,170)( 65,175)( 66,176)( 67,173)( 68,174)( 69,179)( 70,180)( 71,177)( 72,178)( 73,183)( 74,184)( 75,181)( 76,182)( 77,187)( 78,188)( 79,185)( 80,186)( 81,191)( 82,192)( 83,189)( 84,190)( 85,195)( 86,196)( 87,193)( 88,194)( 89,199)( 90,200)( 91,197)( 92,198)( 93,203)( 94,204)( 95,201)( 96,202)( 97,207)( 98,208)( 99,205)(100,206)(101,211)(102,212)(103,209)(104,210)(105,215)(106,216)(107,213)(108,214)(217,327)(218,328)(219,325)(220,326)(221,331)(222,332)(223,329)(224,330)(225,335)(226,336)(227,333)(228,334)(229,339)(230,340)(231,337)(232,338)(233,343)(234,344)(235,341)(236,342)(237,347)(238,348)(239,345)(240,346)(241,351)(242,352)(243,349)(244,350)(245,355)(246,356)(247,353)(248,354)(249,359)(250,360)(251,357)(252,358)(253,363)(254,364)(255,361)(256,362)(257,367)(258,368)(259,365)(260,366)(261,371)(262,372)(263,369)(264,370)(265,375)(266,376)(267,373)(268,374)(269,379)(270,380)(271,377)(272,378)(273,383)(274,384)(275,381)(276,382)(277,387)(278,388)(279,385)(280,386)(281,391)(282,392)(283,389)(284,390)(285,395)(286,396)(287,393)(288,394)(289,399)(290,400)(291,397)(292,398)(293,403)(294,404)(295,401)(296,402)(297,407)(298,408)(299,405)(300,406)(301,411)(302,412)(303,409)(304,410)(305,415)(306,416)(307,413)(308,414)(309,419)(310,420)(311,417)(312,418)(313,423)(314,424)(315,421)(316,422)(317,427)(318,428)(319,425)(320,426)(321,431)(322,432)(323,429)(324,430);
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, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3 >;
References : None.
to this polytope