Polytope of Type {4,3,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,6,4}*1728a
Also Known As : {{4,3}3,{3,6}6,{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1728,30326)
Rank : 5
Schlafli Type : {4,3,6,4}
Number of vertices, edges, etc : 4, 18, 27, 36, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Universal
Non-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 : {4,3,6,2}*864
3-fold quotients : {4,3,6,4}*576
6-fold quotients : {4,3,6,2}*288
9-fold quotients : {4,3,2,4}*192
18-fold quotients : {4,3,2,2}*96
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*s3*s2*s1*s3*s2> of order 3.
4 facets:
4 of 3-fold non-regular quotient of {4,3,6}*432
4 vertex figures:
4 of 3-fold non-regular quotient of {3,6,4}*432a
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432);;
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, 65)( 2, 68)( 3, 67)( 4, 66)( 5, 69)( 6, 72)( 7, 71)( 8, 70)( 9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 49)( 14, 52)( 15, 51)( 16, 50)( 17, 53)( 18, 56)( 19, 55)( 20, 54)( 21, 57)( 22, 60)( 23, 59)( 24, 58)( 25, 45)( 26, 48)( 27, 47)( 28, 46)( 29, 37)( 30, 40)( 31, 39)( 32, 38)( 33, 41)( 34, 44)( 35, 43)( 36, 42)( 73,101)( 74,104)( 75,103)( 76,102)( 77,105)( 78,108)( 79,107)( 80,106)( 81, 97)( 82,100)( 83, 99)( 84, 98)( 86, 88)( 90, 92)( 94, 96)(109,173)(110,176)(111,175)(112,174)(113,177)(114,180)(115,179)(116,178)(117,169)(118,172)(119,171)(120,170)(121,157)(122,160)(123,159)(124,158)(125,161)(126,164)(127,163)(128,162)(129,165)(130,168)(131,167)(132,166)(133,153)(134,156)(135,155)(136,154)(137,145)(138,148)(139,147)(140,146)(141,149)(142,152)(143,151)(144,150)(181,209)(182,212)(183,211)(184,210)(185,213)(186,216)(187,215)(188,214)(189,205)(190,208)(191,207)(192,206)(194,196)(198,200)(202,204)(217,281)(218,284)(219,283)(220,282)(221,285)(222,288)(223,287)(224,286)(225,277)(226,280)(227,279)(228,278)(229,265)(230,268)(231,267)(232,266)(233,269)(234,272)(235,271)(236,270)(237,273)(238,276)(239,275)(240,274)(241,261)(242,264)(243,263)(244,262)(245,253)(246,256)(247,255)(248,254)(249,257)(250,260)(251,259)(252,258)(289,317)(290,320)(291,319)(292,318)(293,321)(294,324)(295,323)(296,322)(297,313)(298,316)(299,315)(300,314)(302,304)(306,308)(310,312)(325,389)(326,392)(327,391)(328,390)(329,393)(330,396)(331,395)(332,394)(333,385)(334,388)(335,387)(336,386)(337,373)(338,376)(339,375)(340,374)(341,377)(342,380)(343,379)(344,378)(345,381)(346,384)(347,383)(348,382)(349,369)(350,372)(351,371)(352,370)(353,361)(354,364)(355,363)(356,362)(357,365)(358,368)(359,367)(360,366)(397,425)(398,428)(399,427)(400,426)(401,429)(402,432)(403,431)(404,430)(405,421)(406,424)(407,423)(408,422)(410,412)(414,416)(418,420);;
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)(217,325)(218,326)(219,327)(220,328)(221,333)(222,334)(223,335)(224,336)(225,329)(226,330)(227,331)(228,332)(229,349)(230,350)(231,351)(232,352)(233,357)(234,358)(235,359)(236,360)(237,353)(238,354)(239,355)(240,356)(241,337)(242,338)(243,339)(244,340)(245,345)(246,346)(247,347)(248,348)(249,341)(250,342)(251,343)(252,344)(253,361)(254,362)(255,363)(256,364)(257,369)(258,370)(259,371)(260,372)(261,365)(262,366)(263,367)(264,368)(265,385)(266,386)(267,387)(268,388)(269,393)(270,394)(271,395)(272,396)(273,389)(274,390)(275,391)(276,392)(277,373)(278,374)(279,375)(280,376)(281,381)(282,382)(283,383)(284,384)(285,377)(286,378)(287,379)(288,380)(289,397)(290,398)(291,399)(292,400)(293,405)(294,406)(295,407)(296,408)(297,401)(298,402)(299,403)(300,404)(301,421)(302,422)(303,423)(304,424)(305,429)(306,430)(307,431)(308,432)(309,425)(310,426)(311,427)(312,428)(313,409)(314,410)(315,411)(316,412)(317,417)(318,418)(319,419)(320,420)(321,413)(322,414)(323,415)(324,416);;
s4 := ( 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);;
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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s0*s1*s2*s0*s1,
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, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432);
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, 65)( 2, 68)( 3, 67)( 4, 66)( 5, 69)( 6, 72)( 7, 71)( 8, 70)( 9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 49)( 14, 52)( 15, 51)( 16, 50)( 17, 53)( 18, 56)( 19, 55)( 20, 54)( 21, 57)( 22, 60)( 23, 59)( 24, 58)( 25, 45)( 26, 48)( 27, 47)( 28, 46)( 29, 37)( 30, 40)( 31, 39)( 32, 38)( 33, 41)( 34, 44)( 35, 43)( 36, 42)( 73,101)( 74,104)( 75,103)( 76,102)( 77,105)( 78,108)( 79,107)( 80,106)( 81, 97)( 82,100)( 83, 99)( 84, 98)( 86, 88)( 90, 92)( 94, 96)(109,173)(110,176)(111,175)(112,174)(113,177)(114,180)(115,179)(116,178)(117,169)(118,172)(119,171)(120,170)(121,157)(122,160)(123,159)(124,158)(125,161)(126,164)(127,163)(128,162)(129,165)(130,168)(131,167)(132,166)(133,153)(134,156)(135,155)(136,154)(137,145)(138,148)(139,147)(140,146)(141,149)(142,152)(143,151)(144,150)(181,209)(182,212)(183,211)(184,210)(185,213)(186,216)(187,215)(188,214)(189,205)(190,208)(191,207)(192,206)(194,196)(198,200)(202,204)(217,281)(218,284)(219,283)(220,282)(221,285)(222,288)(223,287)(224,286)(225,277)(226,280)(227,279)(228,278)(229,265)(230,268)(231,267)(232,266)(233,269)(234,272)(235,271)(236,270)(237,273)(238,276)(239,275)(240,274)(241,261)(242,264)(243,263)(244,262)(245,253)(246,256)(247,255)(248,254)(249,257)(250,260)(251,259)(252,258)(289,317)(290,320)(291,319)(292,318)(293,321)(294,324)(295,323)(296,322)(297,313)(298,316)(299,315)(300,314)(302,304)(306,308)(310,312)(325,389)(326,392)(327,391)(328,390)(329,393)(330,396)(331,395)(332,394)(333,385)(334,388)(335,387)(336,386)(337,373)(338,376)(339,375)(340,374)(341,377)(342,380)(343,379)(344,378)(345,381)(346,384)(347,383)(348,382)(349,369)(350,372)(351,371)(352,370)(353,361)(354,364)(355,363)(356,362)(357,365)(358,368)(359,367)(360,366)(397,425)(398,428)(399,427)(400,426)(401,429)(402,432)(403,431)(404,430)(405,421)(406,424)(407,423)(408,422)(410,412)(414,416)(418,420);
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)(217,325)(218,326)(219,327)(220,328)(221,333)(222,334)(223,335)(224,336)(225,329)(226,330)(227,331)(228,332)(229,349)(230,350)(231,351)(232,352)(233,357)(234,358)(235,359)(236,360)(237,353)(238,354)(239,355)(240,356)(241,337)(242,338)(243,339)(244,340)(245,345)(246,346)(247,347)(248,348)(249,341)(250,342)(251,343)(252,344)(253,361)(254,362)(255,363)(256,364)(257,369)(258,370)(259,371)(260,372)(261,365)(262,366)(263,367)(264,368)(265,385)(266,386)(267,387)(268,388)(269,393)(270,394)(271,395)(272,396)(273,389)(274,390)(275,391)(276,392)(277,373)(278,374)(279,375)(280,376)(281,381)(282,382)(283,383)(284,384)(285,377)(286,378)(287,379)(288,380)(289,397)(290,398)(291,399)(292,400)(293,405)(294,406)(295,407)(296,408)(297,401)(298,402)(299,403)(300,404)(301,421)(302,422)(303,423)(304,424)(305,429)(306,430)(307,431)(308,432)(309,425)(310,426)(311,427)(312,428)(313,409)(314,410)(315,411)(316,412)(317,417)(318,418)(319,419)(320,420)(321,413)(322,414)(323,415)(324,416);
s4 := 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);
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, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s0*s1*s2*s0*s1*s2*s0*s1, 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