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