Polytope of Type {6,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 4
Schlafli Type : {6,12,6}
Number of vertices, edges, etc : 6, 72, 72, 12
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 6
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 : {6,12,3}*864a
3-fold quotients : {6,4,6}*576a
4-fold quotients : {6,6,6}*432a
6-fold quotients : {6,4,3}*288
8-fold quotients : {3,6,6}*216a, {6,6,3}*216a
9-fold quotients : {2,4,6}*192
12-fold quotients : {6,2,6}*144
16-fold quotients : {3,6,3}*108
18-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
24-fold quotients : {3,2,6}*72, {6,2,3}*72
36-fold quotients : {2,4,3}*48, {2,2,6}*48, {6,2,2}*48
48-fold quotients : {3,2,3}*36
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):
P/N, where N=<s1*s2*s1*s2*s1*s3*s2*s1*s2*s3> of order 2.
8 facets:
4 of {6,12}*144c
4 of {6,6}*72c
6 vertex figures:
6 of 2-fold non-regular quotient of {12,6}*288b
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 := ( 1,230)( 2,229)( 3,232)( 4,231)( 5,238)( 6,237)( 7,240)( 8,239)( 9,234)( 10,233)( 11,236)( 12,235)( 13,218)( 14,217)( 15,220)( 16,219)( 17,226)( 18,225)( 19,228)( 20,227)( 21,222)( 22,221)( 23,224)( 24,223)( 25,242)( 26,241)( 27,244)( 28,243)( 29,250)( 30,249)( 31,252)( 32,251)( 33,246)( 34,245)( 35,248)( 36,247)( 37,266)( 38,265)( 39,268)( 40,267)( 41,274)( 42,273)( 43,276)( 44,275)( 45,270)( 46,269)( 47,272)( 48,271)( 49,254)( 50,253)( 51,256)( 52,255)( 53,262)( 54,261)( 55,264)( 56,263)( 57,258)( 58,257)( 59,260)( 60,259)( 61,278)( 62,277)( 63,280)( 64,279)( 65,286)( 66,285)( 67,288)( 68,287)( 69,282)( 70,281)( 71,284)( 72,283)( 73,302)( 74,301)( 75,304)( 76,303)( 77,310)( 78,309)( 79,312)( 80,311)( 81,306)( 82,305)( 83,308)( 84,307)( 85,290)( 86,289)( 87,292)( 88,291)( 89,298)( 90,297)( 91,300)( 92,299)( 93,294)( 94,293)( 95,296)( 96,295)( 97,314)( 98,313)( 99,316)(100,315)(101,322)(102,321)(103,324)(104,323)(105,318)(106,317)(107,320)(108,319)(109,338)(110,337)(111,340)(112,339)(113,346)(114,345)(115,348)(116,347)(117,342)(118,341)(119,344)(120,343)(121,326)(122,325)(123,328)(124,327)(125,334)(126,333)(127,336)(128,335)(129,330)(130,329)(131,332)(132,331)(133,350)(134,349)(135,352)(136,351)(137,358)(138,357)(139,360)(140,359)(141,354)(142,353)(143,356)(144,355)(145,374)(146,373)(147,376)(148,375)(149,382)(150,381)(151,384)(152,383)(153,378)(154,377)(155,380)(156,379)(157,362)(158,361)(159,364)(160,363)(161,370)(162,369)(163,372)(164,371)(165,366)(166,365)(167,368)(168,367)(169,386)(170,385)(171,388)(172,387)(173,394)(174,393)(175,396)(176,395)(177,390)(178,389)(179,392)(180,391)(181,410)(182,409)(183,412)(184,411)(185,418)(186,417)(187,420)(188,419)(189,414)(190,413)(191,416)(192,415)(193,398)(194,397)(195,400)(196,399)(197,406)(198,405)(199,408)(200,407)(201,402)(202,401)(203,404)(204,403)(205,422)(206,421)(207,424)(208,423)(209,430)(210,429)(211,432)(212,431)(213,426)(214,425)(215,428)(216,427);;
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 := ( 1,109)( 2,110)( 3,112)( 4,111)( 5,117)( 6,118)( 7,120)( 8,119)( 9,113)( 10,114)( 11,116)( 12,115)( 13,121)( 14,122)( 15,124)( 16,123)( 17,129)( 18,130)( 19,132)( 20,131)( 21,125)( 22,126)( 23,128)( 24,127)( 25,133)( 26,134)( 27,136)( 28,135)( 29,141)( 30,142)( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)( 37,181)( 38,182)( 39,184)( 40,183)( 41,189)( 42,190)( 43,192)( 44,191)( 45,185)( 46,186)( 47,188)( 48,187)( 49,193)( 50,194)( 51,196)( 52,195)( 53,201)( 54,202)( 55,204)( 56,203)( 57,197)( 58,198)( 59,200)( 60,199)( 61,205)( 62,206)( 63,208)( 64,207)( 65,213)( 66,214)( 67,216)( 68,215)( 69,209)( 70,210)( 71,212)( 72,211)( 73,145)( 74,146)( 75,148)( 76,147)( 77,153)( 78,154)( 79,156)( 80,155)( 81,149)( 82,150)( 83,152)( 84,151)( 85,157)( 86,158)( 87,160)( 88,159)( 89,165)( 90,166)( 91,168)( 92,167)( 93,161)( 94,162)( 95,164)( 96,163)( 97,169)( 98,170)( 99,172)(100,171)(101,177)(102,178)(103,180)(104,179)(105,173)(106,174)(107,176)(108,175)(217,325)(218,326)(219,328)(220,327)(221,333)(222,334)(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,337)(230,338)(231,340)(232,339)(233,345)(234,346)(235,348)(236,347)(237,341)(238,342)(239,344)(240,343)(241,349)(242,350)(243,352)(244,351)(245,357)(246,358)(247,360)(248,359)(249,353)(250,354)(251,356)(252,355)(253,397)(254,398)(255,400)(256,399)(257,405)(258,406)(259,408)(260,407)(261,401)(262,402)(263,404)(264,403)(265,409)(266,410)(267,412)(268,411)(269,417)(270,418)(271,420)(272,419)(273,413)(274,414)(275,416)(276,415)(277,421)(278,422)(279,424)(280,423)(281,429)(282,430)(283,432)(284,431)(285,425)(286,426)(287,428)(288,427)(289,361)(290,362)(291,364)(292,363)(293,369)(294,370)(295,372)(296,371)(297,365)(298,366)(299,368)(300,367)(301,373)(302,374)(303,376)(304,375)(305,381)(306,382)(307,384)(308,383)(309,377)(310,378)(311,380)(312,379)(313,385)(314,386)(315,388)(316,387)(317,393)(318,394)(319,396)(320,395)(321,389)(322,390)(323,392)(324,391);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s0*s1*s0*s1*s0*s3*s2*s1*s0*s1*s2*s3*s2*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)!( 1,230)( 2,229)( 3,232)( 4,231)( 5,238)( 6,237)( 7,240)( 8,239)( 9,234)( 10,233)( 11,236)( 12,235)( 13,218)( 14,217)( 15,220)( 16,219)( 17,226)( 18,225)( 19,228)( 20,227)( 21,222)( 22,221)( 23,224)( 24,223)( 25,242)( 26,241)( 27,244)( 28,243)( 29,250)( 30,249)( 31,252)( 32,251)( 33,246)( 34,245)( 35,248)( 36,247)( 37,266)( 38,265)( 39,268)( 40,267)( 41,274)( 42,273)( 43,276)( 44,275)( 45,270)( 46,269)( 47,272)( 48,271)( 49,254)( 50,253)( 51,256)( 52,255)( 53,262)( 54,261)( 55,264)( 56,263)( 57,258)( 58,257)( 59,260)( 60,259)( 61,278)( 62,277)( 63,280)( 64,279)( 65,286)( 66,285)( 67,288)( 68,287)( 69,282)( 70,281)( 71,284)( 72,283)( 73,302)( 74,301)( 75,304)( 76,303)( 77,310)( 78,309)( 79,312)( 80,311)( 81,306)( 82,305)( 83,308)( 84,307)( 85,290)( 86,289)( 87,292)( 88,291)( 89,298)( 90,297)( 91,300)( 92,299)( 93,294)( 94,293)( 95,296)( 96,295)( 97,314)( 98,313)( 99,316)(100,315)(101,322)(102,321)(103,324)(104,323)(105,318)(106,317)(107,320)(108,319)(109,338)(110,337)(111,340)(112,339)(113,346)(114,345)(115,348)(116,347)(117,342)(118,341)(119,344)(120,343)(121,326)(122,325)(123,328)(124,327)(125,334)(126,333)(127,336)(128,335)(129,330)(130,329)(131,332)(132,331)(133,350)(134,349)(135,352)(136,351)(137,358)(138,357)(139,360)(140,359)(141,354)(142,353)(143,356)(144,355)(145,374)(146,373)(147,376)(148,375)(149,382)(150,381)(151,384)(152,383)(153,378)(154,377)(155,380)(156,379)(157,362)(158,361)(159,364)(160,363)(161,370)(162,369)(163,372)(164,371)(165,366)(166,365)(167,368)(168,367)(169,386)(170,385)(171,388)(172,387)(173,394)(174,393)(175,396)(176,395)(177,390)(178,389)(179,392)(180,391)(181,410)(182,409)(183,412)(184,411)(185,418)(186,417)(187,420)(188,419)(189,414)(190,413)(191,416)(192,415)(193,398)(194,397)(195,400)(196,399)(197,406)(198,405)(199,408)(200,407)(201,402)(202,401)(203,404)(204,403)(205,422)(206,421)(207,424)(208,423)(209,430)(210,429)(211,432)(212,431)(213,426)(214,425)(215,428)(216,427);
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)!( 1,109)( 2,110)( 3,112)( 4,111)( 5,117)( 6,118)( 7,120)( 8,119)( 9,113)( 10,114)( 11,116)( 12,115)( 13,121)( 14,122)( 15,124)( 16,123)( 17,129)( 18,130)( 19,132)( 20,131)( 21,125)( 22,126)( 23,128)( 24,127)( 25,133)( 26,134)( 27,136)( 28,135)( 29,141)( 30,142)( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)( 37,181)( 38,182)( 39,184)( 40,183)( 41,189)( 42,190)( 43,192)( 44,191)( 45,185)( 46,186)( 47,188)( 48,187)( 49,193)( 50,194)( 51,196)( 52,195)( 53,201)( 54,202)( 55,204)( 56,203)( 57,197)( 58,198)( 59,200)( 60,199)( 61,205)( 62,206)( 63,208)( 64,207)( 65,213)( 66,214)( 67,216)( 68,215)( 69,209)( 70,210)( 71,212)( 72,211)( 73,145)( 74,146)( 75,148)( 76,147)( 77,153)( 78,154)( 79,156)( 80,155)( 81,149)( 82,150)( 83,152)( 84,151)( 85,157)( 86,158)( 87,160)( 88,159)( 89,165)( 90,166)( 91,168)( 92,167)( 93,161)( 94,162)( 95,164)( 96,163)( 97,169)( 98,170)( 99,172)(100,171)(101,177)(102,178)(103,180)(104,179)(105,173)(106,174)(107,176)(108,175)(217,325)(218,326)(219,328)(220,327)(221,333)(222,334)(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,337)(230,338)(231,340)(232,339)(233,345)(234,346)(235,348)(236,347)(237,341)(238,342)(239,344)(240,343)(241,349)(242,350)(243,352)(244,351)(245,357)(246,358)(247,360)(248,359)(249,353)(250,354)(251,356)(252,355)(253,397)(254,398)(255,400)(256,399)(257,405)(258,406)(259,408)(260,407)(261,401)(262,402)(263,404)(264,403)(265,409)(266,410)(267,412)(268,411)(269,417)(270,418)(271,420)(272,419)(273,413)(274,414)(275,416)(276,415)(277,421)(278,422)(279,424)(280,423)(281,429)(282,430)(283,432)(284,431)(285,425)(286,426)(287,428)(288,427)(289,361)(290,362)(291,364)(292,363)(293,369)(294,370)(295,372)(296,371)(297,365)(298,366)(299,368)(300,367)(301,373)(302,374)(303,376)(304,375)(305,381)(306,382)(307,384)(308,383)(309,377)(310,378)(311,380)(312,379)(313,385)(314,386)(315,388)(316,387)(317,393)(318,394)(319,396)(320,395)(321,389)(322,390)(323,392)(324,391);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s0*s1*s0*s1*s0*s3*s2*s1*s0*s1*s2*s3*s2*s0*s1 >;
References : None.
to this polytope