Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,6,4}

Atlas Canonical Name {3,6,4}*1728a

Overview

Group
SmallGroup(1728,30326)
Rank
4
Schläfli Type
{3,6,4}
Vertices, edges, …
36, 108, 144, 4
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
{{3,6}12,{6,4|2}}. if this polytope has another name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

9-fold

12-fold

18-fold

24-fold

36-fold

72-fold

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*(s2*s1*s0)^4*(s2*s1)^2> of order 2

4 facets

  • 4 of 2-fold non-regular quotient of {3,6}*432

18 vertex figures

P/N, where N=<(s0*s2*s1)^3*s2> of order 3

4 facets

  • 4 of 3-fold non-regular quotient of {3,6}*432

14 vertex figures

P/N, where N=<s0*s1*(s2*s1*s0)^2*(s2*s1)^2> of order 3

4 facets

  • 4 of 3-fold non-regular quotient of {3,6}*432

12 vertex figures

P/N, where N=<(s1*s0*s2)^5*s1*s2> of order 4

4 facets

  • 4 of 4-fold non-regular quotient of {3,6}*432

9 vertex figures

P/N, where N=<(s0*s2*s1)^4, s0*s1*s0*s2*s1*(s0*(s2*s1)^2)^2*s2> of order 6

4 facets

  • 4 of 6-fold non-regular quotient of {3,6}*432

6 vertex figures

Representations

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

References

None.

to this polytope.