Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6,9}

Atlas Canonical Name {4,6,9}*1728a

Overview

Group
SmallGroup(1728,30216)
Rank
4
Schläfli Type
{4,6,9}
Vertices, edges, …
4, 48, 108, 36
Order of s0s1s2s3
36
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a 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=<s1*s2*s1*s3*(s2*s1)^2*s3*s2> of order 2

18 facets

4 vertex figures

  • 4 of 2-fold non-regular quotient of {6,9}*432
P/N, where N=<(s1*s2)^2> of order 3

18 facets

4 vertex figures

  • 4 of 3-fold non-regular quotient of {6,9}*432

Representations

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

References

None.

to this polytope.