Polytope of Type {12,4,9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,9}*1728
if this polytope has a name.
Group : SmallGroup(1728,30229)
Rank : 4
Schlafli Type : {12,4,9}
Number of vertices, edges, etc : 12, 48, 36, 18
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {6,4,9}*864
3-fold quotients : {4,4,9}*576b, {12,4,3}*576
4-fold quotients : {12,2,9}*432
6-fold quotients : {2,4,9}*288, {6,4,3}*288
8-fold quotients : {6,2,9}*216
9-fold quotients : {4,4,3}*192b
12-fold quotients : {4,2,9}*144, {2,4,9}*144, {12,2,3}*144
16-fold quotients : {3,2,9}*108
18-fold quotients : {2,4,3}*96
24-fold quotients : {2,2,9}*72, {6,2,3}*72
36-fold quotients : {4,2,3}*48, {2,4,3}*48
48-fold quotients : {3,2,3}*36
72-fold quotients : {2,2,3}*24
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> of order 2.
12 facets:
6 of {12,2}*48
6 of {12,4}*96a
12 vertex figures:
12 of 2-fold non-regular quotient of {4,9}*144
Permutation Representation (GAP) :
s0 := ( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)( 60, 72)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)( 92,104)( 93,105)( 94,106)( 95,107)( 96,108)(121,133)(122,134)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)(165,177)(166,178)(167,179)(168,180)(193,205)(194,206)(195,207)(196,208)(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)(204,216)(217,325)(218,326)(219,327)(220,328)(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)(228,336)(229,349)(230,350)(231,351)(232,352)(233,353)(234,354)(235,355)(236,356)(237,357)(238,358)(239,359)(240,360)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)(249,345)(250,346)(251,347)(252,348)(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)(260,368)(261,369)(262,370)(263,371)(264,372)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)(276,396)(277,373)(278,374)(279,375)(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384)(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)(300,408)(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,416)(321,417)(322,418)(323,419)(324,420);;
s1 := ( 1,231)( 2,232)( 3,229)( 4,230)( 5,235)( 6,236)( 7,233)( 8,234)( 9,239)( 10,240)( 11,237)( 12,238)( 13,219)( 14,220)( 15,217)( 16,218)( 17,223)( 18,224)( 19,221)( 20,222)( 21,227)( 22,228)( 23,225)( 24,226)( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)( 32,246)( 33,251)( 34,252)( 35,249)( 36,250)( 37,267)( 38,268)( 39,265)( 40,266)( 41,271)( 42,272)( 43,269)( 44,270)( 45,275)( 46,276)( 47,273)( 48,274)( 49,255)( 50,256)( 51,253)( 52,254)( 53,259)( 54,260)( 55,257)( 56,258)( 57,263)( 58,264)( 59,261)( 60,262)( 61,279)( 62,280)( 63,277)( 64,278)( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)( 72,286)( 73,303)( 74,304)( 75,301)( 76,302)( 77,307)( 78,308)( 79,305)( 80,306)( 81,311)( 82,312)( 83,309)( 84,310)( 85,291)( 86,292)( 87,289)( 88,290)( 89,295)( 90,296)( 91,293)( 92,294)( 93,299)( 94,300)( 95,297)( 96,298)( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)(104,318)(105,323)(106,324)(107,321)(108,322)(109,339)(110,340)(111,337)(112,338)(113,343)(114,344)(115,341)(116,342)(117,347)(118,348)(119,345)(120,346)(121,327)(122,328)(123,325)(124,326)(125,331)(126,332)(127,329)(128,330)(129,335)(130,336)(131,333)(132,334)(133,351)(134,352)(135,349)(136,350)(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)(144,358)(145,375)(146,376)(147,373)(148,374)(149,379)(150,380)(151,377)(152,378)(153,383)(154,384)(155,381)(156,382)(157,363)(158,364)(159,361)(160,362)(161,367)(162,368)(163,365)(164,366)(165,371)(166,372)(167,369)(168,370)(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)(176,390)(177,395)(178,396)(179,393)(180,394)(181,411)(182,412)(183,409)(184,410)(185,415)(186,416)(187,413)(188,414)(189,419)(190,420)(191,417)(192,418)(193,399)(194,400)(195,397)(196,398)(197,403)(198,404)(199,401)(200,402)(201,407)(202,408)(203,405)(204,406)(205,423)(206,424)(207,421)(208,422)(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)(216,430);;
s2 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)(140,143)(145,189)(146,190)(147,192)(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)(155,184)(156,183)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,213)(170,214)(171,216)(172,215)(173,209)(174,210)(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(219,220)(221,225)(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)(236,239)(243,244)(245,249)(246,250)(247,252)(248,251)(253,297)(254,298)(255,300)(256,299)(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)(264,291)(265,309)(266,310)(267,312)(268,311)(269,305)(270,306)(271,308)(272,307)(273,301)(274,302)(275,304)(276,303)(277,321)(278,322)(279,324)(280,323)(281,317)(282,318)(283,320)(284,319)(285,313)(286,314)(287,316)(288,315)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)(341,345)(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)(356,359)(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)(368,403)(369,397)(370,398)(371,400)(372,399)(373,417)(374,418)(375,420)(376,419)(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)(384,411)(385,429)(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)(392,427)(393,421)(394,422)(395,424)(396,423);;
s3 := ( 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, 49)( 14, 52)( 15, 51)( 16, 50)( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 21, 53)( 22, 56)( 23, 55)( 24, 54)( 25, 61)( 26, 64)( 27, 63)( 28, 62)( 29, 69)( 30, 72)( 31, 71)( 32, 70)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 73, 81)( 74, 84)( 75, 83)( 76, 82)( 78, 80)( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92)( 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)(121,157)(122,160)(123,159)(124,158)(125,165)(126,168)(127,167)(128,166)(129,161)(130,164)(131,163)(132,162)(133,169)(134,172)(135,171)(136,170)(137,177)(138,180)(139,179)(140,178)(141,173)(142,176)(143,175)(144,174)(181,189)(182,192)(183,191)(184,190)(186,188)(193,201)(194,204)(195,203)(196,202)(198,200)(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)(229,265)(230,268)(231,267)(232,266)(233,273)(234,276)(235,275)(236,274)(237,269)(238,272)(239,271)(240,270)(241,277)(242,280)(243,279)(244,278)(245,285)(246,288)(247,287)(248,286)(249,281)(250,284)(251,283)(252,282)(289,297)(290,300)(291,299)(292,298)(294,296)(301,309)(302,312)(303,311)(304,310)(306,308)(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)(337,373)(338,376)(339,375)(340,374)(341,381)(342,384)(343,383)(344,382)(345,377)(346,380)(347,379)(348,378)(349,385)(350,388)(351,387)(352,386)(353,393)(354,396)(355,395)(356,394)(357,389)(358,392)(359,391)(360,390)(397,405)(398,408)(399,407)(400,406)(402,404)(409,417)(410,420)(411,419)(412,418)(414,416)(421,429)(422,432)(423,431)(424,430)(426,428);;
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*s2*s1*s0*s1*s2*s1,
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)( 60, 72)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)( 92,104)( 93,105)( 94,106)( 95,107)( 96,108)(121,133)(122,134)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)(165,177)(166,178)(167,179)(168,180)(193,205)(194,206)(195,207)(196,208)(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)(204,216)(217,325)(218,326)(219,327)(220,328)(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)(228,336)(229,349)(230,350)(231,351)(232,352)(233,353)(234,354)(235,355)(236,356)(237,357)(238,358)(239,359)(240,360)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)(249,345)(250,346)(251,347)(252,348)(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)(260,368)(261,369)(262,370)(263,371)(264,372)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)(276,396)(277,373)(278,374)(279,375)(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384)(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)(300,408)(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,416)(321,417)(322,418)(323,419)(324,420);
s1 := Sym(432)!( 1,231)( 2,232)( 3,229)( 4,230)( 5,235)( 6,236)( 7,233)( 8,234)( 9,239)( 10,240)( 11,237)( 12,238)( 13,219)( 14,220)( 15,217)( 16,218)( 17,223)( 18,224)( 19,221)( 20,222)( 21,227)( 22,228)( 23,225)( 24,226)( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)( 32,246)( 33,251)( 34,252)( 35,249)( 36,250)( 37,267)( 38,268)( 39,265)( 40,266)( 41,271)( 42,272)( 43,269)( 44,270)( 45,275)( 46,276)( 47,273)( 48,274)( 49,255)( 50,256)( 51,253)( 52,254)( 53,259)( 54,260)( 55,257)( 56,258)( 57,263)( 58,264)( 59,261)( 60,262)( 61,279)( 62,280)( 63,277)( 64,278)( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)( 72,286)( 73,303)( 74,304)( 75,301)( 76,302)( 77,307)( 78,308)( 79,305)( 80,306)( 81,311)( 82,312)( 83,309)( 84,310)( 85,291)( 86,292)( 87,289)( 88,290)( 89,295)( 90,296)( 91,293)( 92,294)( 93,299)( 94,300)( 95,297)( 96,298)( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)(104,318)(105,323)(106,324)(107,321)(108,322)(109,339)(110,340)(111,337)(112,338)(113,343)(114,344)(115,341)(116,342)(117,347)(118,348)(119,345)(120,346)(121,327)(122,328)(123,325)(124,326)(125,331)(126,332)(127,329)(128,330)(129,335)(130,336)(131,333)(132,334)(133,351)(134,352)(135,349)(136,350)(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)(144,358)(145,375)(146,376)(147,373)(148,374)(149,379)(150,380)(151,377)(152,378)(153,383)(154,384)(155,381)(156,382)(157,363)(158,364)(159,361)(160,362)(161,367)(162,368)(163,365)(164,366)(165,371)(166,372)(167,369)(168,370)(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)(176,390)(177,395)(178,396)(179,393)(180,394)(181,411)(182,412)(183,409)(184,410)(185,415)(186,416)(187,413)(188,414)(189,419)(190,420)(191,417)(192,418)(193,399)(194,400)(195,397)(196,398)(197,403)(198,404)(199,401)(200,402)(201,407)(202,408)(203,405)(204,406)(205,423)(206,424)(207,421)(208,422)(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)(216,430);
s2 := Sym(432)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)(140,143)(145,189)(146,190)(147,192)(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)(155,184)(156,183)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,213)(170,214)(171,216)(172,215)(173,209)(174,210)(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(219,220)(221,225)(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)(236,239)(243,244)(245,249)(246,250)(247,252)(248,251)(253,297)(254,298)(255,300)(256,299)(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)(264,291)(265,309)(266,310)(267,312)(268,311)(269,305)(270,306)(271,308)(272,307)(273,301)(274,302)(275,304)(276,303)(277,321)(278,322)(279,324)(280,323)(281,317)(282,318)(283,320)(284,319)(285,313)(286,314)(287,316)(288,315)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)(341,345)(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)(356,359)(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)(368,403)(369,397)(370,398)(371,400)(372,399)(373,417)(374,418)(375,420)(376,419)(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)(384,411)(385,429)(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)(392,427)(393,421)(394,422)(395,424)(396,423);
s3 := 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, 49)( 14, 52)( 15, 51)( 16, 50)( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 21, 53)( 22, 56)( 23, 55)( 24, 54)( 25, 61)( 26, 64)( 27, 63)( 28, 62)( 29, 69)( 30, 72)( 31, 71)( 32, 70)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 73, 81)( 74, 84)( 75, 83)( 76, 82)( 78, 80)( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92)( 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)(121,157)(122,160)(123,159)(124,158)(125,165)(126,168)(127,167)(128,166)(129,161)(130,164)(131,163)(132,162)(133,169)(134,172)(135,171)(136,170)(137,177)(138,180)(139,179)(140,178)(141,173)(142,176)(143,175)(144,174)(181,189)(182,192)(183,191)(184,190)(186,188)(193,201)(194,204)(195,203)(196,202)(198,200)(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)(229,265)(230,268)(231,267)(232,266)(233,273)(234,276)(235,275)(236,274)(237,269)(238,272)(239,271)(240,270)(241,277)(242,280)(243,279)(244,278)(245,285)(246,288)(247,287)(248,286)(249,281)(250,284)(251,283)(252,282)(289,297)(290,300)(291,299)(292,298)(294,296)(301,309)(302,312)(303,311)(304,310)(306,308)(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)(337,373)(338,376)(339,375)(340,374)(341,381)(342,384)(343,383)(344,382)(345,377)(346,380)(347,379)(348,378)(349,385)(350,388)(351,387)(352,386)(353,393)(354,396)(355,395)(356,394)(357,389)(358,392)(359,391)(360,390)(397,405)(398,408)(399,407)(400,406)(402,404)(409,417)(410,420)(411,419)(412,418)(414,416)(421,429)(422,432)(423,431)(424,430)(426,428);
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*s2*s1*s0*s1*s2*s1, 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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope