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