Polytope of Type {4,12,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,18}*1728c
if this polytope has a name.
Group : SmallGroup(1728,30173)
Rank : 4
Schlafli Type : {4,12,18}
Number of vertices, edges, etc : 4, 24, 108, 18
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 : {4,6,18}*864c
3-fold quotients : {4,12,6}*576d
6-fold quotients : {4,6,6}*288d
9-fold quotients : {4,12,2}*192b
18-fold quotients : {4,6,2}*96c
36-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432);;
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 := ( 1,253)( 2,256)( 3,255)( 4,254)( 5,261)( 6,264)( 7,263)( 8,262)
( 9,257)( 10,260)( 11,259)( 12,258)( 13,285)( 14,288)( 15,287)( 16,286)
( 17,281)( 18,284)( 19,283)( 20,282)( 21,277)( 22,280)( 23,279)( 24,278)
( 25,273)( 26,276)( 27,275)( 28,274)( 29,269)( 30,272)( 31,271)( 32,270)
( 33,265)( 34,268)( 35,267)( 36,266)( 37,217)( 38,220)( 39,219)( 40,218)
( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)( 48,222)
( 49,249)( 50,252)( 51,251)( 52,250)( 53,245)( 54,248)( 55,247)( 56,246)
( 57,241)( 58,244)( 59,243)( 60,242)( 61,237)( 62,240)( 63,239)( 64,238)
( 65,233)( 66,236)( 67,235)( 68,234)( 69,229)( 70,232)( 71,231)( 72,230)
( 73,289)( 74,292)( 75,291)( 76,290)( 77,297)( 78,300)( 79,299)( 80,298)
( 81,293)( 82,296)( 83,295)( 84,294)( 85,321)( 86,324)( 87,323)( 88,322)
( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)( 96,314)
( 97,309)( 98,312)( 99,311)(100,310)(101,305)(102,308)(103,307)(104,306)
(105,301)(106,304)(107,303)(108,302)(109,361)(110,364)(111,363)(112,362)
(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)(120,366)
(121,393)(122,396)(123,395)(124,394)(125,389)(126,392)(127,391)(128,390)
(129,385)(130,388)(131,387)(132,386)(133,381)(134,384)(135,383)(136,382)
(137,377)(138,380)(139,379)(140,378)(141,373)(142,376)(143,375)(144,374)
(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)(152,334)
(153,329)(154,332)(155,331)(156,330)(157,357)(158,360)(159,359)(160,358)
(161,353)(162,356)(163,355)(164,354)(165,349)(166,352)(167,351)(168,350)
(169,345)(170,348)(171,347)(172,346)(173,341)(174,344)(175,343)(176,342)
(177,337)(178,340)(179,339)(180,338)(181,397)(182,400)(183,399)(184,398)
(185,405)(186,408)(187,407)(188,406)(189,401)(190,404)(191,403)(192,402)
(193,429)(194,432)(195,431)(196,430)(197,425)(198,428)(199,427)(200,426)
(201,421)(202,424)(203,423)(204,422)(205,417)(206,420)(207,419)(208,418)
(209,413)(210,416)(211,415)(212,414)(213,409)(214,412)(215,411)(216,410);;
s3 := ( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 21)( 6, 22)( 7, 23)( 8, 24)
( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 25, 33)( 26, 34)( 27, 35)( 28, 36)
( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)( 44, 60)
( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)( 80, 96)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 97,105)( 98,106)( 99,107)(100,108)
(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)(116,132)
(117,125)(118,126)(119,127)(120,128)(133,141)(134,142)(135,143)(136,144)
(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)(152,168)
(153,161)(154,162)(155,163)(156,164)(169,177)(170,178)(171,179)(172,180)
(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)(188,204)
(189,197)(190,198)(191,199)(192,200)(205,213)(206,214)(207,215)(208,216)
(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)(224,240)
(225,233)(226,234)(227,235)(228,236)(241,249)(242,250)(243,251)(244,252)
(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)(260,276)
(261,269)(262,270)(263,271)(264,272)(277,285)(278,286)(279,287)(280,288)
(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)(296,312)
(297,305)(298,306)(299,307)(300,308)(313,321)(314,322)(315,323)(316,324)
(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)(332,348)
(333,341)(334,342)(335,343)(336,344)(349,357)(350,358)(351,359)(352,360)
(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)(368,384)
(369,377)(370,378)(371,379)(372,380)(385,393)(386,394)(387,395)(388,396)
(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)(404,420)
(405,413)(406,414)(407,415)(408,416)(421,429)(422,430)(423,431)(424,432);;
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*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s0*s1*s2*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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432);
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)!( 1,253)( 2,256)( 3,255)( 4,254)( 5,261)( 6,264)( 7,263)
( 8,262)( 9,257)( 10,260)( 11,259)( 12,258)( 13,285)( 14,288)( 15,287)
( 16,286)( 17,281)( 18,284)( 19,283)( 20,282)( 21,277)( 22,280)( 23,279)
( 24,278)( 25,273)( 26,276)( 27,275)( 28,274)( 29,269)( 30,272)( 31,271)
( 32,270)( 33,265)( 34,268)( 35,267)( 36,266)( 37,217)( 38,220)( 39,219)
( 40,218)( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)
( 48,222)( 49,249)( 50,252)( 51,251)( 52,250)( 53,245)( 54,248)( 55,247)
( 56,246)( 57,241)( 58,244)( 59,243)( 60,242)( 61,237)( 62,240)( 63,239)
( 64,238)( 65,233)( 66,236)( 67,235)( 68,234)( 69,229)( 70,232)( 71,231)
( 72,230)( 73,289)( 74,292)( 75,291)( 76,290)( 77,297)( 78,300)( 79,299)
( 80,298)( 81,293)( 82,296)( 83,295)( 84,294)( 85,321)( 86,324)( 87,323)
( 88,322)( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)
( 96,314)( 97,309)( 98,312)( 99,311)(100,310)(101,305)(102,308)(103,307)
(104,306)(105,301)(106,304)(107,303)(108,302)(109,361)(110,364)(111,363)
(112,362)(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)
(120,366)(121,393)(122,396)(123,395)(124,394)(125,389)(126,392)(127,391)
(128,390)(129,385)(130,388)(131,387)(132,386)(133,381)(134,384)(135,383)
(136,382)(137,377)(138,380)(139,379)(140,378)(141,373)(142,376)(143,375)
(144,374)(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)
(152,334)(153,329)(154,332)(155,331)(156,330)(157,357)(158,360)(159,359)
(160,358)(161,353)(162,356)(163,355)(164,354)(165,349)(166,352)(167,351)
(168,350)(169,345)(170,348)(171,347)(172,346)(173,341)(174,344)(175,343)
(176,342)(177,337)(178,340)(179,339)(180,338)(181,397)(182,400)(183,399)
(184,398)(185,405)(186,408)(187,407)(188,406)(189,401)(190,404)(191,403)
(192,402)(193,429)(194,432)(195,431)(196,430)(197,425)(198,428)(199,427)
(200,426)(201,421)(202,424)(203,423)(204,422)(205,417)(206,420)(207,419)
(208,418)(209,413)(210,416)(211,415)(212,414)(213,409)(214,412)(215,411)
(216,410);
s3 := Sym(432)!( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 21)( 6, 22)( 7, 23)
( 8, 24)( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 25, 33)( 26, 34)( 27, 35)
( 28, 36)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)
( 44, 60)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)
( 80, 96)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 97,105)( 98,106)( 99,107)
(100,108)(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)
(116,132)(117,125)(118,126)(119,127)(120,128)(133,141)(134,142)(135,143)
(136,144)(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)
(152,168)(153,161)(154,162)(155,163)(156,164)(169,177)(170,178)(171,179)
(172,180)(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)
(188,204)(189,197)(190,198)(191,199)(192,200)(205,213)(206,214)(207,215)
(208,216)(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)
(224,240)(225,233)(226,234)(227,235)(228,236)(241,249)(242,250)(243,251)
(244,252)(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)
(260,276)(261,269)(262,270)(263,271)(264,272)(277,285)(278,286)(279,287)
(280,288)(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)
(296,312)(297,305)(298,306)(299,307)(300,308)(313,321)(314,322)(315,323)
(316,324)(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)
(332,348)(333,341)(334,342)(335,343)(336,344)(349,357)(350,358)(351,359)
(352,360)(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)
(368,384)(369,377)(370,378)(371,379)(372,380)(385,393)(386,394)(387,395)
(388,396)(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)
(404,420)(405,413)(406,414)(407,415)(408,416)(421,429)(422,430)(423,431)
(424,432);
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*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s0*s1*s2*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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope