Polytope of Type {2,456}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,456}*1824
if this polytope has a name.
Group : SmallGroup(1824,968)
Rank : 3
Schlafli Type : {2,456}
Number of vertices, edges, etc : 2, 456, 456
Order of s₀s₁s₂ : 456
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {2,228}*912
   3-fold quotients : {2,152}*608
   4-fold quotients : {2,114}*456
   6-fold quotients : {2,76}*304
   8-fold quotients : {2,57}*228
   12-fold quotients : {2,38}*152
   19-fold quotients : {2,24}*96
   24-fold quotients : {2,19}*76
   38-fold quotients : {2,12}*48
   57-fold quotients : {2,8}*32
   76-fold quotients : {2,6}*24
   114-fold quotients : {2,4}*16
   152-fold quotients : {2,3}*12
   228-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)( 11, 14)
( 12, 13)( 22, 41)( 23, 59)( 24, 58)( 25, 57)( 26, 56)( 27, 55)( 28, 54)
( 29, 53)( 30, 52)( 31, 51)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 46)
( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 69, 70)( 79, 98)( 80,116)( 81,115)
( 82,114)( 83,113)( 84,112)( 85,111)( 86,110)( 87,109)( 88,108)( 89,107)
( 90,106)( 91,105)( 92,104)( 93,103)( 94,102)( 95,101)( 96,100)( 97, 99)
(117,174)(118,192)(119,191)(120,190)(121,189)(122,188)(123,187)(124,186)
(125,185)(126,184)(127,183)(128,182)(129,181)(130,180)(131,179)(132,178)
(133,177)(134,176)(135,175)(136,212)(137,230)(138,229)(139,228)(140,227)
(141,226)(142,225)(143,224)(144,223)(145,222)(146,221)(147,220)(148,219)
(149,218)(150,217)(151,216)(152,215)(153,214)(154,213)(155,193)(156,211)
(157,210)(158,209)(159,208)(160,207)(161,206)(162,205)(163,204)(164,203)
(165,202)(166,201)(167,200)(168,199)(169,198)(170,197)(171,196)(172,195)
(173,194)(231,345)(232,363)(233,362)(234,361)(235,360)(236,359)(237,358)
(238,357)(239,356)(240,355)(241,354)(242,353)(243,352)(244,351)(245,350)
(246,349)(247,348)(248,347)(249,346)(250,383)(251,401)(252,400)(253,399)
(254,398)(255,397)(256,396)(257,395)(258,394)(259,393)(260,392)(261,391)
(262,390)(263,389)(264,388)(265,387)(266,386)(267,385)(268,384)(269,364)
(270,382)(271,381)(272,380)(273,379)(274,378)(275,377)(276,376)(277,375)
(278,374)(279,373)(280,372)(281,371)(282,370)(283,369)(284,368)(285,367)
(286,366)(287,365)(288,402)(289,420)(290,419)(291,418)(292,417)(293,416)
(294,415)(295,414)(296,413)(297,412)(298,411)(299,410)(300,409)(301,408)
(302,407)(303,406)(304,405)(305,404)(306,403)(307,440)(308,458)(309,457)
(310,456)(311,455)(312,454)(313,453)(314,452)(315,451)(316,450)(317,449)
(318,448)(319,447)(320,446)(321,445)(322,444)(323,443)(324,442)(325,441)
(326,421)(327,439)(328,438)(329,437)(330,436)(331,435)(332,434)(333,433)
(334,432)(335,431)(336,430)(337,429)(338,428)(339,427)(340,426)(341,425)
(342,424)(343,423)(344,422);;
s2 := (  3,251)(  4,250)(  5,268)(  6,267)(  7,266)(  8,265)(  9,264)( 10,263)
( 11,262)( 12,261)( 13,260)( 14,259)( 15,258)( 16,257)( 17,256)( 18,255)
( 19,254)( 20,253)( 21,252)( 22,232)( 23,231)( 24,249)( 25,248)( 26,247)
( 27,246)( 28,245)( 29,244)( 30,243)( 31,242)( 32,241)( 33,240)( 34,239)
( 35,238)( 36,237)( 37,236)( 38,235)( 39,234)( 40,233)( 41,270)( 42,269)
( 43,287)( 44,286)( 45,285)( 46,284)( 47,283)( 48,282)( 49,281)( 50,280)
( 51,279)( 52,278)( 53,277)( 54,276)( 55,275)( 56,274)( 57,273)( 58,272)
( 59,271)( 60,308)( 61,307)( 62,325)( 63,324)( 64,323)( 65,322)( 66,321)
( 67,320)( 68,319)( 69,318)( 70,317)( 71,316)( 72,315)( 73,314)( 74,313)
( 75,312)( 76,311)( 77,310)( 78,309)( 79,289)( 80,288)( 81,306)( 82,305)
( 83,304)( 84,303)( 85,302)( 86,301)( 87,300)( 88,299)( 89,298)( 90,297)
( 91,296)( 92,295)( 93,294)( 94,293)( 95,292)( 96,291)( 97,290)( 98,327)
( 99,326)(100,344)(101,343)(102,342)(103,341)(104,340)(105,339)(106,338)
(107,337)(108,336)(109,335)(110,334)(111,333)(112,332)(113,331)(114,330)
(115,329)(116,328)(117,422)(118,421)(119,439)(120,438)(121,437)(122,436)
(123,435)(124,434)(125,433)(126,432)(127,431)(128,430)(129,429)(130,428)
(131,427)(132,426)(133,425)(134,424)(135,423)(136,403)(137,402)(138,420)
(139,419)(140,418)(141,417)(142,416)(143,415)(144,414)(145,413)(146,412)
(147,411)(148,410)(149,409)(150,408)(151,407)(152,406)(153,405)(154,404)
(155,441)(156,440)(157,458)(158,457)(159,456)(160,455)(161,454)(162,453)
(163,452)(164,451)(165,450)(166,449)(167,448)(168,447)(169,446)(170,445)
(171,444)(172,443)(173,442)(174,365)(175,364)(176,382)(177,381)(178,380)
(179,379)(180,378)(181,377)(182,376)(183,375)(184,374)(185,373)(186,372)
(187,371)(188,370)(189,369)(190,368)(191,367)(192,366)(193,346)(194,345)
(195,363)(196,362)(197,361)(198,360)(199,359)(200,358)(201,357)(202,356)
(203,355)(204,354)(205,353)(206,352)(207,351)(208,350)(209,349)(210,348)
(211,347)(212,384)(213,383)(214,401)(215,400)(216,399)(217,398)(218,397)
(219,396)(220,395)(221,394)(222,393)(223,392)(224,391)(225,390)(226,389)
(227,388)(228,387)(229,386)(230,385);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(458)!(1,2);
s1 := Sym(458)!(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)
( 11, 14)( 12, 13)( 22, 41)( 23, 59)( 24, 58)( 25, 57)( 26, 56)( 27, 55)
( 28, 54)( 29, 53)( 30, 52)( 31, 51)( 32, 50)( 33, 49)( 34, 48)( 35, 47)
( 36, 46)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 61, 78)( 62, 77)( 63, 76)
( 64, 75)( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 69, 70)( 79, 98)( 80,116)
( 81,115)( 82,114)( 83,113)( 84,112)( 85,111)( 86,110)( 87,109)( 88,108)
( 89,107)( 90,106)( 91,105)( 92,104)( 93,103)( 94,102)( 95,101)( 96,100)
( 97, 99)(117,174)(118,192)(119,191)(120,190)(121,189)(122,188)(123,187)
(124,186)(125,185)(126,184)(127,183)(128,182)(129,181)(130,180)(131,179)
(132,178)(133,177)(134,176)(135,175)(136,212)(137,230)(138,229)(139,228)
(140,227)(141,226)(142,225)(143,224)(144,223)(145,222)(146,221)(147,220)
(148,219)(149,218)(150,217)(151,216)(152,215)(153,214)(154,213)(155,193)
(156,211)(157,210)(158,209)(159,208)(160,207)(161,206)(162,205)(163,204)
(164,203)(165,202)(166,201)(167,200)(168,199)(169,198)(170,197)(171,196)
(172,195)(173,194)(231,345)(232,363)(233,362)(234,361)(235,360)(236,359)
(237,358)(238,357)(239,356)(240,355)(241,354)(242,353)(243,352)(244,351)
(245,350)(246,349)(247,348)(248,347)(249,346)(250,383)(251,401)(252,400)
(253,399)(254,398)(255,397)(256,396)(257,395)(258,394)(259,393)(260,392)
(261,391)(262,390)(263,389)(264,388)(265,387)(266,386)(267,385)(268,384)
(269,364)(270,382)(271,381)(272,380)(273,379)(274,378)(275,377)(276,376)
(277,375)(278,374)(279,373)(280,372)(281,371)(282,370)(283,369)(284,368)
(285,367)(286,366)(287,365)(288,402)(289,420)(290,419)(291,418)(292,417)
(293,416)(294,415)(295,414)(296,413)(297,412)(298,411)(299,410)(300,409)
(301,408)(302,407)(303,406)(304,405)(305,404)(306,403)(307,440)(308,458)
(309,457)(310,456)(311,455)(312,454)(313,453)(314,452)(315,451)(316,450)
(317,449)(318,448)(319,447)(320,446)(321,445)(322,444)(323,443)(324,442)
(325,441)(326,421)(327,439)(328,438)(329,437)(330,436)(331,435)(332,434)
(333,433)(334,432)(335,431)(336,430)(337,429)(338,428)(339,427)(340,426)
(341,425)(342,424)(343,423)(344,422);
s2 := Sym(458)!(  3,251)(  4,250)(  5,268)(  6,267)(  7,266)(  8,265)(  9,264)
( 10,263)( 11,262)( 12,261)( 13,260)( 14,259)( 15,258)( 16,257)( 17,256)
( 18,255)( 19,254)( 20,253)( 21,252)( 22,232)( 23,231)( 24,249)( 25,248)
( 26,247)( 27,246)( 28,245)( 29,244)( 30,243)( 31,242)( 32,241)( 33,240)
( 34,239)( 35,238)( 36,237)( 37,236)( 38,235)( 39,234)( 40,233)( 41,270)
( 42,269)( 43,287)( 44,286)( 45,285)( 46,284)( 47,283)( 48,282)( 49,281)
( 50,280)( 51,279)( 52,278)( 53,277)( 54,276)( 55,275)( 56,274)( 57,273)
( 58,272)( 59,271)( 60,308)( 61,307)( 62,325)( 63,324)( 64,323)( 65,322)
( 66,321)( 67,320)( 68,319)( 69,318)( 70,317)( 71,316)( 72,315)( 73,314)
( 74,313)( 75,312)( 76,311)( 77,310)( 78,309)( 79,289)( 80,288)( 81,306)
( 82,305)( 83,304)( 84,303)( 85,302)( 86,301)( 87,300)( 88,299)( 89,298)
( 90,297)( 91,296)( 92,295)( 93,294)( 94,293)( 95,292)( 96,291)( 97,290)
( 98,327)( 99,326)(100,344)(101,343)(102,342)(103,341)(104,340)(105,339)
(106,338)(107,337)(108,336)(109,335)(110,334)(111,333)(112,332)(113,331)
(114,330)(115,329)(116,328)(117,422)(118,421)(119,439)(120,438)(121,437)
(122,436)(123,435)(124,434)(125,433)(126,432)(127,431)(128,430)(129,429)
(130,428)(131,427)(132,426)(133,425)(134,424)(135,423)(136,403)(137,402)
(138,420)(139,419)(140,418)(141,417)(142,416)(143,415)(144,414)(145,413)
(146,412)(147,411)(148,410)(149,409)(150,408)(151,407)(152,406)(153,405)
(154,404)(155,441)(156,440)(157,458)(158,457)(159,456)(160,455)(161,454)
(162,453)(163,452)(164,451)(165,450)(166,449)(167,448)(168,447)(169,446)
(170,445)(171,444)(172,443)(173,442)(174,365)(175,364)(176,382)(177,381)
(178,380)(179,379)(180,378)(181,377)(182,376)(183,375)(184,374)(185,373)
(186,372)(187,371)(188,370)(189,369)(190,368)(191,367)(192,366)(193,346)
(194,345)(195,363)(196,362)(197,361)(198,360)(199,359)(200,358)(201,357)
(202,356)(203,355)(204,354)(205,353)(206,352)(207,351)(208,350)(209,349)
(210,348)(211,347)(212,384)(213,383)(214,401)(215,400)(216,399)(217,398)
(218,397)(219,396)(220,395)(221,394)(222,393)(223,392)(224,391)(225,390)
(226,389)(227,388)(228,387)(229,386)(230,385);
poly := sub<Sym(458)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope