32 



LES HYPEEQUADIUQUES DANS L'ESPACE 



{n'arbâY(i\-2 = [b,fi\h + d){2hd + b,;)d\ 



= 2hjM'~ + 2bJ)'-d^ + hj)jhl + bjjjj'-d^ 

 = 6 + 6^0 + 1 = 18. 



Ainsi l'on trouve les 207 nombres du tableau suivant: 



Nombres {a''' «''= b'' &'' y"' d") = (j(j , ;x, ç r , y-._,-s-) 



(440220 



)=1 



(440211 



)=1 



(440112 



)=1 



(431220 



) = 1 



(431211 



)=1 



(431112 



)=1 



(430320 



) = 2 



(430311 



) = 2 



(430221. 



)=3 



(430212 



)= 2 



(430113 



)=1 



(422220, 



)=1 



(422211 



)=1 



(422112, 



)=1 



(421320 



) = 2 



(421311 



) = 2 



(421221 



)=3 



(421212 



) = 2 



(421113 



)=1 



(420420 



) = 2 



(420411 



) = 2 



(420330 



) = 4 



(420321 



)-4 



(420312 



) = 2 



(420222 



) = 3 



(420213 



)=1 



(413220 



)=1 



(413211, 



)-l 



(413112; 



)=1 



(412320; 



) = 2 



(412311, 



) — •> 



(412221; 



) = 3 



(412212; 



) = 2 



(4121 13; 



)= 1 



(411420, 



= 2 



(411411; 



^ 2 



411330 



) = 4 



( 



411321 



) = 4 



( 



411312 



) = 2 



( 



411222 



)=3 



( 



411213 



)=1 



( 



410430 



) = 4 



( 



410421 



) = 2 



( 



410331 



) = 4 



( 



410322 



) = 3 



( 



410223 



)=1 



( 



332220 



) = 2 



( 



332211 



)-2 



( 



332112 



) = 2 



( 



331320 



) = 4 



( 



331311 



) = 4 



( 



331221 



) = () 



( 



331212 



) = 4 



( 



331113, 



) = 2 



( 



330420 



)= 5 



(' 



330411 



) = 5 



(' 



330330 



)=8 



( 



330321 



)=y 



( 



330312, 



)-5 



( 



330222, 



)=7 



( 



330213; 



) = 3 



( 



330114; 



)= 1 



(< 



323220; 



=^3 



( 



323211; 



= 3 



(' 



32 3 112; 



= 3 



(' 



322320; 



= 



(- 



322311; 



^() 



(< 



322221; 



-9 



(î 



322212; 



= 6 



(; 



322113; 



-3 



(; 



321420; 



= 7 



(' 



321411; 



= 7 



(' 



321330) = 12 

 321321)^13 

 321312)= 7 

 321222)= 10 

 321213) = 

 321114) = 

 320520) = 

 320511) = 

 320430) = 

 320421) = 

 320412) = 

 320331)= 

 320322) = 

 320313) = 

 320223) = 

 320214) = 

 314220) = 

 314211) = 

 314112) = 

 313320) = 

 313311) = 

 313221) = 

 313212) = 

 313113) = 

 312420) = 

 312411) = 

 312330) = 

 312321) = 

 312312) = 

 312222)= 10 

 312213)= 4 

 312114)= 1 

 311520)= 5 

 311511)= 5 

 311430)= 14 

 311 121)=12 



4 



1 



5 



5 



14 



12 



5 



16 



10 



3 



5 



1 



3 



3 



3 



() 







9 



Ü 



3 



7 



7 



12 



13 



7 



311412)= 5 

 311331)=16 

 311322)=10 

 311313)= 3 

 311223)= 5 

 311214)= 1 

 310530) = 10 

 310521)= 5 

 3 10440) = 1(5 

 310431)= 12 

 310422)= 5 

 310332)= 8 

 310323) = 

 310224) = 

 224220) = 

 224211)= 5 

 224112)= 5 

 223320)= 10 

 223311) = 10 

 223221)= 15 

 223212) = 10 

 223113)= 5 

 222420)= 12 

 222411)= 12 

 222330) = 20 

 222321) = 22 

 222312)= 12 

 222222)= 17 

 222213)= 7 

 222114)= 2 

 221520)= 10 

 221511)= 10 

 22 1430) = 24 

 221421) = 22 

 221412)= 10 

 221331) = 28 



