c e t t e o r g a n i s a t i o n peut ê t r e p é r i o d i q u e s u i v a n t 3 dimensions e t de symét r i e cubique. Ces c r i s t a u x cubiques s o n t t o u t à f a i t i n h a b i t u e l s dans l e sens où l e u r o r d r e à longue d i s t a n c e n ' e s t pas l e r é s u l t a t de l a propagation d'un o r d r e m o l é c u l a i r e à c o u r t e d i s t a n c e . On peut l e s v o i r comme des c r i s t a u x formés p a r deux l i q u i d e s s é p a r é s p a r un i n t e r f a

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... c e . Nous l e s c o n s i d è r e r o n s en r e l a t i o n avec l e problème du p a r t a g e de l ' e s p a c e p a r des s u r f a c e s minimales p é r i o d iques. A b s t r a c t -The i n t e r f a c e s a r e t h e l i q u i d -l i q u i d i n t e r f a c e s b u i l t by amphiphilic molecules. They organize space i n two media: p o l a r and p a r a f f i n i c . Under c e r t a i n c o n d i t i o n s t,his o r g a n i z a t i o n may p r e s e n t a 3-d p e r i o d i c i t y of c u b i c symmetry. Such c u b i c c r y s t a l s a r e q u i t e unusual i n t h e s e n s e t h a t t h e i r long range o r d e r i s n o t t h e r e s u l t of t h e propagation of a s h o r t range o r d e r . They can be seen a s c r y s t a l s formed by two l i q u i d s s e p a r a t e d by an i n t e r f a c e . W e s h a l l analyze them i n r e l a t i o n w i t h t h e problem of space p a r t it i o n by p e r i o d i c minimal s u r f a c e s . 1 -INTRODUCTION Amphiphilic molecules, such a s s o a p s , d e t e r g e n t s and l i p i d s , a r e w e l l known f o r t h e i r aggregation p r o p e r t y when put i n presence o f w a t e r and f o r forming t h e s t r u c t u r e s of m i c e l l a r and l i q u i d c r y s t a l l i n e phases w i t h v a r i o u s degrees of o r d e r . The d i l u t e d m i c e l l a r phases a r e disorder e d a t long range and t h e c o n c e n t r a t e d ones may sometimes e x h i b i t a long range o r i e n t a t i o n a l o r d e r of t h e nematic type. The more concentrat e d l y o t r o p i c l i q u i d c r y s t a l s a r e t r a n s l a t i o n a l l y ordered. Most o f t e n , i n t h e l a t t e r c a s e , l a r g e zones of t h e phase diagrams a r e occupied by s t r u c t u r e s o r d e r e d along 1 o r 2 dimensions, such a s t h e w e l l known l am e l l a r o r hexagonal phases. There a r e a l s o a few examples o f phase diagrams where s t r u c t u r e s ordered along 3 dimensions can be found i n r at h e r narrow zones. W e s h a l l be concerned w i t h t h e s e s t r u c t u r e s which, f o r c a s e s known up t o now, have a c u b i c symmetry. They a r e n o t t o be confused w i t h t h e 3-d c r y s t a l l i n e S t a t e s of amphiphilic molecules which a r e c l a s s i c a l molecular c r y s t a l s of complex symmetries. To make appar e n t t h e very p a r t i c u l a r n a t u r e o f t h e s e 3-d s t r u c t u r e s , a s w e l l a s t h e Article published online by EDP Sciences and available at http://dx.