  Consider a smooth point O of a complex analytic surface S. A constellation
based at O is a set of infinitely near points of O, centers of a sequence of
blow-ups above O. Finite constellations are usually encoded in two ways: either
using an Enriques diagram, or using the dual graph of the divisor obtained by
blowing-up the points of the constellation. Both are decorated trees which
encode completely the combinatorics of the constellation. Algorithms of passage
from one to the other are known, but they do not allow to get a geometrical
picture of their relation. We associate to a constellation a geometrical
simplicial complex of dimension two, called its kite, endowed with an affine
structure, and we prove that it contains canonically both the Enriques diagram
and the dual graph. Moreover, the decorations of the two trees may be read very
easily on the affine geometry of the kite. This allows to understand
geometrically the relations between the graphs, as well as their relation with
the valuative tree of Favre and Jonsson, which may be interpreted as the dual
graph of the constellation of all the points infinitely near O. In fact, the
kites of finite constellations get glued into an infinite kite endowed with a
1-dimensional foliation, whose space of leaves is the valuative tree. The
transition towards the computations with continued fractions is ensured by
partial embeddings of the kites into a simplicial complex canonically
associated to a base of a lattice, called its lotus. This last notion is
briefly explored in any dimension.
