  Packing problems, even of objects with regular geometries, are in general
non-trivial. For few special shapes, the features of crystalline as well as
random, irregular two-dimensional (2D) packings are known. The packing of 2D
crosses does not yet belong to the category of solved problems. We demonstrate
in experiments with crosses of different aspect ratios (arm width to length)
which packing fractions are actually achieved by random packing, and we compare
them to densest regular packing structures. We determine local correlations of
the orientations and positions after ensembles of randomly placed crosses were
compacted in the plane until they jam. Short-range orientational order is found
over 2 to 3 cross lengths. Similarly, correlations in the spatial distributions
of neighbors extend over 2 to 3 crosses. Apparently, there is no simple
relation between the geometries of the crosses and peaks in the spatial
correlation functions. Some features of the orientational correlations,
however, are intuitively evident.
