  In this paper, we present a general framework of designing geometrically
shaped constellations for short-packet visible light communications with a
peak- and an average-intensity constraints. By leveraging tools from large
deviation theory, we first characterize the second-order asymptotics of the
optimal constellation shaping region under aforementioned intensity
constraints, which serves as a good performance measure for the best geometric
shaping in finite blocklength. To further incorporate a sufficiently large
coding gain and a nearly-maximum shaping gain, we construct multidimensional
constellations by the nested structure of Construction B lattices, where the
constellation shaping is implemented by controlling the boundary of the
embedded sublattice, i.e., a strategy called coarsely shaping and finely
coding. Fast algorithms for constellation mapping and demodulation are
presented as well. As an illustrative example, we present an energy-efficient
$24$-dimensional constellation design based on the Leech lattice, whose
superiority over existing constellation designs is verified by numerical
results.
