Pure organic molecules exhibiting a suitable concave rigid shape are expected to give porous glasses in the solid state. Such a feature opens new opportunities to avoid crystallization and to improve molecular solubility in relation to the high internal energy of these solid phases. To quantitatively explore the latter strategy, a series of rigid tetrahedral conjugated molecules nC and the corresponding models nR have been synthesized. Related to the present purpose, several properties have been investigated using UV absorption, steady-state fluorescence emission, differential scanning calorimetry, 1H NMR translational self-diffusion, magic angle spinning 13C NMR, and multiple-beam interferometry experiments. The present tetrahedral crosses are up to 8 orders of magnitude more soluble than the corresponding model compounds after normalization to the same molecular length. In addition, they give concentrated monomeric solutions that can be used to cover surfaces with homogeneous films whose thickness goes down to the nanometer range. Such attractive features make cross-like molecular architectures promising for many applications.