In this paper, we consider an intensity modulated direct detection MIMO optical wireless communication (OWC) system. For such a system, a novel super-rectangular cover theory is developed to characterize both the unique identifiability and full reliability. This theory states that a transmitted matrix signal can be uniquely identified if and only if the cover order is equal to the transmitter aperture number, i.e., full cover. In addition, we prove that full reliability is guaranteed for space-time block coded MIMO-OWC over commonly used log-normal fading channels with an ML detector if and only if the STBC enables full cover. In addition, the diversity gain can be geometrically interpreted as the cover order of the super-rectangle, which should be maximized, and the volume of this super-rectangle, as the diversity loss, should be minimized. Using this established error performance criterion, the optimal linear STBC for block fading channels is proved to be spatial repetition code with an optimal power allocation. The design of the optimal non-linear STBC is shown to be equivalent to constructing the optimal multi-dimensional constellation. Specifically, a multi-dimensional constellation from Diophantine equations is proposed and then, shown to be more energy-efficient than the commonly used nonnegative pulse amplitude modulation constellation.