  Luminescence solar concentrators act as semi-transparent photovoltaic cells
and can be applied to large surface areas in modern urban environment. In this
paper their optical efficiencies were analytically derived for different unit
shapes as simple, integral-free expressions. Perimeter length increase for the
same enclosed area requires more photodetectors, yet reduces optical losses per
unit. An exact interplay between these two parameters is presented, which can
be directly applied to the analysis of tiling for large areas. An explicit
expression for the critical size of an LSC unit, above which its inner part
becomes inactive, has been obtained. Fabrication of devices larger than
specified by this limit should be discouraged from efficiency considerations.
