Chains embedded in the tetrahedral lattice have been produced by means of Monte Carlo simulation for athermal and for theta conditions. Nonreversal random walks (random walks without backfolding bonds) have been generated as a reference. Probability distributions of an asphericity factor delta*, of a prolatness factor S*, and of shape factors sf(i)* have been evaluated, the quantities being based on the orthogonal components of the squared radius of gyration taken along the principal axes of inertia. In addition, the correlation between delta* and other shape descriptors as well as between delta* and quantities characteristic of the size of configurations have been evaluated. In accordance with existing literature, the distributions H(delta*) and H(S*) are found to be very broad. The distributions H(sf(1)*) of the small and H(sf(3)*) Of the large shape factor (sf(1)*less than or equal to sf(2)*less than or equal to sf(3)*, sf(1)* + sf(2)* + sf(3)* = I) are clearly distinct from each other, while the distribution of sf(2)* overlaps with that of sf(1)* and (slightly) with H(sf(3)*). Distributions of theta chains ("unperturbed" polymer) coincide fairly well with respective distributions of nonreversal random walks (which in turn are nearly identical to those of (off-lattice) random walks. As a matter of course, other shape descriptors are directly correlated with the asphericity factor delta*. Actually, for all systems evaluated, the global size of configurations is strongly correlated with delta* as well : The larger the asymmetry the larger are the dimensions of the configuration under consideration.