  We study random sequential adsorption (RSA) of a class of solids that can be
obtained from a cube by specific cutting of its vertices, in order to find out
how the transition from tetrahedral to octahedral symmetry affects the
densities of the resulting jammed packings. We find that in general solids of
octahedral symmetry form less dense packing, however, the lowest density was
obtained for the packing build of tetrahedra. The densest packing is formed by
a solid close to a tetrahedron but with vertices and edges slightly cut. Its
density is $\theta_{max} = 0.41278 \pm 0.00059$ and is higher than the mean
packing fraction of spheres or cuboids but is lower than one for the densest
RSA packings built of ellipsoids or spherocylinders. The density
autocorrelation function of the studied packings is typical as for random media
and vanishes very fast with distance.
