Bob Sidenberg
As always I've been exploring the rhombic dodecahedron and the complex relationships of its structural elements. It contains, or is contained within, a wide variety of related geometric shapes -- triangle, tetrahedron, square, cube, rhombus, hexagon, et al. It is part of larger matrices that seem to flow through its square and hexagonal axes and grow through space. It even shares some structural similarity with the pentagonal dodecahedron, in addition to twelve sided-ness.
I try to work from a center point, but have found that the center is always shifting, never constant, temporary, momentary -- in fact, never really a center at all, but part of a larger construct, somewhere in the matrix. Center is simply a useful and arbitrary concept for the study of geometry.
This shows the path from the fourteen vertices of the rhombic dodecahedron to its center -- six square legs and eight hexagonal, originating at the square and hexagonal axes, or in the inner ether. Alas this center exists only if the legs continue in space. If they turn back to form a matrix, all center is lost. Que sera sera.
The mighty rhombic dodecahedron, momentarily ensnared by the cubic matrix, whose exposed joints show that it shares kinship with its captive. Another generation will reverse the advantage.