  The desirable properties when constructing collections of subspaces often
include the algebraic constraint that the projections onto the subspaces yield
a resolution of the identity like the projections onto lines spanned by vectors
of an orthonormal basis (the so-called tightness condition) and the geometric
constraint that the subspaces form an optimal packing of the Grassmannian,
again like the one-dimensional subspaces spanned by vectors in an orthonormal
basis. In this article a generalization of related constructions which use
known packings to build new configurations and which appear in numerous forms
in the literature is given, as well as the characterization of a long list of
desirable algebraic and geometric properties which the construction preserves.
Another construction based on subspace complementation is similarly analyzed.
While many papers on subspace packings focus only on so-called equiisoclinic or
equichordal arrangements, attention is also given to other configurations like
those which saturate the orthoplex bound and thus are optimal but lie outside
of the parameter regime where equiisoclinic and equichordal packings can occur.
Keywords: fusion frame, Grassmannian packing, simplex bound, orthoplex bound,
equichordal, strongly simplicial, equiisoclinic
