  Uniform covers with a finite-dimensional nerve are rare (i.e., do not form a
cofinal family) in many separable metric spaces of interest. To get hold on
uniform homotopy properties of these spaces, a reasonably behaved notion of an
infinite-dimensional metric polyhedron is needed; a specific list of desired
properties was sketched by J. R. Isbell in a series of publications in 1959-64.
In this paper we construct what appears to be the desired theory of uniform
polyhedra; incidentally, considerable information about their metric and
Lipschitz properties is obtained.
