  Our starting point is an iterative construction suited to combinatorics in
arbitarary dimensions d, of totally anisymmetrised p-Riemann 2p-forms (2p\le d)
generalising the (1-)Riemann curvature 2-forms. Superposition of p-Ricci
scalars obtained from the p-Riemann forms defines the maximally Gauss--Bonnet
extended gravitational Lagrangian. Metrics, spherically symmetric in the (d-1)
space dimensions are constructed for the general case. The problem is directly
reduced to solving polynomial equations. For some black hole type metrics the
horizons are obtained by solving polynomial equations. Corresponding Kruskal
type maximal extensions are obtained explicitly in complete generality, as is
also the periodicity of time for Euclidean signature. We show how to include a
cosmological constant and a point charge. Possible further developments and
applications are indicated.
