  We present the first exact polynomial time algorithm for constructing optimal
geometric bottleneck 2-connected Steiner networks containing at most $k$
Steiner points, where $k>2$ is a constant. Given a set of $n$ vertices embedded
in an $L_p$ plane, the objective of the problem is to find a 2-connected
network, spanning the given vertices and at most $k$ additional vertices, such
that the length of the longest edge is minimised. In contrast to the discrete
version of this problem the additional vertices may be located anywhere in the
plane. The problem is motivated by the modelling of relay-augmentation for the
optimisation of energy consumption in wireless ad hoc networks. Our algorithm
employs Voronoi diagrams and properties of block-cut-vertex decompositions of
graphs to find an optimal solution in $O(n^k\log^{\frac{5k}{2}}n)$ steps when
$1<p<\infty$ and in $O(n^2\log^{\frac{7k}{2}+1}n)$ steps when
$p\in\{1,\infty\}$.
