  We aim to find the optimal site locations for a hypothetical network of 1-3
triangular gravitational-wave telescopes. We define the following N-telescope
figures of merit (FoMs) and construct three corresponding metrics: (a)
capability of reconstructing the signal polarization; (b) accuracy in source
localization; and (c) accuracy in reconstructing the parameters of a standard
binary source. We also define a combined metric that takes into account the
three FoMs with practically equal weight. After constructing a geomap of
possible telescope sites, we give the optimal 2-telescope networks for the four
FoMs separately in example cases where the location of the first telescope has
been predetermined. We found that based on the combined metric, placing the
first telescope to Australia provides the most options for optimal site
selection when extending the network with a second instrument. We suggest
geographical regions where a potential second and third telescope could be
placed to get optimal network performance in terms of our FoMs. Additionally,
we use a similar approach to find the optimal location and orientation for the
proposed LIGO-India detector within a five-detector network with Advanced LIGO
(Hanford), Advanced LIGO (Livingston), Advanced Virgo, and KAGRA. We found that
the FoMs do not change greatly in sites within India, though the network can
suffer a significant loss in reconstructing signal polarizations if the
orientation angle of an L-shaped LIGO-India is not set to the optimal value of
~58.2deg(+k*90deg) (measured counterclockwise from East to the bisector of the
arms).
