We determine all possible equilibrium sequences of compact strange-mat
ter stars with nuclear crusts, which range from massive strange stars
to strange white dwarf-like objects (strange dwarfs). The properties o
f such stars are compared with those of their nonstrange counterparts-
neutron stars and ordinary white dwarfs. The main emphasis of this pap
er is on strange dwarfs, which we divide into two distinct categories.
The first one consists of a core of strange matter enveloped within o
rdinary white dwarf matter. Such stars are hydrostatically stable with
or without the strange core and are therefore referred to as ''trivia
l'' strange dwarfs. This is different for the second category which fo
rms an entirely new class of dwarf stars that contain nuclear material
up to similar to 4 x 10(4) times denser than in ordinary white dwarfs
of average mass, M similar to 0.6 M., and still about 400 times dense
r than in the densest white dwarfs. The entire family of such dwarfs,
denoted dense strange dwarfs, owes its hydrostatic stability to the st
range core. One of the striking features of strange dwarfs is that the
entire sequence from the maximum-mass strange star to the maximum-mas
s strange dwarf is stable to radial oscillations. The minimum-mass sta
r is only conditionally stable, and the sequences on both sides are st
able. Such a stable, continuous connection does not exist between ordi
nary white dwarfs and neutron stars, which are known to be separated b
y a broad range of unstable stars. As a result, we find an expansive r
ange of very low mass (planetary-like) strange-matter stars (masses ev
en below similar to 10(-4) M. are possible) that arise as natural dark
-matter candidates, which if abundant enough in our Galaxy, should be
seen in the gravitational microlensing searches that are presently bei
ng performed.