  We study various properties of topological solitons (kinks) of a
field-theoretic model with a polynomial potential of the twelfth degree. This
model is remarkable in that it has several topological sectors, in which kinks
have different masses. We obtain asymptotic estimates for the kink-antikink and
antikink-kink interaction forces. We also study numerically kink-antikink and
antikink-kink collisions and observe a number of interesting phenomena:
annihilation of a kink-antikink pair in one topological sector and the
production in its place of a pair in another sector; resonance phenomena --
escape windows, despite the absence of vibrational modes in the kink excitation
spectra.
