  Superconductivity in quasicrystals poses a new challenge in condensed matter
physics. We measured the resistance and ac magnetic susceptibility of a
Ta$_{1.6}$Te dodecagonal quasicrystal, which is superconducting below $T_c
\sim$ 1 K. We show that the upper critical field increases linearly with a
large slope of $-$4.4 T/K with decreasing temperature down to 0.04 K, with no
tendency to level off. The extrapolated zero-temperature critical field exceeds
the Pauli limit by a factor of 2.3. We also observed flux-flow resistance with
thermally activated behavior and an irreversibility field that is distinct from
the upper critical field. We discuss these peculiarities in terms of the
nonuniform superconducting gap and spin--orbit interaction in quasicrystal
structures.
