  Motivated by blockchain technology for supply-chain tracing of ethically
sourced diamonds, we study geometric polyhedral point-set pattern matching as
minimum-width polyhedral annulus problems under translations and rotations. We
provide two $(1 + \varepsilon)$-approximation schemes under translations with
$O(\varepsilon^{-d} n)$-time for $d$ dimensions and $O(n\log \varepsilon^{-1} +
\varepsilon^{-2})$-time for two dimensions, and we give an
$O(f^{d-1}\varepsilon^{1-2d}n)$-time algorithm when also allowing for
rotations, parameterized on $f$, which we define as the slimness of the point
set.
