An indecomposable equiprojective polytope with eleven vertices

Buffière and Pournin asked whether a convex three-dimensional polytope can be both equiprojective and Minkowski indecomposable. We answer affirmatively with an eleven-vertex polytope whose coordinates belong to {−1, 0, 1}. Every orthogonal projection in a direction parallel to no facet is a heptagon. Its six triangular facets occur in translated pairs, and its six remaining facets are parallelograms; these features give a complete compensation pairing. Requiring edge vectors to close around these faces forces every Minkowski summand to be a translated scaled copy of the whole polytope. We describe the direct search route, give the exact geometry and elementary proofs, and supply a standalone Python verifier using rational arithmetic.