Six points with a contractible Rips shadow and nontrivial fundamental group

The affine projection from a Euclidean Vietoris--Rips complex to its shadow need not be injective on fundamental groups. We give six rational points in three-dimensional space whose Rips complex retracts onto a four-cycle, while its shadow is the union of two convex quadrilaterals containing the origin and is therefore contractible. Scaling and isometric inclusion give the same failure in every ambient dimension at least three and at every positive scale. This refutes the injectivity conjecture of Adamaszek, Frick and Vakili.