The vampire einstein problem asks whether a single tile can tile the plane while forcing a nonperiodic tiling with copies of one handedness. In the weak version, the tile must admit a tiling using copies of one handedness, and every such tiling must be nonperiodic. In the strict version, every tiling by the tile must use one handedness, even when reflections are permitted (Smith et al. 2024).
The word "einstein" comes from the German ein Stein, meaning "one stone," and refers to the use of a single tile shape (University of Waterloo 2023). Smith et al. (2024) suggested "vampire" because the tile is unaccompanied by its reflection, alluding to the folklore that vampires cast no mirror image.
Smith et al. (2024) solved the weak version with the equilateral precursor of the spectre tile, which also permits a periodic tiling if both handednesses are used. They solved the strict version by modifying its edges to obtain spectre tiles, which preclude tilings that mix handednesses.
