Classification of dodecahedral space forms.
Classification of hyperbolic dodecahedron tilings of maximally face-transitive motion groups. (Klassifikation der hyperbolischen Dodekaederpflasterungen von maximalen flächentransitiven Bewegungsgruppen.)
Complex Hadamard matrices and the spectral set conjecture.
By analyzing the connection between complex Hadamard matrices and spectral sets, we prove the direction "spectral ⇒ tile" of the Spectral Set Conjecture, for all sets A of size |A| ≤ 5, in any finite Abelian group. This result is then extended to the infinite grid Zd for any dimension d, and finally to Rd.
Cube tilings as contributions of algebra to geometry.
Cube-Tilings of Rn and Nonlinear Codes.