Determine whether such a spacetime tiling can be obtained by sCNP

Determine whether a G-symmetric spacetime quasi-tiling, if it exists, can be constructed using the symmetric cut-and-project (sCNP) method.

Background

The sCNP construction uses a highly symmetric window or weighting function to generate spacetime quasicrystalline point sets. The thesis explains that the circular or polydisk windows used for Lorentzian quasicrystals are too smooth to lift directly to finite-faced higher-dimensional cells, while the prototiles needed for an inflation-subdivision construction are also unknown.

Consequently, even if an appropriate spacetime quasi-tiling exists, the thesis does not establish a construction within sCNP.