Plato envisioned Earth's building blocks as cubes, a shape rarely found in nature. The solar
system is littered, however, with distorted polyhedra—shards of rock and ice produced by …

Molecular self-assembly plays a very important role in various aspects of technology as well
as in biological systems. Governed by covalent, hydrogen or van der Waals interactions–self …

Given a polytope $ P\subset R^ 3$ and a non-zero vector $ z\in R^ 3$, the plane $\{x\in R^ 3:
zx= t\} $ intersects $ P $ in convex polygon $ P (z, t) $ for $ t\in [t^-, t^+] $ where $ t …

Transverse aeolian ridges–enigmatic Martian features without a proven terrestrial analog–
are increasingly important to our understanding of Martian surface processes. However, it is …

We examine geological crack patterns using the mean field theory of convex mosaics. We
assign the pair n¯∗, v¯∗ of average corner degrees (Domokos et al. in A two-vertex theorem …

Planets are often covered with thin cracked shells. From mud films to lithospheres of rock or
ice, fracture networks form two-dimensional (2D) tessellations of convex polygons whose …

We introduce and study a general framework for modeling the evolution of crack networks.
The evolution steps are triggered by exponential clocks corresponding to local micro-events …

An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of
an edge of another tile. In this paper we show that for any integer k≥ 3, there exists a normal …

Plato claimed that the regular solids are the building blocks of all matter. His views,
commonly referred to as the geometric atomistic model, had enormous impact on human …