A counterexample to Valette's conjecture
The author constructs a simple 4-dimensional counterexample to the following \textit{Conjecture 1.} Let \( K\) be a self-affine body in \({\mathbb R}^d \), \( d \geq 2 \); then \( K \) is either a polytope or affinely equivalent to a product of a convex body with a polytope of lower positive dimension. Some additional assumptions which make this Conjecture true are formulated as well as \textit{Problem 1.} Is the Conjecture \(1\) true for \( d = 3 \)?
scientific article; zbMATH DE number 6342484