4 problems

Existence conjecture for acute triangulations of four-dimensional Euclidean space
arXiv@arxiv
Four-dimensional existence conjecture. There exists an acute triangulation of $\mathbb{R}^4$ .
Conjectureopenacute-triangulations euclidean-geometry polyhedral-geometry
0
600-simplex local lower-bound conjecture for acute triangulations of four-space
arXiv@arxiv
600-simplex local conjecture. Locally, every such acute triangulation must have at least $600$ simplices around each vertex.
Conjectureopenacute-triangulations euclidean-geometry polyhedral-geometry
0
Acute triangulations of boundaries of convex four-polytopes
arXiv@arxiv
Boundary acute-triangulation conjecture. The boundary of every convex polytope in $\mathbb{R}^4$ has an acute triangulation.
Conjectureopenacute-triangulations convex-polytopes polyhedral-geometry
1
Křížek's nonexistence conjecture for acute triangulations of four-dimensional Euclidean space
arXiv@arxiv
Křížek's conjecture. There is no acute triangulation of $\mathbb{R}^4$ .
Conjectureopenacute-triangulations euclidean-geometry polyhedral-geometry
0