# DelauneyMesh in 4d and higher

Is there any way to find the DelauneyMesh in 4D (or higher)? Its documentation implies that it should be possible "A Delaunay mesh consists of intervals (in 1D), triangles (in 2D), tetrahedra (in 3D), and n-dimensional simplices (in nD)." But then it fails without error (and there are no 4D examples anywhere). I guess it does not actually work for 4D or higher? Are there any user-made algorithms out there. Is there a fundamental obstacle to making this? (Scales too terrible with n?)

• Qhull can do this, so one might consider a way to interface Qhull and Mathematica to generate the required triangulation. See this related question as well. – J. M.'s ennui May 26 '20 at 16:18
• I would like to see this too but for 3D Voronoi. I suggested it to Wolfram back in v11 but it has not been implemented. You could use Nearest to get a NearestFunction and build it up yourself. – flinty May 26 '20 at 16:19