  The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the
icosahedron and the tetrahedron is the smallest volume that can show up in
Delaunay tessalation. No periodic lattice is consistent with either and hence
these dense packings are geometrically frustrated. Because icosahedra can be
assembled from almost perfect tetrahedra, the terms "icosahedral" and
"polytetrahedral" packing are often used interchangeably, which leaves the true
origin of geometric frustration unclear. Here we report a computational study
of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible
with the symmetry of the densest crystal, while polytetrahedral order is not.
We observe that, under otherwise comparable conditions, crystal nucleation in
4d is less facile than in 3d. This suggest that it is the geometrical
frustration of polytetrahedral structures that inhibits crystallization.
