View source for Deep hole

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''in a lattice''

Let $P$ be a collection of points in $\mathbf R$ (usually a [[Lattice|lattice]]). A hole is a point of $\mathbf R$ whose distance to $P$ is a local maximum. A deep hole is a point of $\mathbf R$ whose distance to $P$ is the absolute maximum (if such exists).

If $P$ is a lattice, then the holes are precisely the vertices of the Voronoi cells (cf. [[Voronoi diagram|Voronoi diagram]]; [[Parallelohedron|Parallelohedron]]).

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.H. Conway,   N.J.A. Sloane,   "Sphere packings, lattices and groups" , ''Grundlehren'' , '''230''' , Springer  (1988)  pp. 6; 26; 33; 407</TD></TR></table>