  Latin squares are well studied combinatorial objects. In this paper we
generalize the concept and propose new objects like Latin triangles, free Latin
squares, Latin tetrahedra, free Latin cubes, etc. We start with a classic
definition of Latin squares followed by one based on the concept of latinized
board. A Latin square appears then as a combinatorial design whose points are
geometric and whose lines (the rows and columns) are invariant under the
symmetries of the square.
  The generalization that follows proceeds by 1. broadening this geometric
symmetry 2. considering more general configurations of points and 3. admitting
lines that intersect more freely. The resulting concept is the Latin board.
Finally, we particularize Latin boards to define Latin polytopes, Latin
polygons and Latin polyhedra.
