After reading many papers about problems of minimum polygon covering, I found out that there are four different types of units that are considered for covering polygons, in increasing order of generality: squares, rectangles, convex shapes and star shapes.

In theory, there can be many other covering units, for example: it is possible to cover a polygon with triangles (this is different than the problem of triangulation because the units in a covering may overlap), pentagons, hexagons... but, I haven't found any paper discussing such covering problems.

My question is: are you aware of any papers discussing the problem of finding a minimum covering of a polygon with shapes other than the four classes above?

I am particularly interested in covering a polygon with right-angled isosceles triangles, isolateral triangles or other regular polygons.

[NOTE: Cross-posted from cs.SE after I received the Tumbleweed badge for it]

spiralswere considered in this paper: O'Rourke, J.; Supowit, K. (1983). "Some NP-hard polygon decomposition problems".IEEE Transactions on Information Theory29 (2): 181. – Joseph O'Rourke Jun 23 '14 at 12:19coversby L-shapes... – Joseph O'Rourke Jun 23 '14 at 12:20