An integer triangle dissection is a triangle dissection of an integer triangle into smaller integer triangles. The original triangle and every piece therefore have integer side lengths.
A specific type of triangle dissection consists of a triangle 
together with an interior point 
such that the original side lengths and the additional three
line segments created by connecting the triangulation point with the vertices are all
integers. An example of such a dissection
is illustrated above (Pegg).
Other possible dissections allow cut lines to be drawn from arbitrary points along the sides. Allowing only primitive triangles without any parallel lines, isosceles triangles, or similar triangles, the smallest three-piece integer dissection of each of the four possible types is illustrated above.
Similarly, the smallest four-piece integer dissection for each of the 23 possible types is shown above.
Two 5-piece dissections are illustrated above (Pegg).
