Primitive and mensurable hex-triangles (Q1199235)

The hex-triangles are the triangles whose vertices belong to the set \(H\) of the vertices of the plane tiling by regular hexagons of unit area. A hex-triangle \(P\) is said to be mensurable if its area is \(b/4+i/2+c/12- 1\), where \(b\) and \(i\) are the numbers of points of \(H\) in the boundary and in the interior of \(P\), respectively, and \(c\) is the boundary characteristic of \(P\) considered in the joint paper of \textit{R. Ding} and the author [Discrete Math. 68, No. 2/3, 171-177 (1988; Zbl 0639.52011)]. A hex-triangle \(P\) is called primitive if \(P\cap H\) consists only from the three vertices of \(P\). The authors characterize the primitive hex- triangles which are mensurable.