|top view constructed starting from the base||
We start by inscribing the base in a triangle whose sides must contain three sides of the polygon; it is the base of a tetrahedron and we choose its apex S.
Here a lateral edge of the tetrahedron is also one for the tectohedron.
The vertices A and B, chosen on the two other lateral edges of the tetrahedron starting at S, define two ridgepole edges.
We can now draw the cut through A.
The drawing of the cut through B allows us to place the vertex C, and to draw the cut through C.
The method consist thus to start from the apex of the tetrahedron and to choose gradually the other vertices which define the ridgepole edges. At each stage we can draw the cut through the last chosen vertex.
|net constructed starting from the top view||
The points to be constructed (in yellow) permit to draw the sides of the lateral faces (dashed line segments in blue).
Properties to be respected during the construction:
remark: the choice of the first point (for example A) determines the hight of the tectohedron, thus it must be chosen at a distance from the base far greater as the one of the corresponding vertex; we construct the other points gradually (in any direction).
The construction becomes more tricky if, on the top view, the vertex S of the tetrahedron has been chosen outside of the base polygon.
||convex polyhedra - non convex polyhedra - interesting polyhedra - related subjects||April 2008 |