Specifics of mutually intersecting regular pyramids with a common base (Q1980288)

This is an analysis of some features of two intersecting pyramids with a common base, which is a regular polygon. The main result states that: The mutual intersection of two pyramids with an even number of sides and a common base of a regular polygon, with two main edges parallel to the line built across their vertices, and of the same height intersect in \(\frac{n}{2}-1\) pairs of sides (\(n\) being the number of the common base angles). Their mutual section is a broken planar straight-line, with \(\frac{n}{2}-1\) sides when viewed from above. Projected in a projection plane parallel to the two main edges and the line built across their vertices, and perpendicular to their common base, it is a line starting from the internal side or edge and terminating in the plane obtained by the intersection of each pair of surrounding sides, whose common base edge is parallel to the projection plane. For the entire collection see [Zbl 1445.53003].