All vertices of a pyramid lie on the facets of a cube
Source: Sharygin contest 2008. The correspondence round. Problem 22
September 3, 2008
geometry3D geometrypyramidgeometry proposed
Problem Statement
(A.Khachaturyan, 10--11) a) All vertices of a pyramid lie on the facets of a cube
but not on its edges, and each facet contains at least one vertex. What is the
maximum possible number of the vertices of the pyramid?
b) All vertices of a pyramid lie in the facet planes of a cube but not on the lines
including its edges, and each facet plane contains at least one vertex. What is the
maximum possible number of the vertices of the pyramid?