The View Obstruction Problems for Boxes

Let Sⁿ denote the region 0<x_i < ∞ (i=1,.... n) of the n-dimensional Euclidean space Rⁿ, n≥2. Let C be a closed convex body in Rⁿ with O as an interior point. For P∈Rⁿ, let C+P be the translation of C through the vector P and for real α>0, let α C be the magnification of C by the factor α. Define
Δ(C,α)=∪{αC+(1/2N₁,..., 1/2N_n):N₁ odd positive integers}.