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I am trying to prove the graph-theoretic generalization of the following geometric observation: let $ \mathbb{P}$ be a finite set of distinct points in the Euclidean plane and $ card\left(CH\left(\mathbb{P}\right)\right)\ge4$ , where $ CH\left(\mathbb{P}\right)\subseteq\mathbb{P}$ denotes the set of points constituting to the convex hull of $ \mathbb{P}$ , then the following observation can be made:Read more

Consider 2 orthogonal edges, 2 orthogonal face diagonals, and 2 non-orthogonal face diagonals of a cube. How many different ways can these be chosen such that: a) they all lie in three mutually perpendicular faces of the cube which share a vertex b) the two non-orthogonal face-diagonals D1,D2 are pairwise orthogonal to the two edgesRead more