\begin{align} 2^d & \leq _{\text{(1)}} \max \left\{ \# S \, |\, S \subseteq \mathbb {R}^d, \angle (s_i, s_j, s_k) \leq \frac{\pi }{2} \text{ for every } \{ s_i, s_j, s_k\} \subseteq S \right\} \\ & \leq _{\text{(2)}} \max \left\{ \# S \, |\, S \subseteq \mathbb {R}^d \text{ such that for any two points } \{ s_i, s_j\} \subseteq S, \right. \nonumber \\ & \qquad \qquad \left. \text{there is a strip } S(i, j) \text{ that contains } S, \text{ with } s_i \text{ and } s_j \text{ lying in the parallel boundary hyperplanes of } S(i, j) \right\} \\ & =_{\text{(3)}} \max \left\{ \# S \, |\, S \subseteq \mathbb {R}^d \text{ such that the translates } P - s_i, s_i \in S, \text{ of the convex hull } P := \text{conv}(S) \right. \nonumber \\ & \qquad \qquad \left. \text{intersect in a common point, but they only touch} \right\} \\ & \leq _{\text{(4)}} \max \left\{ \# S \, |\, S \subseteq \mathbb {R}^d \text{ such that the translates } Q + s_i \text{ of some d-dimensional convex polytope } Q \subseteq \mathbb {R}^d \text{ touch pairwise} \right\} \\ & =_{\text{(5)}} \max \left\{ \# S \, |\, S \subseteq \mathbb {R}^d \text{ such that the translates } Q^* + s_i \text{ of some d-dimensional centrally symmetric convex polytope } Q^* \subseteq \mathbb {R}^d \text{ touch pairwise} \right\} \\ & \leq _{\text{(6)}} 2^d. \end{align}