My colleagues and I like sitting all together. But as the team grows this is becoming difficult. I thought the solution will be to leave the flat floor plan and add more dimensions so we can grow the team, ensure each member has his/her space and yet we remain close together.
If we want everyone to be exactly the same distance from each other we can only put $n+1$ people in $\mathbb{R}^n$ (euclidean distances). This seems rather expensive, needing to add so many dimensions to our office as the team grows(Especially as I have yet to find an architect willing to work with more than 3).
If we are willing to have some variability in distances between team members we can do better. For instance if we place our desks on a hypercube we can put $2^n$ points with a maximal distance ratio of $\sqrt(n)$.(Distance between two nearest vs two farthest).
Is this optimal? Can we improve? This is a multi objective, lower distance ratio or more points, so I'm interested in anything on the pareto optimal front.