Daniel is standing in the middle of an equilateral triangle-shaped room. He wants to touch all three walls and return back to the center of the room. If the shortest distance between Daniel and a wall is \(1\), then \(d\) is the shortest distance Daniel has to walk to complete his task. Find \(d^2\).
Details and Assumptions
Walking to a vertex of the triangular room counts as touching both walls adjacent to the vertex.