Def: M₂₄ consists of all metric spaces such that

1. All distances are 1 or 2.

2. d(x,y) + d(x,z) + d(y,z) ≤ 4

Why M₂₄

1. A step in the direction of the goal (better than 2-competitive
   randomized algorithm for the 2-server problem).

2. Allows a simple example of the knowledge state method.

3. An interesting class in its own right, derived from the
   cross polytopes, an infinite family of regular convex
   polytopes, generalizing the octahedron.