Convex hull of all ${−1,1}_{D}$ (Cartesian product power) D-tuples, e.g. in 3D:

```
( 1, 1, 1)
( 1, 1, -1)
( 1, -1, 1)
( 1, -1, -1)
(-1, 1, 1)
(-1, 1, -1)
(-1, -1, 1)
(-1, -1, -1)
```

From this we see that there are $2_{D}$ vertices.

Two vertices are linked iff they differ by a single number. So each vertex has D neighbors.