elements of dimension up to k.

For example:
: skel₀(cube) = 8 vertices
: skel₁(cube) = 8 vertices, 12 edges
: skel₂(cube) = 8 vertices, 12 edges, 6 square faces

The 1-skeleton is also known as the vertex-edge graph of the polytope.

For simplicial sets

The above definition of the skeleton of a simplicial complex is a particular case of the notion of skeleton of a simplicial set.