The vertex count of a shape is the total number of vertices in the shape. It can be considered to be the total extent of all the shape's 0-subfacets in 0-dimensional space. Extruding a shape into a prism doubles the vertex count. Joining a shape into a pyramid increases the vertex count by 1.
Vertex count is unitless.
A vertex is a point where n + |x| multiple faces meet in n dimensions.