14. As shown in the figure, a piece of cardboard can be cut to make a polyhedral paper model (fold along the dotted lines, stick along the solid lines). What is the total number of faces, vertices, and edges of this polyhedron?

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14. The total number of faces, vertices, and edges of a polyhedron is 74.
14.【Solution】The number of faces of the polyhedron can be directly counted from the net, 12 squares plus 8 triangles, totaling 20 faces. The diagram below is a schematic of the upper part of the polyhedron, which has 9 vertices; similarly, the lower part also has 9 vertices. In total, there are 18 vertices.

The number of edges can be counted in three layers: the upper layer, from the diagram, has 15 edges; the lower layer also has 15 edges; the middle part has 6 edges, making a total of
$$
\begin{array}{l}
15 \times 2+6=36 \text { (edges) } \\
20+18+36=74 \text { (units). }
\end{array}
$$

Answer: The total number of faces, vertices, and edges of the polyhedron is 74 units.