Chapter 13: Visualizing 3-D in 2-D

Visualizing 3-D in 2-D covers representing solids on flat paper — isometric sketches, front/top/side views, and nets that fold up into a 3-D shape — plus Euler's formula linking a polyhedron's faces, vertices and edges: F+V=E+2. A cube checks out neatly: 6 faces + 8 vertices = 14, and 12 edges + 2 = 14.

A net that looks plausible but doesn't actually fold into a closed solid is the most common construction error — mentally folding it before finalising an answer catches this. This chapter is also unusual for testing diagram-reading and spatial reasoning rather than pure calculation, and it's a direct prerequisite for the very next chapter, where "seeing" a solid's faces clearly becomes essential.