When a net folds, each cut edge on its outer boundary meets one other cut edge. Find the pairs by following corners and lengths, not by where the edges sit on the page.
This lesson belongs to surface development concepts. It builds on connecting a solid to its flat development.
What types of edge does a net have?
Three types.
- Fold lines: shared edges where two faces stay attached.
- Seams: cut edges that meet another cut edge when folded.
- Free rims: cut edges that stay open, such as the top of an open box.
Worked example: an open box
An original open-top box has a base 40 mm by 30 mm and a height of 20 mm. Its net is a cross: the base in the middle, with a side face attached to each base edge.
The four sides are a 40 × 20 front, a 40 × 20 back, a 30 × 20 left and a 30 × 20 right.
Fold lines. The four base edges, of lengths 40, 40, 30 and 30, are already attached to the sides.
Seams. The four vertical corners of the box are cut, so each appears on two neighbouring side faces. Each is 20 mm. The net shows 8 edges of 20 mm, which pair up into 4 corners.
Free rims. The top edges of the four sides form the open rim, of lengths 40, 40, 30 and 30.
Count check: four sides of four edges each give 16 edge slots. Adding the base’s 4 gives 20 slots. Fold lines use 8 slots, seams use 8 and the free rim uses 4, and 8 + 8 + 4 = 20.
The mistake: matching by position
Looking at the cross, the front side’s left edge sits close to the left side’s long outer edge on the page. A student pairs them because they are near. But the front’s left edge is 20 mm and the left side’s outer edge is 30 mm.
| Method | Pair chosen | Lengths | Result |
|---|---|---|---|
| Nearest on page | Front left edge and left side’s outer edge | 20 and 30 | Impossible |
| Corner and length | Front left edge and left side’s 20 mm end edge | 20 and 20 | Meets at the same corner |
A quick test is to fold the picture in your head corner by corner, and check the lengths before you commit.
Labelling trick
Name the four top corners of the solid P, Q, R and S. On the net, each seam edge carries the letters of the corner it reaches. Two edges with the same letter pair rejoin.
Check yourself
An open box has a square base of side 25 mm and height 10 mm, with a cross-shaped net. How many seam pairs are there, and how long is each? What is the total length of free rim?
Answer
There are 4 seam pairs, one for each vertical corner, and each is 10 mm long.
The free rim is the top of four sides, each 25 mm, so 4 × 25 = 100 mm.
What to study next
Next, practise spotting faults in checking a development for missing faces or incompatible lengths, or try the development practice set.
If you want a teacher to give you fresh nets to label, see online one-to-one Engineering Drawing tuition.