Nets That Are Not Cubes

Count the panels first

A cube pattern always has six squares. Every other solid has its own fixed panel count, and the count is decided by the solid, not by the item — so counting panels names the family before you fold anything.

• Rectangular box — six panels in a cross, and each face dimension appears on exactly two of them.
• Square pyramid — five: a square base with four triangles hinged to its edges.
• Profiled block — two end panels plus one wall rectangle per edge of the end profile.
• Tapered figure — six: a base, four flaps, and a top panel attached beyond one of the flaps.
• Cylinder — three: one rectangle and two discs.
• Glued cube assembly — six squares per cube, minus two for every glued joint.

Strip and caps

The block families all use the same construction: a row of rectangles that wraps around the walls, with two identical end panels that cap it. Here is the simplest one the practice section draws.

Five panels: three rectangles in a strip and two triangles. That count alone tells you the profile is a triangle, and a triangle has three edges, so the walls need three rectangles.

Three rules govern the strip, and all three are arithmetic you can do on the page:

1. Each rectangle's width is one edge of the cap profile, taken in order as you travel around the profile. Rectangle one wraps the first edge, rectangle two the second, and so on.
2. The strip's total width is therefore the profile's perimeter.
3. Every rectangle in the strip has the same height, and that height is the solid's depth — the distance from one cap to the other.

Rule one is what betrays a slope. In the wedge above, the middle rectangle is visibly wider than either of its neighbours: it wraps the triangle's long side, and a hypotenuse is longer than either leg. A profile edge that runs at an angle always produces a rectangle whose width no square-cornered profile could have produced.

More profile edges, more rectangles — nothing else changes:

Eight panels here. The two caps are L-shaped, an L has six edges, and there are six rectangles in the strip. Trace the six widths against the six edges of the L and you have read the whole solid off the pattern.

Base and flaps

Tapered figures are laid out differently: one panel in the middle for the base, four flaps hinged to its four edges, and the top panel attached beyond one of those flaps rather than to the base.

Two things to check on a pattern like this. All four flaps share one slant height — they are drawn the same distance out from the base, because on the solid they all lean from the base edge to the top edge over the same slope. And the flap tips must exactly frame the attached top panel: fold the four flaps up and their short edges are the four sides of the top. If the tips do not match the top panel's dimensions, the taper you are being shown is not the taper the pattern draws.

An unrolled wall

The curved family is a single rectangle with a disc hanging off the top edge and another off the bottom.

The rectangle is the tube's wall, unrolled: its width is the circumference, not the diameter, and its height is the height of the tube. The two discs are the ends. The practice prompt for this family states the convention outright — it asks which cylinder results when the pattern is rolled up, printed side out — so any marking drawn on the rectangle ends up on the outside of the tube.

A cube assembly, unfolded whole

The hardest patterns in the section unfold a glued assembly of cubes across its entire surface. Every exposed face of the assembly becomes one unit square of the pattern, so the count is exact: six squares per cube, minus two for every glued joint — one lost from each of the two cubes that meet there.

Eighteen squares. Four cubes at six squares each is twenty-four, and three glued joints take away two apiece, which leaves eighteen. Five cubes joined at four places would give thirty minus eight, or twenty-two squares.

The result is always one connected sheet of unit squares — but do not expect it to be a tidy blob. The unfolding can wrap around and enclose a gap, and roughly a quarter of the assemblies the generator draws do exactly that. A hole in the middle of the pattern is not a defect and not a clue.

Read the count, then the shape

A ✓

B

C

D

Five panels — two triangles and three rectangles — so the solid is a wedge: two triangular ends joined by three faces, one of which is the slope. The marked figure is that wedge. Separating it from the three near misses is arithmetic on the strip widths, which the elimination lesson takes up; the reading you owe the pattern before any of that is the panel count.

The takeaway

Count the panels first: the number is fixed by the solid, so it names the family. A strip of rectangles between two matching caps is a block, and each rectangle's width is one edge of the cap profile taken in order around it, all at the one shared height that is the depth. A base with four equal-slant flaps and a top beyond one of them is a tapered figure; one rectangle and two discs is a tube, whose width is the circumference. A field of unit squares is a cube assembly — six per cube, minus two per glued joint.