Wrong Solid: Dimension, Taper and Feature Traps

When the markings are not the point

Plenty of patterns carry no shading at all. A profiled block, a tapered figure, an assembly of cubes, a can with a band rolled around it — the pattern is just an outline, and there is nothing to track from face to face. The wrong answers cannot move a marking, so they change the solid instead: its proportions, the position or size of a cut, or whether a sloping wall is sloping at all.

This family behaves completely differently from the marked-cube traps, and it is worth saying why plainly. Every length you need is printed on the pattern. The strip that wraps the block is as long as the profile's edges laid end to end; the flaps of a tapered figure are exactly as long as its slant; the squares of an assembly's pattern are exactly its exposed faces. So these items are settled by arithmetic, not by mental rotation. If you find yourself turning the solid in your head to compare a depth, you have chosen the harder route.

Blocks with a cut in them

The commonest shape-only item is a block whose end panels carry a profile: an L, a T, a U with a channel, a staircase, a notch in the top edge. The end panels state every dimension the block has, and the wrong options edit one of them.

A ✓

B

C

D

The notch in the top edge of the end panels must sit at the same offset in every view of the folded solid, and its walls must match the pattern — straight-sided or sloped. Wrong options slide the notch along the block, change its depth, or swap a V-cut for a square cut.

Read the correct answer's own reasoning above and notice what it asks you to compare: an offset, a depth, and whether the walls of the cut are straight or sloped. That is the entire family. A cut can be slid along the block, made deeper or wider, or have its shape swapped between a square cut and a V. The block itself can gain or lose a unit of depth. Nothing is ever added or removed — you are always comparing one number against one number.

So measure on the flat pattern before you look at the options. Count the squares along each arm of the profile, and count in from the edge to the start of the cut:

Two squares in, one deep. Now the option that shows it three squares in is a wrong answer you can name in a second, without deciding which way round anything faces.

Tapered figures

A tapered pattern is a base rectangle with four trapezoid flaps. The flaps are not free: they share one slant length and their short edges have to frame the top face exactly, so the pattern fixes both the height and the amount of taper before you fold anything.

A

B

C ✓

D

The four trapezoid flaps share one slant height, and their short edges must exactly frame the attached top rectangle — that fixes the taper and the height of the solid. Compare each option's top face against its base: the wrong choices are too tall, too shallow, or taper by the wrong amount (one is a straight-sided box).

The reasoning printed below the item names what the wrong options do: too tall, too shallow, tapering by the wrong amount — and one of them a plain straight-sided box, the taper removed altogether. That last one is worth naming, because it looks so clean that it reads as the simple answer. A pattern whose side flaps are trapezoids cannot fold into a box; the sloping edges have nowhere to go.

Assemblies of cubes

Cube assemblies unfold into a full-surface pattern: every square of the pattern is one exposed face of the finished object. The wrong answers keep the shape connected and keep the cube count identical — one cube is lifted from an end of the assembly and reattached somewhere else.

A ✓

B

C

D

Counting cubes will never separate these options, because the count is exactly what the mutation preserves. Count faces instead. The pattern has one square per exposed face, so an assembly that attaches a cube in a different place hides a different number of faces at its joints and no longer accounts for all the squares. Which way round the assembly reads is a separate question, settled by the earlier topic on handedness.

Rolled bands

A can's pattern is a rectangle with stripes across it. Roll the rectangle and each stripe becomes a band winding around the can, and the geometry of that band is completely determined by the stripe: how far the stripe travels across the rectangle sets how far the band wraps, the stripe's thickness sets the band's width, and the number of stripes sets the number of bands.

A

B

C ✓

D

The wrong answers move exactly those three numbers: a band that wraps too far around, a band that runs straight up the side instead of winding at all, a band drawn at double width, a can carrying a different number of bands from the pattern, and a can with squat proportions. Compare stripe to band, one quantity at a time. The direction the band winds is a fourth trap and a different kind — it is a handedness question, and it belongs to the mirror topic.

How to spend the time

1. Read the numbers off the pattern first. The profile's arm lengths, the offset and depth of the cut, the count of stripes, the number of squares. Say them out loud before you look right.
2. Test one number at a time across all four options. A single dimension usually kills two of them, and it is far faster than assessing whole solids.
3. Do not rebuild the solid in your head. Mental rotation is the expensive tool, and this family never requires it.

Drill the shape-only families at easy and medium on the pattern folding practice generator, where the profiled blocks live.

The takeaway

When a pattern has no markings, the wrong answers change the figure itself: a cut slid along or deepened or widened, a square cut swapped for a V, a unit of depth added, a taper reduced or removed entirely, one cube of an assembly reattached elsewhere, a band that wraps too far or runs straight up or comes in the wrong number. Every one of those is a number that the flat pattern already states. Read the numbers first and compare them one at a time — mental rotation is not what this family is testing.