Two Species of Item: Shape-Only and Marked

Two species of item

Before you fold anything, decide which kind of item is in front of you. Shape-only items carry no shading anywhere: the pattern is a bare outline, and its dimensions alone decide the answer.

A

B

C

D

Marked items carry shading or drawn detail on particular faces. Here the four options are often the same solid, and what separates them is where the marks sit and which way they face.

A

B

C

D

Roughly a third of the section carries no shading at all, so this is not a rare special case — it is most of an item every few questions.

Which check to run first

Naming the species tells you what to measure. On a shape-only item the pattern is a set of dimensions: how many panels there are, how long each edge runs, how deep the block is. Each option either matches those dimensions or it does not, and the item is settled by arithmetic on the pattern rather than by mental rotation.

On a marked item the four solids usually share one shape, so measuring gets you nowhere. The answer turns on face relationships instead: which marked faces sit next to which, and how each mark is turned on the face it occupies. Running the wrong check is the most common way to waste thirty seconds on this section — decide the species first, then start.

The shading vocabulary

Patterns use three shading styles: solid black, diagonal hatching, and stippled gray — a field of small dots. A mark may cover a whole face or only part of one: a half, a triangle, a band, or a die's pips.

Folding preserves the style. Black stays black, hatching stays hatching, stipple stays stipple. No fold converts one style into another, so a figure whose hatched face has become solid black is not the same figure the pattern describes.

The pattern

Folded — styles unchanged

The solids you will meet

The section is not all cubes. Across the practice generator and the real test you will meet decorated cubes — whole-face shades, half and diagonal shades, and dice pips; rectangular boxes; square pyramids; profiled prisms, which are blocks whose end profile carries a cut, a step, a notch or a channel, including the marked house with its shaded roof, door and window; tapered frustums; glued cube assemblies; and rolled cylinders carrying helical bands.

Practice serves them by difficulty. Easy items draw on whole-face shaded cubes, rectangular boxes and profiled prisms. Medium adds part-face shaded cubes, dice, tapered frustums, pyramids and cylinders. Hard drops the boxes, the pyramids and the whole-face cubes entirely, and brings in glued cube assemblies and the house.

One caution about that easy tier. A cube with entire faces shaded is a scaffold, not a species to expect on test day: none of the fifteen catalogued live items is a plain fully-shaded-face cube. Whole-face shading is where the official worked example lives, and it is the cleanest place to learn the rules, because a whole-face shade has a position but no direction. Real cubes shade part of a face — a half, a triangle, a pattern of pips — and that is precisely what makes them harder.

The takeaway

Two species: shape-only items, decided by the pattern's dimensions, and marked items, decided by the relationships between marked faces. Identify which you have before you start, because the two demand different checks. The three shading styles — black, hatching, stipple — survive folding unchanged, and the solids range well beyond cubes to boxes, pyramids, profiled prisms, frustums, cube assemblies and cylinders. Drill all of them in the pattern folding practice generator.