Rotation and Mirror Checks

Turning an option is free

The instructions say the object may be turned in any direction before it enters the aperture, and the openings are drawn accordingly: an option is presented at whatever rotation the item felt like, not at the orientation of the view that produced it. So an opening lying on its side is not thereby wrong. Turn it in your head — or turn your mental view — and compare shapes, never orientations.

Some properties of an outline survive that turn and some do not, and knowing which is which tells you what you are allowed to compare.

• Survives a turn: the number of features and of corners (the census from the previous lessons), the area, the lengths of the edges, and the two overall dimensions taken as an unordered pair — a three-by-five outline is three-by-five however it is laid down.
• Does not survive a turn: which side a notch sits on, which way a step rises, and whether the drawing reads as tall or wide.

Compare the survivors and you are comparing the shape. Compare the rest and you are comparing the drawing.

A flip is free too

This is the point most people get backwards. The mirror of a view's outline is an outline of the same object. Turn the object end for end and you are looking at its opposite face, and the outline of that face is exactly the mirror of the one you started with. Since the rules let you turn the object any way you like before insertion, the mirrored shape is the same opening as the original — there are eight ways to lay one outline down, four turns and four flips, and all eight are one opening.

That gives chirality its real job. An outline is chiral when no rotation carries it onto its mirror — the shape above is, a rectangle is not, because a rectangle's mirror is just the rectangle turned. Chirality does not decide whether a mirrored opening works. What it decides is whether "flipped" is visible at all, and on a chiral outline it is very visible. So you will meet options that look backwards, and looking backwards is never by itself a reason to cross one off.

FRONT VIEW

TOP VIEW

When a mirror image cannot pass

A mirrored opening fails when it is the mirror of the wrong thing. There are two ways for that to happen.

The first is mirroring across views. Items are built so that no two of an object's three outlines are turns or flips of one another, so a shape that is the flip of the top outline is emphatically not the front or end outline. "It matches once I flip it" is only worth something once you have said what it matches.

The second is the real trap: an outline mirrored only in part.

Exact front outline

One notch moved

One notch has been moved to where its reflection would sit; nothing else was touched. The result has the same width, the same height, the same area and the same features as the object's front outline, and it reads at a glance as "that shape, flipped" — but it is not. In a genuine flip every feature crosses over together. Here the notch changed ends while the corner step and the side notch stayed put, so the notch now sits at the same end as the side notch, where on the object the two are at opposite ends. No turn and no flip of any of the object's three outlines produces this shape, and the opening is always the exact shape of one of them, so it is out. Nor is this hypothetical: wrong openings really are built from a variant of the object with a single feature shifted along its axis while everything else stays where it was.

The check that works

Do not ask whether an option looks like your shape. Anchor on one feature and ask where the others sit relative to it, working around the loop. A turn moves every feature together and keeps that arrangement; a flip reverses the direction you travel around the loop but again moves everything together. Only a broken shape moves one feature and leaves the rest — and that is the one you are hunting.

The takeaway

Rotations and flips are both free, so an option that looks turned or backwards is not wrong for that reason: all eight ways of laying an outline down are the same opening. Compare only what a turn cannot change, and settle a suspected mirror by checking the features against each other rather than against the page. What kills a mirror-like option is that it is a mirror of a different view, or a shape mirrored in one feature only — neither is the exact outline the rules promise. Practice on real items in the keyholes practice generator.