Leo+DadMade for Leo
Views of Prisms and Solids
Rung 3 of 3 · The traps

Hidden Edges, and Why One View Is Never Enough

A single view can lie to you — two completely different solids can share the same front view. Dashed lines are how a drawing whispers "there's more here than you can see".


ExploreToggle the dashed “hidden edges”. Then hit “surprise me”.
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Squashing a solid flat throws away its depth — and that's exactly where things go wrong. Two solids that are very different behind the front can flatten into the same front view.

Hidden Edges, Drawn Dashed

When you draw a solid, some of its real edges sit behind the parts you can see. You can't see them, but they're really there — so they get drawn as dashed lines instead of solid ones. In the toy, toggle the hidden edges on and off: the dashed lines are the back corners of each solid, tucked out of sight. A solid line means "edge you can see"; a dashed line means "edge that's there but hidden".

Say it plainly: solid line = an edge you can see. Dashed line = a real edge hiding behind something. Never leave hidden edges out — they're part of the shape.

The Proof That One View Isn't Enough

Press "surprise me". You'll see two solids that look identical from the front — both give the same L-shaped front view — yet they're genuinely different objects. One is a thin L slab; the other is twice as deep. The front view alone can't tell them apart, because flattening from the front hid all that depth. That's why a single drawing is never a safe description of a solid.

So Always Use More Than One View

To pin a solid down for certain, you need the front, the side and the top. The side view is what would expose the difference between those two L-solids — one would look thin, the other deep. Three views together leave no room for two different solids to sneak through. When a question gives you only one view and asks "what's the solid?", the honest answer is often "it could be several things" — and that's the insight this rung is really about.

Us, Thinking Out Loud

Why does flattening a solid sometimes lose information you can't get back?

If I gave you only the top view of a mystery solid, what couldn't you possibly know?