A third direction
What Makes a Shape 3D?
A flat shape has length and width; a solid adds depth, and with it faces, edges and corners.
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Step 1 of 5
Flat shapes live in two directions.
A square has length and width and nothing else. Drawn on paper it takes up area but holds no space, because there is no depth to it.
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Step 2 of 5
A solid adds depth and so holds space.
Pull a square out of the page and it sweeps through a third direction, becoming a cube that can genuinely contain something.
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Step 3 of 5
Solids are described by faces, edges and corners.
A face is a flat surface, an edge is where two faces meet, and a corner is where edges meet. A cube has six, twelve and eight.
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Step 4 of 5
Curved solids break the tidy counting.
A cylinder has two flat circles and one curved surface wrapping round, so the neat face-edge-corner count stops applying cleanly.
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Step 5 of 5
Every solid unfolds into a flat net.
Cut along enough edges and a solid lies flat as a net, which is exactly how cardboard boxes are cut, printed and then folded.
A cube can be unfolded into eleven genuinely different nets, and picking the efficient one saves cardboard at scale.
The short version
A solid shape adds depth to a flat one, giving it faces, edges and corners, and space inside that a flat shape can never have.
Try it yourself
Carefully unfold a cereal box along its glued seams. What you get is the flat net the whole box was cut from.
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