Convex bodies
Overview
Important
A convex body is a solid shape in space where, for any two points inside the shape, the straight line segment connecting them is also completely inside the shape. Convex bodies are important in geometry because they have simple and useful properties.
Important properties
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If you pick any two points inside a convex body, the whole segment between them stays inside the body.
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Examples of convex bodies: cubes, spheres, tetrahedra, and cylinders.
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Non-examples: shapes with dents or holes, like a crescent moon or a doughnut (torus), are not convex.
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Convex bodies have no 'inward' curves or indentations.