Sphere inscribed in a prism
Overview
Important
A sphere is said to be inscribed in a prism if it fits perfectly inside the prism, touching all its faces but not crossing any. This means the sphere is tangent to every face of the prism.
Important properties
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For a sphere to be inscribed, the prism must have enough symmetry (for example, a right prism with a regular polygon as its base).
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The center of the inscribed sphere is equidistant from all the faces of the prism.
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The radius of the inscribed sphere is equal to the shortest distance from the center to any face.
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Not every prism can have an inscribed sphere; the base must allow a circle to be inscribed (i.e., the base must be tangential).