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Polyhedra (Cubes, Pyramids etc): Does these solids consist of the boundary points only, or do they include interior points ?

I'm confused whether a general polyhedron (solid object: cube, pyramid etc.) include the boundary points of the surface only or if they include the interior points also ?

Pictures of these solid objects always show half transparent sides and "nothing" on the inside. Also reading about the sphere (http://en.wikipedia.org/wiki/Sphere), this object does not include the interior points, but only the points of radius $r$ from the origin.

Could someone clarify the definition of a solid object in $n$-dimensional space ? Wikipedia use the term without explanation. - and tell me whether objects like those already written down (also cylinder etc.) include boundary points (points on the "outside") only ?

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Convex polyhedra are normally defined to be the intersection of half spaces in $\mathbb{R}^3$ which would indeed mean that they are solid. Context will normally tell you which case is being considered however, for instance it is common to speak of the boundary of the tetrahedron because it is a simplicial complex which is homeomorphic to the sphere - some might just call this a tetrahedron and then denote the intersection of half spaces to be the 'solid tetrahedron'. Conventions will vary I'm afraid.

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  • $\begingroup$ Could you give a link to the definition of "solid" ? $\endgroup$ – Shuzheng Mar 9 '14 at 17:57
  • $\begingroup$ I don't think "solid" has a standard definition. I might go for something like 'A solid is subset of $\mathbb{R}^n$ which is equal to the closure of its interior'. $\endgroup$ – Dan Rust Mar 9 '14 at 18:03

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