there is no convention in general. it depends on what is measured and how. a fish tank maybe quoted different to a milling machine, to a swimming pool.
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No, a point has no length, width, or height and thus has no dimensions. It is defined by a set of coordinates, but itself has no dimensions. A line has length but no width or height, and thus has 1 dimension. a plane has length and width, but no height, and thus has 2 dimensions. a space has length, width and height, and thus has 3 dimensions.
Length is one of the dimensions. Length, width, height etc. which can describe an object are called its dimensions.
Spacial dimensions are the dimensions in space such as length,height and depth.
The dimensions of a Kleenex box are length, width and height. The volume of the box is equivalent to length times width times height.
Length, width and height.