3-D or 3D abbreviates "three dimensional" and is often related to a stereoscopic display that exploits binocular vision.
Three dimensional objects have volume and may be measured and described using three orthogonal directions.
In animation, 3-D sometimes refers to shaded, modeled shapes that have an apearance of depth, as opposed to the "flat" rendering of conventional cell animation. An example of this was seen in a particular episode of the animated video cartoon The Simpsons, where Homer escapes his flatland-like world and enters a universe of higher dimensionality. The figure renderings and visual effects in this episode were accomplished using 3D computer graphics.
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In that case, it would make sense for the fl pieces to be arranged three rows deep on the top level instead of the bottom level, and for the kings and queens of both sides to face each other on the same file.
Unfortunately, the three sides are in a relationship such that one is, in effect, before, and the other is after, the third player, so the array is not symmetric with only two players.
Also, the top and bottom three levels are small rectangles; the green area simply shows where these rectangles stand in relation to the central 5 x 5 square of the five middle levels, so that alignment is unambiguous.