Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Specified by or exhibiting four dimensions, such as the three spatial dimensions and single temporal dimension of relativity theory.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Having four dimensions; being measurable along four mutually perpendicular axes.
 adj. Relating to the four dimensions of spacetime (three spatial dimensions with the addition of time as the fourth)
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. involving or relating to the fourth dimension or time
Etymologies
Sorry, no etymologies found.
Examples

He likened the complex process to "fourdimensional chess."

It is contained in fourdimensional space, and is defined as the set of points at a fixed distance from a given point, just as the twodimensional sphere (skin of an orange or surface of the earth) is defined as the set of points in threedimensional space at a fixed distance from a given point (the center).

A very important thing to remember: The dark star calculations are done for a threedimensional Euclidean space, while the black hole calculations are done for a fourdimensional Lorentzian spacetime (there is a big difference between the two).
“Black Holes – a Simplified Theory for Quantum Gravity NonSpecialists”

If we have local coordinates defined, we can then represent the metric tensor in matrix form, where, for our fourdimensional spacetime, we will have a 4×4 matrix with elements gμν.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

Finally you can do a sort of fourdimensional chart plotting one variable on the horizontal axis, a second of the vertical, and a third reflected in the size of a circle representing the data point, and a fourth indicated by the color of the circle.

He showed that the physics inside a hypothetical universe with five dimensions and shaped like a Pringle is the same as the physics taking place on the fourdimensional boundary.
Discourse.net: Shadows on Plato's Cave: Giant Hologram Version

Julian: Your desire for a dinghy is merely the tesseract shadow cast by the fourdimensional dinghy itself

Since the work of Einstein, we know that the stage on which the universe acts out its drama is not threedimensional space but fourdimensional spacetime, and moreover that stage, spacetime itself, is dynamic and plays its own part in the evolving action.
Stephen Hawking at 70: still the brightest star in the scientific universe

In my next story I posited humans in a fourdimensional cage, put there by more powerful offstage aliens.

In reality, there are three space dimensions, so the light would actually form an expanding or contracting sphere in 3D space rather than a circle in 2D, and the light cone would actually be a fourdimensional shape.
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