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We live in a three-dimensional space.

But what would a four-dimensional space look like?

It's difficult to visualize, but the simplest description of the fourth dimension is that it is all space reachable by traveling at right angles to three-dimensional space.

So, imagining the fourth dimension isn't easy.

**Describing Dimensions**

But, just as modern technology lets two-dimensional pictures take on a three-dimensional look, computer simulations can help mathematicians begin to visualize a four-dimensional space.

The number of dimensions in a space tells us how many coordinates are needed to specify a point within that space.

In one dimension, only one coordinate is needed.

So a line is one-dimensional because just one coordinate, x, specifies a point on it.

In two dimensions the two coordinates x and y show the horizontal and vertical position of a point.

With three dimensions, the three coordinates, x, y and z, give the horizontal, depth and vertical position of a point.

Mathematicians therefore use four coordinates w, x, y and z to describe a four-dimensional space.

The one-dimensional line had two obvious points at either end.

The two-dimensional square had four, and the three-dimensional cube had eight.

The sequence suggests that a four-dimensional object would have sixteen points where its lines meet - called vertices.

The result is a hypercube, called a tesseract, with 16 vertices, 24 faces, and 32 edges.

**Tesseract **

Every one of its edges is straight, and all angles between them are right angles, which is hard to depict with two or three-dimensional imagery.

But the fourth dimension's abstract nature hasn't stopped architects from trying to work with it.

**La Grande Arche de la Défense**

**Paris, France**

In Paris, La Grande Arche was built with a resemblance to a tesseract.

Its peculiar structure gives us a glimpse into a four-dimensional world.