The Tesseract

The Geometry of the Tesseract

Christina Sng for Maths@Singapore

Of all the mathematical shapes, the tesseract is the one that intrigues me the most.

The tesseract is also known as a hypercube. It is four-dimensional cube, in the way a cube is the three-dimensional equivalent to a square.

As it is impossible to show a four-dimensional object in three-dimensional space and on a two-dimensional screen, one can instead imagine a cube within a cube where each vertice forms a right angle to another.

A tesseract composes of 8 cubes with 3 to an edge, and has 16 vertices, 32 edges, 24 squares, and 8 cubes.

The fascinating aspect of the tesseract is that it contains lines of equal length meeting each other at right angles, which means each two-dimensional face of a tesseract is a square and each three-dimensional face of a tesseract is a cube.

The tesseract has been popular in the media, featured in the Marvel Cinematic Universe as a “crystalline cube-shaped containment vessel for the Space Stone, one of the six Infinity Stones that predate the universe and possesses unlimited energy,” as described in the Marvel Movies Wiki.

It has been widely employed in art and fiction.

In his 1954 masterpiece, Crucifixion, Salvador Dali painted a tesseract.

In Robert Heinlein’s 1940 short story “And He Built a Crooked House.”
he included a tesseract building .

Madeleine L’Engle calls a tesseract, “a shortcut between three-dimensional places” in her 1962 book “A Wrinkle in Time.”

There is no doubt the tesseract brings a sense of awe. Close your eyes now and imagine it.

Visit What Is a Tesseract or Hypercube? to find out more.

Image credit: Jason Hise

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