She returned the smile, then looked across the room to her youngest brother, Charles Wallace, and to their father, who were deep in concentration, bent over the model they were building of a tesseract: the square squared, and squared again: a construction of the dimension of time. It was a beautiful and complicated creation of steel wires and ball bearings and Lucite, parts of it revolving, parts of it swinging like pendulums.*
I wrote a couple of months ago about four-dimensional geometry. Today I'd like to continue our progress through transdimensional gulfs and sinister alien geometries by discussing the 120-cell in some detail, and also describing the workflow I used to print the three-dimensional sections and net shown below.– Madeleine L'Engle, A Swiftly Tilting Planet
As usual when trying to understand the fourth dimension, it's easiest to proceed by way of analogy with lower dimensions. Imagine a two-dimensional creature, like A. Square of Flatland, existing in a planar universe. Such a creature would have an essentially one-dimensional field of vision, much as our field of vision is essentially two-dimensional (like a painting or a television screen). How would we describe a dodecahedron, that is, a polyhedron formed from twelve regular pentagons, to such a creature?
(Click to read more; I've got a lot going on in this post.)