Hang a cube from one of its vertices. Now, if you slice
it horizontally through its center, you get a hexagon.
What if you do this with a 4-dimensional cube,
i.e., a tesseract? The slice will yield
a 3-dimensional object--- what does it look like?
Answer: you get a octahedron!
Use lower dimensional analogies to help students
visualize higher dimensional objects.
The Math Behind the Fact:
It is not hard to see (using symmetry arguments)
that the object you get must be regular. By analogy
with the slice of the 3-cube, the slice of the
4-cube must cut every "face". The number of "faces"
of a 4-cube is eight. The only regular 8-sided solid
is an octahedron.
Visualizing high dimensional objects can be taxing,
How to Cite this Page:
Su, Francis E., et al. "Slices of Hanging Cubes."
Math Fun Facts.