Human Hypercube

Speaking of hypercubes, here's representation with people. We can build up to a hypercube by starting with a 0-dimensional point. 'Stretching' that in one direction gives us a 1-dimensional line segment. Stretch the line segment in a direction at 90° from the line segment and we get a 2-dimensional square. Stretching that 90° from the plane of the square gives us a 3-dimensional cubes. Now, stretch the cube at 90° from its volume (yes, I know it hurts to try to think like that. It's only impossible in the real-world, not in your mind!) and you'll have a 4-dimensional hypercube.

The pictures above show the changes from 0-d to 4-d.

1. Describe how the number of vertices changes. Write a formula.
2. Describe how the number of line segments changes from one figure to the next. Write a formula.
3. Describe how the number of squares changes. Yep, formula.
4. Describe how the number of cubes changes.
5. Predict the properties of a 5-d hypercube. Can you draw one?


  1. This is great. I like the way this representation of a hyper cube distinguishes the vertices and the edges in a human context. Nice.

  2. This is perfect illustration of sotion hupercube or metapsyhology cube with 16 types of person, or 24 types of person. Actualy this is combination of Tetractys(monad, diad-bifurcated, triad-modality, quadra-space/mater) matrixes, visualised as tetrahedrons, octahedron, cubooctahedron, and tesseract.