Tesseract (4D cube) sim
Turn a 4D cube through the fourth dimension and watch its 3D shadow turn inside out.
Geometry: the fourth dimension · covers the Enrichment, University intro topic
What the sim shows
A wire cube seen in perspective, looking straight at one face, looks like a square inside a square with the corners joined. A tesseract is the same idea one dimension up: 16 corners at ±1 on four axes x, y, z and w, joined by 32 edges, bounded by 8 cubes. We can't see four dimensions, so this shows its 3D shadow, seen from w = 3: corners with larger w are nearer the viewer and look bigger. Turning in the XW plane mixes x with the unseen w direction. Nothing in the tesseract bends or stretches (every 4D edge stays 2 long), yet in the shadow the coloured cube grows from 3/4 size, turns inside out (the inner and outer cubes swap places) and becomes the outer cube at 180° (3/2 size), then shrinks back. Its corners move to different w, so mid-turn it looks lopsided.
- Marked corner (1, 1, 1, −1): the readout follows its w, the fourth coordinate
- Coloured: one of the eight cubes that make up a tesseract
- Shadow edges: the 32 edges of the tesseract
Use it in your lessons
- Try it here: anyone can unlock 2 figures free, and a free account unlocks up to 5. Runs on a laptop, a Chromebook or a phone; nothing to install.
- Present it and share student links with the teacher plan, from US$5 a month, billed yearly.
- Put it on your own website or LMS for US$9, paid once, or every sim from US$29 a month.
Free guide: 12 practicals as sims, and how to run one in a lesson →
Need a version for your exact set-up? Have one made: US$49 a figure in an order of 5.