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How to draw a 4D hypercube

apr 2021 –– 1 min read

A hypercube is a higher dimensional cube. In four-dimensions, it's also known as a tesseract.[wiki]

This page show you a simple way to think & draw in four dimensions, to expand your mind & impress your 3-dimensional peers!

A zero-dimensional point A one-dimensional line A two-dimensional square A three-dimensional square A four-dimensional hypercube

A hypercube is a cube pushed through a new dimension.

It's a cube at every point along the new direction. Try to imagine that –– extruding a cube out in some direction.

You could imagine doing that upwards, inwards, outwards, left, right, or any direction we can imagine. That's the best we can do in 2 or 3 dimensions. But, a true hypercube is extending into a new (perpendicular) dimension we can't quite see.

Instructions

Step 1: Draw a square Step 2: Draw another square, nearby and offset the first square. Step 3: Connect the two cubes with lines at each of their corners, 8 in total. Viola! You have a hypercube.

You can experiment with drawing your second cube at other sizes & positions to make for interesting perspectives on the hypercube.

Another perspective on a hypercube: the second cube is smaller and inside the first. Another hypercube: the second cube is further to the right and appears more like a long box.

Try with other shapes as well: pyramids, 5-D hypercubes, etc.!

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