Cube

Equation

$x^6 + y^6 + z^6 - 1$

Properties:

• degree 6
• smooth
• bounded
• not really a cube
• basically a sphere

Some story

The `cube' is not really a cube. It has no corners, but instead is smooth. Taking the power of the variables to infinity produces a cube, and is related to the various metrics for distance.

Random projection is all good, and no need for a custom bounding sphere. Just let 'er rip.

Funnily enough, if you decompose a sphere you get a regular polyhedron, but you don't with this.

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