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I recently saw an advertisement for a fun gadget: a 20-sided die levitating (via active magnetic control) over a pad (with an array of electromagnets, I assume). In the video demonstrating the gadget, the die floated stationary in space, but rotating slowly about an axis that - I assume/guess - passed through the center of the magnet embedded in it.

Does this "free axis" of rotation always exist in such a system? Is it possible to totally constrain (via the active magnetic control from the pad, and/or an alternate design of magnet or magnets inside the die) the translation and rotation of the die?

The above is the primary question I hope to have answered here. If somebody wants to go beyond, I've got some additional stuff I'm curious about below that might make this question more interesting/useful.

If this is possible, is it possible in a configuration that the die (outside of an external magnetic field) would still be fair - that is, not biased to fall on any specific side? In my head, I'm imagining a die floating above a pad, and then arbitrarily controlled (via manipulation of the field generated by the pad above which it levitates) to spin or "bounce" around. Perhaps on a larger scale and alternate layout, this could be used as a controllable omnidirectional wheel?

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  • $\begingroup$ Great post! However make sure to limit each post to asking only one question. $\endgroup$ Commented Nov 27, 2025 at 23:18
  • $\begingroup$ Ah, good point. The final paragraph should probably be split out into a separate question. For anybody answering, please feel free to disregard that. I’m on my phone but will edit if I get a chance. $\endgroup$ Commented Nov 28, 2025 at 0:39

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If you have just one magnet and one pad then you cannot constrain the object completely. With two magnets and two pads it would be possible.

The pad is an electromagnet that generates an inhomogeneous field - the field gets weaker as you move further away from the pad. This field then acts on a magnet inside the levitating object. The magnet acts as a magnetic dipole (compass needle). It aligns itself with the field (the needle points along the field). The magnet will oppose any rotation that would cause its moment to deviate from the local field direction. But it can rotate freely around an axis that coincides with its magnetic moment. The magnet is also attracted to the region where the field is stronger (towards the pad) - this is what keeps the object in the air - the magnetic attraction balances out the gravity. (But it is unstable - the field needs to be actively controlled to keep the object stationary. If the field were static the magnet would either fall or snap to the pad.)

If the object were to contain two magnets, placed sufficiently far from each other so that each magnet would mainly interact only with its "own" pad you could constrain the rotation completely. All you have to do is make sure that the two magnetic dipoles do not point along the same line.

In principle you could imagine adding magnets and pads with the goal to keep the object suspended while also rotating it freely. It would be relatively straightforward to control the rotation around the vertical axis. But achieving smooth rotation around an arbitrary axis would likely be a challenge.

Possible solution might be using a sphere of a soft magnetic material instead of discrete permanent magnets. Soft magnetic material has no net magnetization (density of magnetic moment) if there is no field. But it gets easily magnetized - in an external field it will have magnetization that points along the local field. In an ideal case such a sphere would not be constrained to rotation around the field direction - it could rotate freely (the magnetic moment would not be 'locked' with respect to the spare material, it would keep pointing along the field even as the sphere rotates). In practice the sphere would still somewhat prefer to rotate around the field direction and would show a bit of "friction" if rotated around a different axis (this would be related to the hysteresis losses as the material magnetization changes). In principle you could tune this friction such that you can use it to spin the sphere around an arbitrary axis (using rotating magnetic field from some auxiliary pads) while keeping it suspended (using the 'main' pad above the sphere). Once you have that you put the sphere inside a die and you are done.

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  • $\begingroup$ I was able to follow this, thank you! As a follow up, this appears to be assuming the levitation magnet is hanging below an actively-controlled pad, and that each pad has only 1 electromagnet. Is my understanding of your assumptions correct? That's not quite the scenario I had in mind, but I think the principles still apply in a meaningful way. When you described multiple magnets "sufficiently far from each other" what kind of distances are we talking? I guess in my head, once multiple magnets were close together the composite magnetic moment became the new free axis. $\endgroup$ Commented Nov 28, 2025 at 14:21
  • $\begingroup$ @Helpful Yes, the pad that holds the object should be above it (it attracts the magnet). Sufficiently far means that you can pair up the magnets and pad: each magnet is mainly affected by its pad and all other pads have much weaker influence. If the magnet pad distance is designed to be say 1 cm than the other magnets should be several cm away so the pad field is much weaker at their positions. $\endgroup$ Commented Nov 30, 2025 at 9:35

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