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Quaternion Cube

Interesting design!

By the way, the Catch-24 encoding was based on the quaternion multiplication table, where the units x(i), y(j), z(k) denote a 180° rotation along 3 axes, and the square root of the unit corresponds to a 90° rotation.Q8.jpg
Multiplication of quaternions means concatenation of rotations.
 
if i, j, and k squared equal -1, it should be the same. but if you multiply 2 different quaternions(not including 1) you get another quaternion?
im very confused
This looks really coll tho. reinds me of a redi cube
Not true. If you square different numbers, you can get the same result (for example, both -2 and 2 squared equales to 4). But I agree that quaternions are really difficult to understand, since they are 4 dimensional things. To add even more to the confusion, multiplication is not even commutative anymore: i*j = k, but j*i = -k.

The YouTube channel 3b1b has an excellent video on the visualisation of quaternions, but even with that (and some background from abstract algebra and hypergeometry) it's not easy to wrap your head around.
 
Not true. If you square different numbers, you can get the same result (for example, both -2 and 2 squared equales to 4).
The square of a unit quaternion is a 180 degree rotation along its axis (i.e. not quite the same as the square of a number).
Multiplication of quaternions means concatenation of rotations. For example, we multiply the quaternion of the initial position of the cube by the quaternion of the product of rotation quaternions F B:
Two move.jpg
 
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