Cubist Planes

An invitation to myself to create an explorable model around this projection.

Puzzling over the geometry of the 2d projection of a Rubik's cube is already expanding my mind. I'm building my own model in SVG and javascript. notebook github

Reflecting on the current state of the model I've created, I'm using SVG transformations to position all the circles. What's happening here may not be self evident. This following svg <circle> does not specify the cx and cy attributes. That means it is drawn at the origin: 0, 0. It does specify the radius, stroke and fill. My love of turtle geometry is hiding in the transform attribute: a rotate() and translate() is a turtle's turn and move. In effect, it moves the coordinate system before drawing the circle.

The model I have positions the faces of cubelets at the intersections of circles in a satisfying way. But it does not lend itself to the rotations I want to be able to animate.

The puzzle has me reviewing some trigonometry. Notably the Law of Cosines. wikipedia

Implementing turtle geometry is already a fun study of the Law of Sines. wikipedia

As I contemplate the intersections of circles I'm struck by a new-to-me understanding of the radical axis of non-concentric circles. wikipedia

It might be interesting to explore common abstractions between a Rubik's cube and Triple Cross. See Solution to Triple Cross.