#torusposting

So just in case you though my game nDimensional Time Travel Chess couldnt get any worse, I fixed the bug that was breaking hypertoroids. This specific hypertoroid is a radial extrusion of a regular torus along 4 dimensional space. We start with an offset circle like so

And we start extruding radially. What that means is we just push out the face a little bit rotating around the center each time. Now in real life these would be infinitely small, we we're working with computers and human time so we just choose small enough steps

Here's what we see a quarter of the way through

Here you can start to see the donut

And here's the finished product.

For step 1 at least. Now we move onto step two. We move the donut back into place of the original circle and repeat the process

Now for the next step things are a little confusing for our 3D human brains no matter what we do, but especially so if we connect the rings like we did last time. So unfortunately we just have to imagine that these are still connected through 4D space, but we'll only show slices where we have enough room to think about them as their own 3D slices

Just like we would be able to imagine traveling along the donut surface between its little rings (red arrow), a 4D creature would be able to easily imagine being able to travel along the donut's themselves (blue arrow) and those two directions are 90 degrees from one another, making them orthogonal and adding an extra-dimension to the surface

Here's how I typically label and refer to these axes

And finally, here's the finished product of step 2

Now if we repeat the process again

Haha just kidding lol. This is already a crazy enough chess board for me personally. Unless... c: But yeah, definitely one of the crazier boards I've made. Haven't played it yet, but if my torus board was any indicator, this one is possibly just, straight up unplayable ngl. Still, might be fun to try anyway