Cayley plane

Imagine you drew a picture of a pair of sunglasses on a piece of paper. The sunglasses have two lenses, one for each eye, and a wire frame that connects them together. Now imagine that you take the entire paper, including the sunglasses drawing, and fold it in half so that the lenses and frame line up perfectly with each other.

When you do this, you create what's called a "reflection" of the original sunglasses drawing. The reflected image looks just like the original drawing, but everything is flipped horizontally. If you were wearing these sunglasses in real life and looked at your reflection in a mirror, this is what you would see!

Now let's take this concept a bit further. Imagine that you have a 3D object, like a cube. You can also create a "reflection" of this object, but instead of flipping it horizontally, you'll flip it through a different dimension. For example, you could reflect the cube through a plane (or flat surface) like a mirror. When you do this, you'll end up with a new, "reflected" cube that looks like a mirror image of the original cube.

Finally, let's talk about the Cayley plane. This is a type of plane that's a bit more complicated than just a flat mirror. It's named after a mathematician named Arthur Cayley, who studied these kinds of reflections in higher dimensions.

Instead of just flipping an object through one plane, the Cayley plane reflects an object through multiple planes at once. This creates a new, "reflected" object that has a completely different shape and geometry than the original object.

Overall, the Cayley plane is a mathematical concept that helps us understand how shapes and objects can be transformed through complex reflections in higher dimensions.