Exploring 4D Sphere and Hyperdonuts

2D Cut of 3D Sphere

What it means to make an ultra-thin slice into a lower dimension. We then slide the sphere up and down into 3D, where the circle traces out the surface of the sphere. At the circle, the rest of the sphere sticks up/down in a 90 degree direction from the 2D universe.

3D Cut of 4D Sphere

Already collapsing the 4D sphere ( glome ) into an ultra-thin 3D slice. Then, we move the glome into the 4D up/down direction. This motion makes the 3D sphere evolve like a 2D circle-cut of a sphere. The rest of it sticks into the 4D up/down at 90 degrees from our 3D universe.

3D Cut of 4D Torisphere #1

A 4D hyperdonut that is a "small circle stretched over big sphere". We see the 'big sphere' part get cut in half, and evolve like a circle-cut of a sphere. This makes a torus in place of the 2D circle-cut .

2D Cut of 3D Donut #1

Just like the sphere-cut, here is a 2D slice of a torus. There are two unique ways to slice it into 2D. One can call a torus a " small circle stretched along big circle ". This is cutting through its big circle, making two little circles side by side.

3D Cut of 4D Spheritorus #1

A 4D hyperdonut made by a " small sphere stretched along big circle". Here is cutting through its 'big circle' part, making two 3D spheres in a row. Moving the shape into the 4D up/down makes the spheres evolve just like a 2D cut of a torus.

3D Cut of 4D Ditorus #1

A 4D hyperdonut made by a " little torus stretched along big circle". There are three ways to break it down. It's also a small circle along medium along big. Or, a small circle along big torus. Cutting through its 'biggest circle' part makes two tori in a row evolve like a 2D cut of a torus.

3D Cut of 4D Tiger

A 4D hyperdonut made by a " small circle stretched along big duocylinder edge". A duocylinder is a 4D coffee can cylinder-like shape, but with two curved rolling sides and no flat sides at all. Both rolling sides meet up at a single sharp 90 degree edge, that snakes around the shape. The edge is two 'big circles' multiplied together. Here is cutting through one of the big circles, making two tori evolve like a 2D torus cut.

2D Cut of 3D Donut #2

The other way to cut a torus. This is slicing through its small circle, leaving behind two big circles, as a concentric pair.

3D Cut of 4D Torisphere #2

Here is cutting through the small circle part of the " circle stretched over big sphere" hyperdonut. This cut leaves behind two big spheres, as a concentric pair.

3D Cut of 4D Spheritorus #2

Cutting through the small sphere part of the " small sphere stretched over big circle" hyperdonut. This cut leaves behind a torus, with ITS small circle evolving like the 2D cut of a sphere.

3D Cut of 4D Ditorus #2

Cutting through the medium circle part of the " small circle stretched over medium stretched over big " hyperdonut. This leaves behind the small and big circle parts, making two concentric tori, in the major (big) diameter.

3D Cut of 4D Ditorus #3

Cutting through the small circle part of the " small circle stretched over medium stretched over big " hyperdonut. This leaves behind the medium and big circle parts, making two concentric tori, in the minor (smallest) diameter.