Spheration (InstanceTopic, 3)

From Hi.gher. Space

Spheration is a kind of modeller's finish, like a paint. It is not intended to add new topology to the shape, but to give a thin thing substance.

This particular finish converts thin things into solid objects. One can see an example of spheration at the Atomium, a left-over from the Brussels Expo. This shows the vertices and edges of a cube, which are all connected to a central cell. To make these real, there are spheres at the vertices, and thinner lines connecting the spheres.

The popular Zometool is an example of a tool for making solid examples of vertices and lines, which in turn indicate the shape to build.

The mathematical specification is that all points at some distance r from a thin thing (like a line), is part of the solid representation of that thing. One might use different values of r for different dimensions, usually in descending order (a point's r is bigger than a line's r).

A torus is a spherated circle. This is the result of points a sphere might cut if it travels around the circle.

A tiger is a spherated bi-glomolatric prism. A 'glomolatrix' is a round line-fabric as itself, that is, a circle's circumference. The bi- means that you use two of them. The prism is a product, which creates a cartesian intersection (points in A plus points in B are in the product points in AB). This is still a thin 2d surface in 4D. To give it substance, we need to flesh it out or puff it up, by including points at some distance r from it.

The section of a spherated object, when taken at right angles to the object, gives a spheric (eg circular, spheric, glomic), cross-section.