Hyperspace:Home Intro Time Width Walls Bridges Rounds
Bridges unite. Specifically, in any given dimension, a bridge carries a line. Correspondingly, we group here terms that do not change their dimensionality. The section on walls deals with role-names.
Because what we're naming does not change as dimension changes, it is essentially the same fabric to everyone. Just as a bridge carries a line, we have names for fabrics (manifolds) of every kind.
The nature of space is envisaged to be fabric of various dimensions. One then works this fabric into various shapes, accordingly to different results. The technical term for this fabric is a manifold
The fabric does not have to lie straight. We can render it into spheres or whatever. This gives us names for all of the assorted polytopes etc.
Hedrix is the name for two-dimensional cloth. By itself, it can be taken to mean planohedrix, but this usage is best avoided unless one is heavily involved in flat surfaces.
Note that we can make cloth into any shape, but it retains its essential dimensionality. The manifold of the cloth can give rise to things like sleeves, tunnels, and bridges, without ever loosing its essential hedrix nature at any point.
We cut from hedrix, 'solid' shapes which we sew together to make other things. A mounted polytope is thus something like a patch. Mounting is in the sense of what one does to a picture or a trophy on the wall.
The rules of mounting require that the polytopes share one or more full polytopes. That is, if the interior of something is common to both surfaces, then all of the interior and all of the shared polytope surface is common to the mounted polytope.
One might mount polygons by making them share an edge, or a vertex. But if an edge is shared, then every vertex on the edge is also shared.
One then makes from mounted polygons, many different things.
The names of the cloth and derived patches are as follows.
A polytope in 8D is thought of as being covered in 7D patches, and hence is a polyzetton. A polytope in 3D is thought of being covered in 2D patches, and hence a polyhedron.
A hedrid thing is something that is solid in 2d, and thin elsewhere. For example, a hexagon is hedrid. The term covers any general shape, and is not related to polytopes etc.
A hedrous thing is some sort of lumpy hedrid thing, that may be tossed and turned into shape. One might describe a rolled out peice of modeling-clay, complete with lumps etc, as a hedrous mass. This term allows us to describe general outlines of shapes in higher dimensions. A ridge in 3d is essentially latrous (line-shaped), although it may have some width, etc. It would not be describe as hedrid.
The residents of a general dimension are described as bours (be-ers).
In the Abbot-quote, the Sphere is a chorobour (resident in a chorix or 3-space) while the square is a hedrobour (2d resident).
Hyperspace:Home Intro Time Width Walls Bridges Rounds