**Hyperspace:**Home Intro Time Width **Walls** Bridges Rounds

Walls divide. Specifically, walls divide solid space. The names under here are more about roles rather than fabric. Whatever the dimensionality of the wall, the role is constant: it divides space. Bridges deal with the dimensionality of the fabric: a bridge carries a line, which is a one-dimensional fabric.

While the notion of solid space is used, one refers to higher and lower dimensions accordingly.

For our purposes, we make a solid any figure that contains every point of some n-sphere as part of its body. A hexagon is solid in 2D, because it can contain a circle, while it is not solid in 3D, because it does not contain all of a sphere. None the same, the circle is solid in the plane, because it contains all of a disk.

**Cells** are to be thought of as a fragment of foam, being solid in the
space they fill. Cells (like rooms) are divided by each other by **Walls**.
Walls meet at **Sills**. Note that it is legitimate to talk of cells in
different dimensions to all-space. In three dimensions, one might speak of
hexagons in a tiling as cells, bounded by linear walls.

In the polygloss, a plane is a dividing space. If one wants a non-dividing space,
one mught use something like a planifold (flat manifold). A *plata* or
*plate* is something cut from a plane, a polytope solid in the plane.

A **face** is a fragment of the plane where we can draw our smiley. That
is, a face is a kind of plata where we stick eyes, mouth, nose, and any other
orifices we might want our poly-being to want. The facing side is the side
one can see.

The facing side of a spherical thing (like a planet) is a *disk* or
sphere solid in the plane.

In the first instance, plane (like plain) is something that keeps our
way out of gravity. That is, it limits the region of fall. In practice,
it is usually safe to imagine the surface of the planet as a sphere or
glomoplane.
**Plat** is a form of *flat* but has the meaning of being solid in a dividing
space.

The surface of a 3d sphere is a glomohedrix. This is a glome-shaped 2-dimensional cloth. A solid sphere is a glomohedron.

A **Sphere** is taken to be then a solid space, not further than the
radius from its centre.
A **Disk** is properly the solid space of an N-1 dimensional sphere.

A margin divides the surface of a solid into plata or faces.

Margins are made out of marginix, or *cutting cloth*. Anything made
out of marginix, will, by a sweep through time and space, divide two things,
and marginix is the only cloth that can be *woven*.

One *demarks* a thing, not *delineates* it. Demarking is the drawing
of margins to divide the surface into plata.

The extent of a given dimension is given in its root stem + age, eg 2-space =

Content can be measured in prismic, tegmic, and spheric units, as well as a few others. If one specifically wants to define eg

Hyperspace is taken to be space over all-space: ie over-solid space. The all-space lives in a hyper-plane, ie a dividing surface in hyperspace.

The significance of Abbot's story is that 3d is hyperspace to 2d, and that we can understand hyperspace by looking at the projections and outcomes in our own space.

Tilings are to be read as the separated surface of a hyper-space polytope. For example, a 2d tiling of squares {4,4} can also be taken to be the surface of a very large polyhedron, {4,4}, with interior as half of all-space.

The surface of polyhedron becomes the surcell of the aperihedron or tiling.

For tilings, it is customary to give the surcell or "surface" dimension, rather than the content or solid dimension of the underlying hyperspace polytope.

**Hyperspace:**Home Intro Time Width **Walls** Bridges Rounds

© 2003-2009 Wendy Krieger