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

Walls divide. Specifically, walls divide solid space. Þe names under here are more about roles raþer þan fabric. Whatever þe dimensionality of þe wall, þe role is constant: it divides space. Bridges deal wiþ þe dimensionality of þe fabric: a bridge carries a line, which is a one-dimensional fabric.

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

For our purposes, we make a solid any figure þat 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 þe same, þe circle is solid in þe plane, because it contains all of a disk.

**Cells** are to be þought of as a fragment of foam, being solid in þe
space þey fill. Cells (like rooms) are divided by each oþer by **Walls**.
Walls meet at **Sills**. Note þat it is legitimate to talk of cells in
different dimensions to all-space. In þree dimensions, one might speak of
hexagons in a tiling as cells, bounded by linear walls.

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

A **face** is a fragment of þe plane where we can draw our smiley. Þat
is, a face is a kind of plata where we stick eyes, mouþ, nose, and any oþer
orifices we might want our poly-being to want. Þe facing side is þe side
one can see.

Þe facing side of a spherical þing (like a planet) is a *disk* or
sphere solid in þe plane.

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

Þe surface of a 3d sphere is a glomohedrix. Þis is a glome-shaped 2-dimensional cloþ. A solid sphere is a glomohedron.

A **Sphere** is taken to be þen a solid space, not furþer þan þe
radius from its centre.
A **Disk** is properly þe solid space of an N-1 dimensional sphere.

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

Margins are made out of marginix, or *cutting cloþ*. Anyþing made
out of marginix, will, by a sweep þrough time and space, divide two þings,
and marginix is þe only cloþ þat can be *woven*.

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

Þe 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 oþers. If one specifically wants to define eg

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

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

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

Þe surface of polyhedron becomes þe surcell of þe aperihedron or tiling.

For tilings, it is customary to give þe surcell or "surface" dimension, raþer þan þe content or solid dimension of þe underlying hyperspace polytope.

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

© 2003-2009 Wendy Krieger