Shape

176 II Seeing How It Works
And notice, too, basic elements and boundary elements touch, as here
for a plane, a line (edge), and an endpoint.
Embedding can be used to define many more things. For example, when do basic
elements intersect, and when do they abut? There are properties like collinearity,
coplanarity, etc. And there’s inside and outside, and convexity. Defining things in
this way to see how far you can go is a lot of fun, but it’s high time for shapes.
Counting Points and Seeing Parts
Shapes are formed when basic elements of a given kind are combined, and their properties
follow once the embedding relation is extended to define their parts.
There are noticeable differences between shapes containing points and shapes
made up of lines, planes, or solids. First, shapes containing points can be made in
just one way if the order in which points are located doesn’t matter, and in finitely
many ways even if it does. Distinct shapes are always defined if different points are
combined. In contrast, there are indefinitely many ways to make shapes of other
kinds. Certainly, distinct shapes contain different basic elements, but different combinations
of lines, planes, or solids needn’t define distinct shapes when these elements
fuse.
The shape
can be made with eight lines