Solid Geometry
is the geometry of three-dimensional space, the kind of space we live in ...Three Dimensions
It is called three-dimensional, or 3D because there are three dimensions: width, depth and height.
Properties
Solids have properties (special things about them), such as:- volume (think of how much water it could hold)
- surface area (think of the area you would have to paint)
- how many vertices (corner points), faces and edges they have
Polyhedra and Non-Polyhedra
There are two main types of solids, "Polyhedra", and "Non-Polyhedra":
Counting Faces, Vertices and Edges
When we count the number of faces (the flat surfaces), vertices (corner points), and edges of a polyhedron we discover an interesting thing:
The number of faces plus the number
of vertices
minus the number of edges equals 2
This can be written neatly as a little equation:minus the number of edges equals 2
F + V − E = 2
It is known as Euler's Formula (or the "Polyhedral Formula") and is very useful to make sure we have counted correctly!
Let's review parallel and perpendicular lines.
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