3D
SOLIDS
We live in a three-dimensional world. Points become lines, lines become planes, and planes fold up to enclose space. This is the study of Volume and Capacity.
The Extrusion Principle
Most 3D shapes (Prisms and Cylinders) are simply 2D shapes stretched out into the third dimension. Volume is just the area of the base times the height of the stretch.
Extrusion
Polyhedra
Solids with flat faces that are polygons. Includes prisms, pyramids, and the Platonic solids.
Non-Polyhedra
Solids with curved surfaces. Includes cylinders, cones, and spheres.
Structural Anatomy
Face
2D SurfaceA flat surface that forms part of the boundary of a solid object.
Edge
1D LineA line segment where two faces meet.
Vertex
0D PointA point where three or more edges meet. (Plural: Vertices)
Euler's Formula
F + V - E = 2For any convex polyhedron, the number of faces plus the number of vertices minus the number of edges always equals 2.
Euler's Formula Check
For a Cube: 6 Faces + 8 Vertices - 12 Edges = 2