The 2-dimensional shapes of a polygon can be applied in a 3-dimensional figure. Such characteristics define polyhedra. Polyhedron is a very general terms and can include some very complex shapes.
Polyhedron (plural, polyhedra): A three-dimensional figure made up with polygon faces
Face: A polygon in a polyhedron.
Lateral Face: A face that is not the base.
Edge: The line segment where two lateral faces intersect.
Lateral Edge: The line segment where two lateral faces intersect.
Vertex (plural, vertices): The point where two edges intersect.
Regular Polyhedron: A polyhedron where all the faces are congruent regular polygons.
A polyhedron has these properties:
Two common types of polyhedra include prisms and pyramids. Prisms and pyramids are named by their bases.
This formula can be used to find the number of vertices (V), faces (F), or edges (E) on a polyhedron:
F + V = E + 2
If a figure does not satisfy Euler’s formula, the figure is not a polyhedron.
A regular polyhedron has the following characteristics:
Named after the Greek philosopher Plato, the five regular polyhedra are:
A polyhedron is semi-regular if all of its faces are regular polygons and satisfies Euler’s formula.