Example 1
Is the figurea polyhedron?Yes. A figureis a polyhedronif it has all of the propertiesof a polyhedron.This figure:- Is 3-dimensional.
- Is constructedentirelyof flat polygons(trianglesand rectangles).
- Has facesthat meetin edgesand edgesthat meetin vertices.
- Has no gapsbetweenedges.
- Has no non-polygonfaces(e.g.,curves).
- Has no concavefaces.
Sincethe figurehas all of the propertiesof a polyhedron,it is a polyhedron.
Example 2
Is the figurea polyhedron?No. This figurehas faces,edges,and vertices,but all of its surfacesarenotflat polygons.Lookat the end
surfacemarkedA. It is flat, but it has a curvededgeso it is not a polygon.SurfaceB is not flat (planar).
Example 3
Is the figurea polyhedron?