Polyhedron
A polyhedron is a three-dimensional solid whose faces are all flat polygons — shapes made of straight lines. Cubes, rectangular prisms, and pyramids are all polyhedra. Spheres and cylinders are NOT polyhedra because their surfaces are curved. The word “polyhedron” comes from Greek, meaning “many faces.” Key properties of a polyhedron include its faces (flat polygon sides), edges (where faces meet), and vertices (corner points). This geometry concept is part of 7th grade math in Saxon Math, Course 2, where students classify 3D shapes and calculate their properties.
Key Concepts
Property If a solid has only flat surfaces that are polygons, the solid is called a polyhedron .
Examples A cube is a polyhedron because all its faces are flat squares. A pyramid is a polyhedron because it's built from a flat base and triangular faces. A sphere is NOT a polyhedron because its surface is curved, not made of flat polygons.
Explanation Think of a polyhedron as a 3D shape built entirely from flat puzzle pieces, like triangles or squares. Unlike a smooth, curvy basketball (a sphere), polyhedrons have sharp corners and straight edges. If you can build it with paper polygons without any bending or curving, you've probably made a polyhedron! Cubes and pyramids are perfect examples.
Common Questions
What is a polyhedron?
A polyhedron is a three-dimensional solid with flat faces that are all polygons. Examples include cubes, rectangular prisms, and pyramids. Curved shapes like spheres and cylinders are not polyhedra.
What are the faces, edges, and vertices of a polyhedron?
Faces are the flat polygon surfaces. Edges are the line segments where two faces meet. Vertices are the corner points where three or more edges meet.
What is the difference between a polyhedron and a regular solid?
A polyhedron is any solid with flat polygon faces. A regular polyhedron (Platonic solid) has faces that are all the same regular polygon. There are only five Platonic solids: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
Is a cylinder a polyhedron?
No. A cylinder has circular faces and a curved surface, which are not polygons. Only solids with entirely flat polygon faces qualify as polyhedra.
What are some examples of polyhedra?
Common polyhedra include cubes (6 square faces), rectangular prisms, triangular prisms, square pyramids, triangular pyramids (tetrahedra), and pentagonal prisms.
When do students learn about polyhedra?
Polyhedra are typically introduced in 7th grade math as part of a geometry unit on three-dimensional shapes.
Which textbook covers polyhedra?
Saxon Math, Course 2 covers polyhedra and their properties.