Understanding Polyhedra: Definitions, Types, and Properties

Polyhedron

A solid bounded by at least four polygonal faces.

Face

A polygonal surface of a solid figure.

Vertex of a Polyhedron

The point at which three or more edges meet.

Edge

A line segment where two faces of a polyhedron meet.

Diagonal of a Polyhedron

A line segment joining two vertices that are not on the same face.

Prisms

Polyhedra bounded by two parallel polygonal faces and several parallelogram faces. The side edges are all parallel and equally long.

The Height of the Prism

Perpendicular distance between the two parallel faces.

Right Prisms

A prism is a right prism if the sides are rectangles (or squares). In right prisms, the side edges are perpendicular to the bases. If the sides are not rectangles (rhomboids, for example), it is an oblique prism.

Regular Prisms

Right prisms with regular polygons as bases.

Parallelepipeds, or Cuboids

Prisms with all rectangle (or square) faces.

Pyramids

Polyhedra bounded by a number of triangles that meet at a common vertex, the apex, and a polygonal base.

The Height of a Pyramid

The segment perpendicular from the apex to the base edge. So it is the height of the lateral faces.

A Pyramid is Regular

If its base is a regular polygon and the vertex projects vertically just in the middle point of the base.

Truncated Pyramid

If a pyramid is cut by a plane that is parallel to the plane containing the end of the pyramid, it determines a shape called a truncated pyramid.

Regular Polyhedra

Polyhedra with all congruent faces.

Tetrahedron

A regular polyhedron with four faces that are equilateral triangles.

Cube

A regular polyhedron with six faces that are squares.

Octahedron

A regular polyhedron with eight faces that are equilateral triangles.

Dodecahedron

Twelve faces pentagons.

Circular Shapes

A three-dimensional shape generated when a flat shape revolves around one of its sides.