A. POLYHEDRA

A polyhedron is a 3D shape bounded by polygons. These polygons are called faces.

The edges of a polyhedron are the lines where the faces meet.

Its vertices are the corners where the faces meet.

A regular polyhedron must meet two criteria:

+ Its faces are identical regular polygons.

+ The same number of faces meet at each of the polyhedron´s vertices.

A prism is a polyhedron bounded by two identical polygons, called bases, and several rectangles, called lateral faces. The height of a

prism is the distance between the bases.

A regular prism is a prism whose bases are regular polygons.

A cuboid is a polyhedron with six faces that are perpendicular to one another. Its faces are rectangles or squares (then called cube).

A pyramid is a polyhedron with a polygonal base and triangular lateral sides which meet at a vertex called the apex.

A regular pyramid is a pyramid whose base is a regular polygon and whose lateral sides are isosceles or equilateral triangles.

B. NON-POLYHEDRA (SOLIDS OF REVOLUTION)LID

A non-polyhedron is a solid where any surface is not flat. For example:

Some of the most non-polyhedra are the solids of revolution. A solid of revolution is 3D shape obtained when a plane shape rotates around a

straight line. This line is called the axis of revolution.

Cylinders, cones and spheres are the most known solids of revolution.

A cylinder is the solid of revolution that is generated when a rectangle rotates around of its sides.

A cone is the solid of revolution that is generated when a right-angled triangle rotates around of its cathetii or legs.

A sphere is the solid of revolution that is generated when a circle rotates around one of its diameters.

A cylinder is a geometric shape bounded by two identical circles, called bases, and a curved lateral face. The height of a cylinder is the

distance between its bases.

The lateral face of a cylinder (without its bases) is a rectangle whose dimensions are the height of the cylinder and the length of the base

circumference.

A cone is a geometric shape bounded by a plane circular base and a curved lateral face that ends in an apex.

The curved lateral face of a cone is a circular sector wherein:

+ The radius is the cone generatrix.

+ The sector arc length is the perimeter of the cone´s base.

In cones there is a “special” link between the radius of the base, the height of the cone and its generatrix. Pythagoras is to blame.

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C. VOLUME

VOLUME OF PRISMS AND PYRAMIDS

VOLUME OF SOLIDS OF REVOLUTION