i. A polyhedron is a solid figure contained by plane figures: if it be contained by four plane figures it is called a tetrahedron; by six, a hexahedron; by eight, an octahedron; by twelve, a dodecahedron; and if by twenty, an icosahedron.
ii. If the plane faces of a polyhedron be equal and similar rectilineal figures, it is called a regular polyhedron.
iii. A pyramid is a polyhedron of which all the faces but one meet in a point. This point is called the vertex; and the opposite face, the base.
iv. A prism is a polyhedron having a pair of parallel faces which are equal and similar rectilineal figures, and are called its ends. The others, called its side faces, are parallelograms.
v. A prism whose ends are perpendicular to its sides is called a right prism; any other is called an oblique prism.
vi. The altitude of a pyramid is the length of the perpendicular drawn from its vertex to its base; and the altitude of a prism is the perpendicular distance between its ends.
vii. A parallelopiped is a prism whose bases are parallelograms. A parallelopiped is evidently a hexahedron.
viii. A cube is a rectangular parallelopiped, all whose sides are squares.
ix. A cylinder is a solid figure formed by the revolution of a rectangle about one of its sides, which remains fixed, and which is called its axis. The circles which terminate a cylinder are called its bases or ends.
x. A cone is the solid figure described by the revolution of a right-angled triangle about one of the legs, which remains fixed, and which is called the axis. The other leg describes the base, which is a circle.