Polyhedron A polyhedron is a three dimensional region of space bounded by polygons.
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Faces The faces of a polyhedron are each of the two dimensional polygons that border the polyhedron.
Edges The edges of a polyhedron are the sides of the faces of the polyhedron. Two faces have an edge in common.
Vertices The vertices of a polyhedron are the vertices of each of the faces of the polyhedron. Three faces coincide with the same vertex.
Dihedral Angles The dihedral angles are formed between two faces of all neighboring polygons.
Polyhedral Angles Polyhedral angles are formed by three or more faces of the polyhedron and have a common vertex.
Diagonals The diagonals of a polyhedron are the line segments joining two vertices not belonging to the same face.
Euler's formula It is verified that in all convex polyhedra: No. of faces + No. of vertices = No. of de edges + 2.
Types of Polyhedra by the Number of Faces Tetrahedron: Polyhedron of 4 faces. Pentahedron: Polyhedron of 5 faces. Hexahedron: Polyhedron of 6 faces. Heptahedron: Polyhedron of 7 faces. Octahedron: Polyhedron of 8 faces. Nonahedron: Polyhedron of 9 faces. Decahedron: Polyhedron of 10 faces. Undecahedron: Polyhedron of 11 faces. Dodecahedron: Polyhedron of 12 faces. Icosahedron: Polyhedron of 20 faces.
Prisms Prisms are polyhedra that have two parallel, equally sized faces called bases and their lateral faces are parallelograms.
The height of a prism is the distance between the bases. The lateral edges of a prism are equally sized parallel edges. Unfold of a Prism
Pyramid A pyramid is a polyhedron, whose base can be any polygon and whose lateral faces are triangles with a common vertex (apex of the pyramid).
The height of the pyramid is the measure of the perpendicular line segment from the apex to the base. The apothem of a regular pyramid is the height of one of its lateral faces. Unfold of a Pyramid
Cylinder A cylinder is a solid of revolution generated by a rectangle that rotates around one of its sides.
The axis is the fixed side about which the rectangle turns. The bases are the two circles that generate the sides perpendicular to the axis. The height is the distance between the two bases. Unfold of a Cylinder
Cone The cone is a solid of revolution generated by a right triangle that rotates around one of its legs.
The axis is the fixed leg about which the triangle turns. The base is the circle that forms the other leg. The height is the distance from the apex to the base. The slant height is the distance from any point on the circumference to the apex of the cone. By the Pythagorean theorem the slant height of the cone is equal to:
Unfold of a Cone
Spherical Surface A spherical surface is the surface generated by rotating a circle about its diameter.
Sphere A sphere is the region of the space that is inside a spherical surface.
The center is the interior point that is equidistant to all points on the surface of the sphere. The distance from the center to any point on the surface of the sphere. The diameter is the distance from one point through the center to another point.