Solid Geometry
Pyramids

Right pyramidal frustum
Regular Polyhedrons

Pyramid
A solid whose base is a polygon and whose lateral faces are triangles with a common vertex (apex) is called a pyramid.
A right pyramid is a pyramid in which the line joining the centroid of the base (the point of coincidence of the medians) and the apex is perpendicular to the base.
A regular pyramid is a right pyramid whose base is a regular polygon and lateral faces are congruent isosceles triangles.
The volume of a pyramid is one third of the product of the area of the base and the perpendicular distance from the vertex to the base.
 The surface area of a pyramid: S = B + Slat The volume of a pyramid: V = 1/3 · B · h,
where B is the base area,  Slat  is the lateral surface area and h is the height of the pyramid.
Regular square pyramid
A regular square pyramid has square base and lateral faces are four congruent isosceles triangles making the same angle with the base.
 - surface - volume
Regular triangular pyramid
A regular triangular pyramid has an equilateral triangle base, and three congruent isosceles triangles as lateral faces making the same angle with the base.
 R -the radius of the circumcircle,  r -the radius of the incircle - surface - volume
Regular hexagonal pyramid
A regular hexagonal pyramid has a regular hexagon base, and six congruent isosceles triangles as lateral faces making the same angle with the base.
 - surface - volume
Right pyramidal frustum
 B : B1 = (h + x)2 : x2 - surface P, P1 - bottom and top base perimeter - volume
Regular Polyhedrons
Tetrahedron
Octahedron
Tetrahedron

Octahedron

The equilateral triangles are faces of, the tetrahedron (4-faced), the octahedron (8) and the icosahedron (20), while the dodecahedron consists of 12 regular pentagons.
Geometry and use of trigonometry contents - B