TETRAHEDRON



See the tetrahedron rotating around the x, y, z axis.
Properties of the Tetrahedron
  • Faces: 4 triangles
  • Vertices: 4, each with 3 edges meeting
  • Edges: 6
  • Dihedral angle: 70°32'
    • The Symmetry
    Surface Area

    If we know the distance (r) from the center of the tetrahedron to one of its vertices, the lengths (a) of the edges is given by a = (2√6) / 3,
    then the area of one triangle is (a × h) / 2, where h = √[a² - (a/2)²].
    And the area of the tetrahedron is 4 × the area of one triangle.
    Volume
    The volume of a tetrahedron in terms of its edge length: V = a³(√2 / 12)
    In a more general case, i.e. any tetra hedron with vertices a, b, c, d.

    To calculate the volume, first we treat all edges like vectors. Then,