DODECAHEDRON



See the dodecahedron rotating around the x, y, z axis.
Properties of the Dodecahedron
  • Faces: 12 pentagons
  • Vertices: 20, each with 3 edges meeting
  • Edges: 30
  • Dihedral angle: 116°34'
    • The Symmetry
    Surface Area

    12 pentagons make up this dodecahedron. Click here to see how to calculate the area of a pentagon.
    Volume
    The dodecahedron is made up of 12 pyramids with pentagon as the base.

    The volume of one pyramid = (base area × height) /3 = 12 × the volume of pyramid.
    To calculate the height of the pyramid, use the Pythagoras theorem,
    height = √(R² - r²), where R is the radius of the dodecahedron and r is the radius of each pentagon.
    V = 15 + [(7√5) / 4]a³