Encyclopedia > Dodecahedron

  Article Content

Dodecahedron

A dodecahedron is a Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. Its dual is the icosahedron. Canonical coordinates for the vertices of a dodecahedron centered at the origin are (0,±1/τ,±τ), (±1/τ,±τ,0), (±τ,0,±1/τ), (±1,±1,±1), where τ = (1+√5)/2 is the golden mean. Five cubes can be made from these, with their edges as diagonals of the dodecahedron's faces, and together these comprise the regular polyhedral compound of five cubes. The stellations of the dodecahedron make up three of the four Kepler-Poinsot solids[?].

The term dodecahedron is also used for other polyhedra with twelve faces, most notably the rhombic dodecahedron[?] which is dual to the cuboctahedron and occurs in nature as a crystal form. The normal dodecahedron is sometimes called the pentagonal dodecahedron to distinguish it.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
List of battles 1400 BC-600 AD

... at sea. 371 BC July Battle of Leuctra Spartans under king Cleombrotus[?] lose to the Thebans under Epaminondas - Cleombrotus is killed. This ends the period of ...