Polygons and PolyhedraMore on Polyhedra
Platonic solids are particularly important polyhedra, but there are countless others.
Truncated Tetrahedron
8 faces, 12 vertices, 18 edges
Cuboctahedron
14 faces, 12 vertices, 24 edges
Truncated Cube
14 faces, 24 vertices, 36 edges
Truncated Octahedron
14 faces, 24 vertices, 36 edges
Rhombicuboctahedron
26 faces, 24 vertices, 48 edges
Truncated Cuboctahedron
26 faces, 48 vertices, 72 edges
Snub Cube
38 faces, 24 vertices, 60 edges
Icosidodecahedron
32 faces, 30 vertices, 60 edges
Truncated Dodecahedron
32 faces, 60 vertices, 90 edges
Truncated Icosahedron
32 faces, 60 vertices, 90 edges
Rhombicosidodecahedron
62 faces, 60 vertices, 120 edges
Truncated Icosidodecahedron
62 faces, 120 vertices, 180 edges
Snub Dodecahedron
92 faces, 60 vertices, 150 edges
Applications of Polyhedra
Plato was wrong in believing that all elements consists of Platonic solids. But regular polyhedra have many special properties that make them appear elsewhere in nature – and we can copy these properties in science and engineering.
Radiolaria skeleton
Icosahedral virus
Many viruses, bacteria and other small organisms are shaped like
Buckyball molecule
Montreal Biosphere
Many molecules are shaped like regular polyhedra. The most famous example is
It was discovered in 1985 when scientists researched interstellar dust. They named it “Buckyball” (or Buckminsterfullerene) after the architect
Fluorite octahedron
Pyrite cube
Most crystals have their atoms arranged in a regular grids consisting of
Octagonal space frames
Louvre museum in Paris
Tetrahedra and octahedra are incredibly rigid and stable, which makes them very useful in construction. Space frames are polygonal structures that can support large roofs and heavy bridges.
Football
Polygonal role-playing dice
Platonic solids are also used to create dice. because of their summetry, every side has the
The