# Platonic Solids

Platonic
solids are convex polyhedra with equivalent faces, which are
regular polygons. There are only five of them, and they are all
fairly easy to build.

## Tetrahedron

The tetrahedron
is composed out of 4 triangular faces. It has 4 vertices and 6 edges.
Since its triangular edges are stable without support, 4 spheres and
6 bars are sufficient for its construction.

## Octahedron

The octahedron
is composed out of 8 triangular faces. It has 6 vertices and 12 edges.
Since its triangular edges are stable without support, 6 spheres and
12 bars are sufficient for its construction.

## Icosahedron

The icosahedron
is composed out of 20 triangular faces. It has 12 vertices and 30 edges.
Since its triangular edges are stable without support, 12 spheres and
30 bars are sufficient for its construction.

The second and third icosahedrons here use a bridge-like structure for its edges.
See my page on scaling polyhedra for
details.

## Cube

The cube is
composed out of 6 square faces. It has 8 vertices and 12 edges.
The square faces need support, for which there are two simple options:
Use small bars for the edges and stabilize each face with a long
bar as a diagonal. For this construction, 8 spheres, 12 short bars,
and 6 long bars are needed. The other option is to use long
bars for the edges and to support the faces with 4-star built out
of one sphere and 4 short bars each. This construction requires
12 spheres, 12 long bars, and 24 short bars.

The cube in the second picture uses a bridge-like structure for its
edges. See my page on scaling polyhedra for
details.

## Dodecahedron

The dodecahedron
is composed out of 12 pentagonal faces. It has 20 vertices and
30 edges. The easiest way to build it is to stabilize each face
with a 5-star. Such a construction requires 32 spheres and 90
bars.