The Platonic solids are the only 5 regular convex polyhedra (3D shapes). All faces in
a particular Platonic solid are of the same type of regular polyhedron, and are assembled
in the same way around each edge and each vertex.
The five types of Platonic solids are:
Tetrahedron - 4 triangular faces
Regular Hexahedron (cube) - 6 square faces
Octahedron - 8 triangular faces
Dodecahedron - 12 pentagonal faces
Icosahedron - 20 triangular faces
Statues of the 5 Platonic solids in Bagno, Germany:
Whether or not you have read my book, here are some other resources, tips, and
websites that you may find useful for learning more about Platonic solids.
Disclosure: In some cases, our company may receive a commission payment if you
purchase a product or service after following one of these links.
Anyway, here are the links:
Polydron® Frameworks® Platonic Solids
This is a kit for constructing 3D "frame work" models of Platonic solids. It is an excellent way to get a better and more intuitive understanding of these polyhedra, their faces, edges, and vertices.
One of the best ways to learn about polyhedra is to construct them yourself.
Polydron is a construction set for building 3D-shapes and a great way to become intimately familiar with different types of polyhedra.
Though marketed mainly as a children's activity, the sets are suitable for both children and adults, and can be used to construct a
wide variety of 3D polyhedra.
This is a book about constructing 3D origami models (models made by paper-folding without using tears or cuts) of Platonic solids and other polyhedra.
The book covers all five Platonic solids, as well as variations, models with color effects, as well as some other types polyhedral shapes.
There are some very attractive sets of crystals and semi-precious stones (amethyst, onyx, hematite, etc.) that you can buy.
To be fair these are usually aimed at people interested in new age beliefs, spiritual practices, reiki, etc., rather than mathematicians.
I personally am skeptical of such matters, but regardless of my beliefs, such crystals sets can be very aesthetically pleasing (see example to the right for example),
as well mathematically interesting.
Of course, I can not endorse any spiritual or other claims made by the vendors of such sets.
Please also be aware that mathematical accuracy may not always be the highest priority for sellers of such crystal sets.
Some sets may contain shapes which are not mathematically accurate Platonic solids,
and/or may include additional shapes other than the 5 Platonic solids (tetrahedron, cube, octahedron, dodecahedron, octahedron).
For example, many crystals sets of "Platonic solids" also include a ball/sphere and a star made from two tetrahedra (known as a "Merkaba star")
in addition to the 5 actual Platonic solids.
This is a large and comprehensive book about polyhedra of all types. It contains many diagrams,
and covers both the mathematics, and the history behind the math.
This is a book about constructing models of regular and semi-regular polyhedral solids.
The book explains how to make models of all uniform polyhedra and some of the stellated
forms. An excellent book, although it may not be to everyone's taste - be sure to read the
reviews on Amazon before deciding if it is for you.
A general overview of the Platonic solids from Wikipedia.
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