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The Polyhedra poster set

The Platonic Solids poster Truncation poster The Kepler-Poinsot Solids poster The Compound of Five Cubes poster The Great Dirhombicosidodecahedron poster

The posters illustrate three families of polyhedra and two individual more complex examples:

Each poster describes the polyhedra and also gives brief mathematical or historical information.

See below for more information about the background notes as well as samples from the notes. Larger images of the posters may be seen by going to the Poster Gallery.

“The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.”—Aristotle

The Polyhedra background notes

A descriptive booklet accompanies the posters, explaining the mathematics behind the images in the posters and related topics.

The Polyhedra backround notes page 1 The Polyhedra backround notes page 2 The Polyhedra backround notes page 3 The Polyhedra backround notes page 4

The four pages of background notes give more information about the polyhedra on the five posters and about polyhedra in general. The topics covered are:

The notes help interested students and teachers explore further, and provide ideas for activities connected to the theme of the posters.

Extracts from the background notes

Types of Polyhedra

An example polygram

A polyhedron is a solid bounded by plane polygons, called the faces. Only polyhedra with regular faces are considered here, but regular star-polygons, or polygrams, like that shown alongside, are included as possible faces. The arrangement of faces around a vertex is referred to as the vertex configuration.

A polyhedron is either convex or non-convex. For example, there are nine regular polyhedra, the five convex Platonic solids and the four non-convex Kepler-Poinsot solids, shown on The Beauty of Mathematics posters.

Uniform Polyhedra

The truncated tetrahedron

A uniform polyhedron has regular faces and identical vertices. Excluding the prisms and antiprisms, there are 75 uniform polyhedra, 18 of them convex and 57 non-convex. Apart from prisms and antiprisms, the convex uniform polyhedra are the five Platonic solids and the thirteen Archimedean (or semi-regular) solids. Sixteen are illustrated on The Beauty of Mathematics poster Truncation; the other two are the tetrahedron, and the truncated tetrahedron shown alongside.


The stella octangula as a stellation

Apart from truncation, another method of creating one polyhedron from another is stellation. To stellate a polyhedron, the facial planes are extended in a symmetrical way until they intersect. There are no stellations of the tetrahedron or cube—their planar faces never intersect again however far they are extended. The only stellation of the octahedron is the stella octangula, illustrated on The Beauty of Mathematics poster The Platonic Solids. The diagram alongside shows how the faces of the octahedron are extended.

On this page

Clicking a link will scroll the page to the relevant section.


Visit the Poster Gallery to see larger images of the posters.

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“Thanks again for an excellent collection of posters.”

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Poster size

All posters are A2 size:

42 cm by 59.4 cm


The front face of each poster is covered with a wipe-clean laminated film.

Booklet size

Each booklet of background notes has four A4 pages and includes many diagrams.