Prisms & Antiprisms

The Prisms and Antiprisms have the same characteristics as the Archimedian solids: they are convex with identical vertices, and the faces are regular polygons of more than one kind.

The distinction between the Archimedian solids and the Prisms and Antiprisms is mostly historical. However, there are some broad differences; the Archimedian solids are ball-like, whereas the Prisms and Antiprisms are more disk-like. More striking is the fact that there is an infinite number of Prisms and Antiprisms!


A Prism is formed by taking two identical N-gons (a polygon with N sides) for a top and bottom, and then connecting them with squares all around. Three example prisms are shown below. You can see that as the number of sides of the top and bottom increases the resulting solid looks more and more like a disk.

Triangular Prism (4,4,3) Pentagonal Prism (4,4,5) Hexagonal Prism (4,4,6)

As with the Archimedian solids, since the vertices are all identical, listing the polygons that surround each vertice fully describes a prism or antiprism. For example, the Hexagonal Prism shown above has 2 squares and one hexagon surrounding each vertex, so it identified by the numbers (4,4,6).


An Antiprism is formed by taking two identical N-gons for a top and bottom, and then connecting them with equalateral triangles all around. Three Antiprisms are shown below.

Square Antiprism (3,3,3,4) Pentagonal Antiprism (3,3,3,5) Hexagonal Antiprism (3,3,3,6)

It is not uncommon that a polyhedron can be classified in more than one way. Perhaps you noticed that in the above examples that the Square Prism and the Triangular Antiprism were conspicuously missing. You have already seen these solids in another article; can you give their alternate names?

Square prism (4,4,4) Triangular Antiprism (3,3,3,3)

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