Catalan solid facts for kids

Catalan solids are a special group of 3D shapes in geometry. Think of them as the "partners" or "duals" to another famous group of shapes called Archimedean solids. There are exactly thirteen Catalan solids, just like there are thirteen Archimedean solids. They are named after a Belgian mathematician from the 1800s, Eugène Charles Catalan.

Each Catalan solid is a type of convex polyhedron. This means they are solid 3D shapes with flat faces, straight edges, and sharp corners, and they don't have any dents or holes. A cool thing about Catalan solids is that all their faces are the same shape.

What Makes Catalan Solids Special?

Catalan solids are unique because of their relationship with Archimedean solids. Imagine you have an Archimedean solid. If you place a dot in the middle of each face of that solid and then connect those dots, you would form its "dual" shape. That dual shape is a Catalan solid!

For example, the rhombic dodecahedron is a Catalan solid. It is the dual of the cuboctahedron, which is an Archimedean solid. This special connection means that the number of faces on a Catalan solid is the same as the number of corners (vertices) on its Archimedean partner, and vice-versa.

Who Was Eugène Catalan?

Eugène Charles Catalan was a mathematician who lived in Belgium during the 19th century (from 1814 to 1894). He studied many areas of mathematics, including geometry. The Catalan solids are named after him because he was the first to describe and classify these interesting shapes. His work helped us understand more about the world of polyhedra and their unique properties.

How Many Catalan Solids Are There?

There are exactly 13 different Catalan solids. Each one is the dual of one of the 13 Archimedean solids. This means they form a perfect pair! They are all convex, and every face on a single Catalan solid is identical to the others. However, unlike Archimedean solids, their faces are not always regular polygons (like perfect squares or triangles with all equal sides and angles).

Images for kids

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  A rhombic dodecahedron with its face configuration.

See also

In Spanish: Sólidos de Catalan para niños