What is goldberg polyhedron?

The Goldberg polyhedron is a type of polyhedron that was first described by Michael Goldberg in 1937. It is also known as the Goldberg-Coxeter construction, as it was further developed by mathematician H.S.M. Coxeter.

The Goldberg polyhedron is created by taking a face of a Platonic solid and adding new faces to it by dividing its edges into two or more segments of equal length, and then connecting the new points to create new triangular or quadrilateral faces. The process is repeated until no new faces can be added without intersecting existing ones.

There are many different Goldberg polyhedra that can be constructed using this method, depending on which face of the Platonic solid is used as the starting point and how the edges are divided. For example, starting with a regular dodecahedron and dividing its edges into thirds, one can create a Goldberg polyhedron with 62 faces, 20 of which are regular hexagons and 12 of which are regular pentagons.

The Goldberg polyhedron is interesting from a mathematical perspective because it has many symmetries and can be used to generate interesting geometric patterns. It has also been used in various applications, such as computer graphics and material science.