Geodesic polyhedron
They are the dual of corresponding Goldberg polyhedra, of which all but the smallest one (which is a regular dodecahedron) have mostly hexagonal faces.
Geodesic polyhedra are a good approximation to a sphere for many purposes, and appear in many different contexts.
Geodesic polyhedra are available as geometric primitives in the Blender 3D modeling software package, which calls them icospheres: they are an alternative to the UV sphere, having a more regular distribution.
In Magnus Wenninger's Spherical models, polyhedra are given geodesic notation in the form {3,q+}b,c, where {3,q} is the Schläfli symbol for the regular polyhedron with triangular faces, and q-valence vertices.
There are 3 symmetry classes of forms: {3,3+}1,0 for a tetrahedron, {3,4+}1,0 for an octahedron, and {3,5+}1,0 for an icosahedron.
The dual notation for Goldberg polyhedra is {q+,3}b,c, with valence-3 vertices, with q-gonal and hexagonal faces.
There are 3 symmetry classes of forms: {3+,3}1,0 for a tetrahedron, {4+,3}1,0 for a cube, and {5+,3}1,0 for a dodecahedron.
The subgrids can be extracted by looking at a triangular tiling, positioning a large triangle on top of grid vertices and walking paths from one vertex b steps in one direction, and a turn, either clockwise or counterclockwise, and then another c steps to the next primary vertex.
The primary face of the subdivision is called a principal polyhedral triangle (PPT) or the breakdown structure.
Goldberg polyhedra are also related in that applying a kis operator (dividing faces into triangles with a center point) creates new geodesic polyhedra, and truncating vertices of a geodesic polyhedron creates a new Goldberg polyhedron.
