This is a list of selected

geodesic polyhedra A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles. They are the dual of corresponding Goldberg polyhed ...

and

Goldberg polyhedra In mathematics, and more specifically in polyhedral combinatorics, a Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons. They were first described in 1937 by Michael Goldberg (mathematician), Michael Goldberg (1902–1990 ...

, two infinite classes of

polyhedra In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on t ...

. Geodesic polyhedra and Goldberg polyhedra are

duals ''Duals'' is a compilation album by the Irish rock band U2. It was released in April 2011 to u2.com subscribers. Track listing :* "Where the Streets Have No Name" and "Amazing Grace" are studio mix of U2's performance at the Rose Bowl, Pas ...

of each other. The geodesic and Goldberg polyhedra are parameterized by integers ''m'' and ''n'', with

m > 0

and

n \ge 0

. ''T'' is the triangulation number, which is equal to

T = m^2 + mn + n^2

Icosahedral

Octahedral

Tetrahedral

References

* Reprinted by Dover 1999 {{ISBN, 978-0-486-40921-4 Mathematics-related lists