triakis

Triakis refers to a geometric concept with multiple meanings, primarily in polyhedra and number theory. In the context of polyhedra, a triakis is a type of Catalan solid. These are the dual polyhedra of the uniform Archimedean solids. Specifically, a triakis is formed by attaching a triangular pyramid to each face of a polyhedron. For example, the triakis tetrahedron has 12 faces, the triakis octahedron has 24 faces, and the triakis icosahedron has 60 faces. These polyhedra are characterized by having faces that are isosceles triangles.

The term "triakis" can also appear in number theory, particularly in relation to the number of divisors of an integer. A number is called "triakis" if it has exactly three divisors. The only numbers with exactly three divisors are the squares of prime numbers. For instance, 4 (which is 2 squared) has divisors 1, 2, and 4. Similarly, 9 (which is 3 squared) has divisors 1, 3, and 9. This specific usage is less common than the geometric definition. When encountered without further context, "triakis" most often refers to the geometric solids.