The augmented triangular prism is a polyhedron constructed by attaching an equilateral square pyramid onto the square face of a triangular prism. As a result, it is an example of Johnson solid. It can be visualized as the chemical compound, known as capped trigonal prismatic molecular geometry.
The augmented triangular prism is composite: it can be constructed from a triangular prism by attaching an equilateral square pyramid to one of its square faces, a process known as augmentation. This square pyramid covers the square face of the prism, so the resulting polyhedron has six equilateral triangles and two squares as its faces. A convex polyhedron whose faces are all regular polygons, but which is not uniform, is a Johnson solid, after American mathematician Norman W. Johnson who listed the 92 such polyhedra. The augmented triangular prism is among them, enumerated as the forty-ninth Johnson solid .
An augmented triangular prism has a surface area by adding the area of six equilateral triangles and two squares. Its volume can be obtained by slicing it into a regular triangular prism and an equilateral square pyramid, and adding their volume subsequently. With edge length , the formulations are:
The augmented triangular prism has three-dimensional symmetry group of the two-fold pyramidal symmetry of order four. Its dihedral angle (i.e., the angle between two polygonal faces) can be calculated by adding the angle of an equilateral square pyramid and a regular triangular prism in the following:
In the geometry of chemical compounds, a polyhedron may commonly be visualized an atom cluster surrounding a central atom. The capped trigonal prismatic molecular geometry describes clusters for which this polyhedron is an augmented triangular prism. An example of such compound is the potassium heptafluorotantalate.