In geometry, the augmented triangular prism is a polyhedron constructed by attaching an equilateral square pyramid onto the square face of a triangular prism.
It can be visualized as the chemical compound, known as capped trigonal prismatic molecular geometry.
The augmented triangular prism can be constructed from a triangular prism by attaching an equilateral square pyramid to one of its square faces, a process known as augmentation.
[2] A convex polyhedron in which all faces are regular is Johnson solid, and the augmented triangular prism is among them, enumerated as 49th Johnson solid
[3] An augmented triangular prism with edge length
has a surface area, calculated by adding six equilateral triangles and two squares' area:[2]
Its volume can be obtained by slicing it into a regular triangular prism and an equilateral square pyramid, and adding their volume subsequently:[2]
Its dihedral angle can be calculated by adding the angle of an equilateral square pyramid and a regular triangular prism in the following:[4] In the geometry of chemical compounds, a polyhedron may commonly visualize an atom cluster surrounding a central atom.
The capped trigonal prismatic molecular geometry describes clusters for which this polyhedron is an augmented triangular prism.