In geometry, the augmented pentagonal prism is a polyhedron that can be constructed by attaching an equilateral square pyramid onto the square face of pentagonal prism. It is an example of Johnson solid.

Construction

The augmented pentagonal prism can be constructed from a pentagonal 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 four equilateral triangles, four squaress, and two regular pentagons as its faces. A convex polyhedron in which all faces are regular is Johnson solid.

Properties

has a surface area, calculated by adding the area of four equilateral triangles, four squares, and two regular pentagons: Its volume can be obtained by slicing it into a regular pentagonal prism and an equilateral square pyramid, and adding their volume subsequently:

The augmented pentagonal prism has a three-dimensional symmetry group of order four. It has five dihedral angles (an angle between two polygonal faces), obtained by adding the equilateral square pyramid and the regular pentagonal prism's angle. These angles are as follow:

• ,

• an angle between two adjacent square faces is the internal angle.

• .

• , and the dihedral angle of a regular pentagonal prism between its base and its lateral face.

• , for which adding the dihedral angle of an equilateral square pyramid between its base and its lateral face, and the dihedral angle of a regular pentagonal prism between two adjacent squares.

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