It is categorized as a Johnson solid if all of the edges are equal in length, forming equilateral triangular faces and a regular pentagonal base.

Pentagonal pyramids occur as pieces and tools in the construction of many polyhedra.

They also appear in the field of natural science, as in stereochemistry where the shape can be described as the pentagonal pyramidal molecular geometry, as well as the study of shell assembling in the underlying potential energy surfaces and disclination in fivelings and related shapes such as pyramidal copper and other metal nanowires.

A pentagonal pyramid has six vertices, ten edges, and six faces.

[3] A pentagonal pyramid is said to be regular if its base is circumscribed in a circle that forms a regular pentagon, and it is said to be right if its altitude is erected perpendicularly to the base's center.

: the pyramid is left invariant by rotations of one, two, three, four-fifths around its axis of symmetry, the line connecting the apex to the center of the base.

It is also mirror symmetric relative to any perpendicular plane passing through a bisector of the base.

[5] It is self-dual, meaning its dual polyhedron is the pentagonal pyramid itself.

[6] When all edges are equal in length, the five triangular faces are equilateral and the base is a regular pentagon.

Because this pyramid remains convex and all of its faces are regular polygons, it is classified as the second Johnson solid

The volume of every pyramid equals one-third of the area of its base multiplied by its height.

Attaching its base to the pentagonal face of another polyhedron is an example of the construction process known as augmentation, and attaching it to prisms or antiprisms is known as elongation or gyroelongation, respectively.

[13] Relatedly, the removal of a pentagonal pyramid from polyhedra is an example of a technique known as diminishment; the metabidiminished icosahedron

are the examples in which their constructions begin by removing pentagonal pyramids from a regular icosahedron.

[14] In stereochemistry, an atom cluster can have a pentagonal pyramidal geometry.

This molecule has a main-group element with one active lone pair of electrons, which can be described by a model that predicts the geometry of molecules known as VSEPR theory.

[16] Fejer et al. (2009) modeled the formation of virus shells, known as capsids, from pieces shaped like pentagonal and hexagonal pyramids.

These shapes were chosen to resemble those of the protein subunits of natural viruses.

By appropriately choosing the attractive and repulsive forces between pyramids, they found that the pyramids could self-assemble into icosahedral shells reminiscent of those found in nature.

[17] Gryzunova (2017) studied the relaxation of internal elastic stress fields due to disclinations in twinned copper particles.

Such a shape is the pentagonal pyramid, which allows growth to a large size and preserves symmetry.

This can be done by activating cathode by the process of initial crystal growth in the electrolyte, by the movement of aluminum and silicon oxides' abrasive particles.