Pentahedron

In geometry, a pentahedron is a polyhedron with five faces or sides. There are no face-transitive polyhedra with five sides, and there are two distinct topological types. Notable polyhedra with regular polygon faces are:
The pentahedra can be used as space-filling.

Concave

An irregular pentahedron can be a non-convex solid: Consider a non-convex quadrilateral as the base of the solid, and any point not in the base plane as the apex.

Hosohedron

There is a third topological polyhedral figure with 5 faces, degenerate as a polyhedron: it exists as a spherical tiling of digon faces, called a pentagonal hosohedron with Schläfli symbol. It has 2 vertices, 5 edges, and 5 digonal faces.