In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, a pentahedron (plural: pentahedra) is a polyhedron

Polyhedron

In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

 with five faces. Since there are no face-transitive polyhedra with five sides and there are two distinct topological types, this term is less frequently used than tetrahedron

Tetrahedron

In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...

 or octahedron

Octahedron

In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....

.

With regular polygon

Regular polygon

A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...

 faces, the two topological forms types are the square pyramid

Square pyramid

In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry.- Johnson solid :...

 and triangular prism

Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides....

. Geometric variations with irregular faces can also be constructed.

Name	Picture	Vertices	Edges	Faces	Faces by type
Square pyramid Square pyramid In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry.- Johnson solid :... (Pyramid family Pyramid (geometry) In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base.... )		5	8	5	4 triangles 1 square
Triangular prism Triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.... (Prism family Prism (geometry) In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a... )		6	9	5	2 triangles 3 squares

The square pyramid can be seen as a degenerate triangular prism where one edge of its side edges is collapsed into a point, losing one edge and one vertex, and changing two squares into triangles.

Hosohedron

There is a third topological polyhedral figure with 5 faces, degenerate as a polyhedron, it exists as a spherical tiling of digon

Digon

In geometry, a digon is a polygon with two sides and two vertices. It is degenerate in a Euclidean space, but may be non-degenerate in a spherical space.A digon must be regular because its two edges are the same length...

 faces, called a pentagonal hosohedron with Schläfli symbol {2,5}. It has 2 (antipodal point

Antipodal point

In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite to it — so situated that a line drawn from the one to the other passes through the centre of the sphere and forms a true diameter....

) vertices, 5 edges, and 5 digonal faces.