In Geometry, an Elementary Polyhedron is a Polyhedron which does not contain a cycle of edges that can be sliced by a plane. This is the opposite of a Composite polyhedron which contains a cycle of edges that all lie on the same plane. When a composite polyhedron is sliced by a plane which aligns with one of these cycles of edges, two new polyhedra are produced which, together, contain all the faces of the original polyhedron and two new polygonal faces. If an elementary polyhedron is sliced by the plane, atleast one of the faces will be split by the planar cut. An equivalent definition of Elementary polyhedra would be that they are the polyhedra which cannot be constructed by joining together two polyhedra along a single face.

Convex Elementary Polyhedra with Regular Faces

Elementary Polyhedra are usually discussed in the context of Johnson solids, which are strictly convex polyhedra with regular polygonal faces. The term "Elementary Polyhedra" is often used to refer to only those Johnson solids which are elementary polyhedra, though there are many other elementary polyhedra with regular faces that are not Johnson solids.

Seventeen of the Johnson Solids are elementary:

1. Square pyramid

2. Pentagonal pyramid

3. Triangular cupola

4. Square cupola

5. Pentagonal cupola

6. Pentagonal rotunda

63. Tridiminished icosahedron

80. Parabidiminished rhombicosidodecahedron

83. Tridiminished rhombicosidodecahedron

84. Snub disphenoid

85. Snub square antiprism