A simple polyhedron, also called a simplicial polyhedron, is a polyhedron that is topologically equivalent to a sphere (i.e., if it were inflated, it would
produce a sphere) and whose faces are simple polygons.

The number of simple polyhedra on , 2, ... nodes are 0, 0, 1, 1, 1, 2, 5, 14, 50, 233, 1249,
... (OEIS A000109).

The skeletons of the simple polyhedra correspond to the triangulated
graphs, the smallest of which are illustrated above.

Bokowski, J. and Schuchert, P. "Equifacetted 3-Spheres as Topes of Nonpolytopal Matroid Polytopes." Disc. Comput. Geom.13,
347-361, 1995.Bowen, R. and Fisk, S. "Generation of Triangulations
of the Sphere." Math. Comput.21, 250-252, 1967.Dillencourt,
M. B. "Polyhedra of Small Orders and Their Hamiltonian Properties."
Tech. Rep. 92-91, Info. and Comput. Sci. Dept., Univ. Calif. Irvine, 1992.Federico,
P. J. "Enumeration of Polyhedra: The Number of 9-Hedra." J. Combin.
Th.7, 155-161, 1969.Gardner, M. "Mathematical Games:
On the Remarkable Császár Polyhedron and Its Applications in Problem
Solving." Sci. Amer.232, 102-107, May 1975.Grünbaum,
B. Convex
Polytopes. New York: Wiley, p. 424, 1967.Lederberg, J.
"Hamilton Circuits of Convex Trivalent Polyhedra (up to 18 Vertices)."
Amer. Math. Monthly74, 522-527, 1967.Sloane, N. J. A.
Sequence A000109/M1469 in "The On-Line
Encyclopedia of Integer Sequences."