Pentagonal Prism
Definition and meaning of Pentagonal Prism in chemistry.
A pentagonal prism is a polyhedron with two parallel pentagonal (five-sided) bases connected by five rectangular faces. In chemistry, this shape is best known as the carbon-cage skeleton of pentaprismane (C10H10), a synthesized hydrocarbon; true fivefold symmetry does not occur in ordinary periodic crystal lattices.
In more detail
A pentagonal prism has 7 faces (2 pentagons + 5 rectangles), 15 edges, and 10 vertices, satisfying Euler's formula (V − E + F = 2). Pentagonal prisms are not found as crystal forms of ordinary, periodic crystals: the crystallographic restriction theorem limits crystal lattices to 2-, 3-, 4-, and 6-fold rotational symmetry, so fivefold symmetry is excluded from classical crystallography and appears only in aperiodic quasicrystals. In coordination chemistry, 'pentagonal prismatic' is not a recognized coordination geometry, five-coordinate complexes instead adopt trigonal bipyramidal or square pyramidal geometry, six-coordinate complexes can adopt trigonal prismatic geometry (as in MoS2), and seven-coordinate complexes can adopt pentagonal bipyramidal geometry (five equatorial ligands plus two axial ligands). The clearest genuine chemical realization of the pentagonal prism shape is structural, not crystallographic: pentaprismane, a cage hydrocarbon with formula C10H10, has ten CH units occupying the ten vertices of a pentagonal prism, connected by fifteen C-C bonds corresponding to the polyhedron's fifteen edges.
Key facts
| Faces | 7 faces total: 2 pentagonal bases and 5 rectangular sides |
|---|---|
| Edges and Vertices | 15 edges and 10 vertices |
| Chemistry Application | Skeleton of the cage hydrocarbon pentaprismane (C10H10); not a recognized crystal form or coordination geometry |
| Field | Organic Chemistry |
Pentaprismane (C10H10) was first synthesized by Philip Eaton's group in the early 1980s and belongs to the prismane family of cage hydrocarbons, alongside triprismane (C6H6, a triangular prism) and cubane (C8H8, a square prism). By contrast, the mineral beryl, a beryllium aluminum silicate with formula Be3Al2Si6O18, crystallizes in the hexagonal system; like all ordinary minerals it cannot display true pentagonal prismatic crystal faces, because fivefold symmetry is forbidden in periodic crystals by the crystallographic restriction theorem.
Frequently asked questions
Is 'pentagonal prismatic' a recognized coordination geometry?
No. A pentagonal prism has ten vertices, so it cannot describe a five-coordinate complex. Five-coordinate complexes typically adopt trigonal bipyramidal or square pyramidal geometry. The genuine pentagon-based coordination geometry is pentagonal bipyramidal, a seven-coordinate arrangement with five ligands in an equatorial pentagon and two ligands in axial positions.
Where does the pentagonal prism shape actually occur in chemistry?
Its clearest chemical realization is pentaprismane (C10H10), a synthesized cage hydrocarbon whose ten CH units sit at the ten vertices of a pentagonal prism, not as a mineral crystal form. Ordinary periodic crystals are restricted by the crystallographic restriction theorem to two-, three-, four-, and sixfold symmetry, so true pentagonal symmetry occurs only in aperiodic quasicrystals, not standard minerals.