Pentagonal antitegum

The pentagonal trapezohedron is a trapezohedron based on the pentagon, constructed as the dual of a pentagonal antiprism. It has 10 kites as faces, with 2 order–5 and 10 order–3 vertices. .

Each face of this polyhedron is a kite with its longer edges $$\frac{3+\sqrt5}{4} ≈ 2.61803$$ times the length of its shorter edges. These kites have 3 angles measuring 108° and 1 measuring 36°.

The pentagonal trapezohedron can be constructed from the regular dodecahedron by augmenting tall pyramids on two opposite faces.