Square antitegum

The tetragonal trapezohedron is a trapezohedron based on the square, constructed as the dual of a square antiprism. It has 8 kites as faces, with 2 order–4 and 8 order–3 vertices. .

Each face of this polyhedron is a kite with its longer edges $$\frac{2+\sqrt2}{2}$$ times the length of its shorter edges.