Square antitegum

The square antitegum or squate, also known as the tetragonal trapezohedron, is an antitegum 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 $$\frac{2+\sqrt2}{2} ≈ 1.70711$$ times the length of its shorter edges.