Decagonal antitegum

The decagonal antitegum or dat, also known as the decagonal trapezohedron, is an antitegum based on the decagon, constructed as the dual of a decagonal antiprism. It has 20 kites as faces, with 2 order–10 and 20 order–3 vertices. .

Each face of this polyhedron is a kite with its longer edges $$3+\sqrt5+\sqrt{\frac{25+11\sqrt5}{2}} ≈ 10.21586$$ times the length of its shorter edges.