In geometry, a diminished trapezohedron is a polyhedron in an infinite set of polyhedra, constructed by removing one of the polar vertices of a trapezohedron and replacing it by a new face (diminishment).

They're also related to the gyroelongated pyramids, as augmented antiprisms and which are Johnson solids for n = 4, 5.

There are three special case geometries of the diminished trigonal trapezohedron.

The Chestahedron, named after artist Frank Chester, is constructed with equilateral triangles around the base, and the geometry adjusted so the kite faces have the same area as the equilateral triangles.

The three rhombic faces fold out flat to form half of a hexagram.