The chestahedron was discovered by Frank Chester, an American artist and geometrician. It has seven faces of equal size but not of equal shape; therefore it is not a Platonic solid. Four of the faces are equilateral triangles and three are kites that evolve in the transformation process.
In this Demonstration you can control the transformation and rotate the solid. Three views are provided: (1) the tetrahedron without and (2) with the outer tetrahedron and (3) the chestahedron.