A rhombus is an equilateral quadrilateral. When one (all) of the angles is 90°, the rhombus is a square. A square is a rhombus that can be made using tangram shapes.

Any other rhombus requires angles other than 90°. The only tangram angle available other than 90° is 45°. A tangram rhombus with 45° angles would require two angled edges and two "square" edges all to have the same length. Such a collection of edge lengths is not possible using tangram pieces.

Any other rhombus requires angles other than 90°. The only tangram angle available other than 90° is 45°. A tangram rhombus with 45° angles would require two angled edges and two "square" edges all to have the same length. Such a collection of edge lengths is not possible using tangram pieces.