Because of the tools they were limited to, the Greeks were only able to construct five shapes.

The Greeks, due to the limitations of their tools, were only able to construct five shapes. These shapes are known as the Platonic Solids, named after the ancient Greek philosopher Plato. They are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

Here are the steps they might have taken to construct these shapes:

1. Tetrahedron: Start with a single point. Draw three lines from this point, all of the same length and all at the same angle to each other. Connect the ends of these lines to form a triangle. This is the base of the tetrahedron. Then draw a line from each corner of the triangle to a new point above the base, and connect these lines.

2. Cube: Start with a single point. Draw four lines from this point, all of the same length and at right angles to each other, to form a square. This is the base of the cube. Then draw a line from each corner of the square to a new point above the base, and connect these lines to form the top square.

3. Octahedron: Start with a tetrahedron. Then add a point above the base and connect this point to each corner of the base. Then add a point below the base and connect this point to each corner of the base.

4. Dodecahedron: Start with a cube. Then add a point above each face of the cube and connect these points to each corner of the face. This will form a pentagon above each face of the cube.

5. Icosahedron: Start with an octahedron. Then add a point above each face of the octahedron and connect these points to each corner of the face. This will form a triangle above each face of the octahedron.

These constructions would have been done using a straightedge and compass, the primary geometric tools available to the Greeks.