Anyone

+---------------------+------------------------+-----------------------------+----------------------+
| Polygon            | Compass & Straightedge | Angle Trisector (Cube Roots) | Neusis Construction |
+---------------------+------------------------+-----------------------------+----------------------+
| 3-gon (Triangle)   | ✔️                      | ✔️                           | ✔️                    |
| 4-gon (Square)     | ✔️                      | ✔️                           | ✔️                    |
| 5-gon (Pentagon)   | ✔️                      | ✔️                           | ✔️                    |
| 6-gon (Hexagon)    | ✔️                      | ✔️                           | ✔️                    |
| 7-gon (Heptagon)   | ✖️                      | ✖️                           | ✔️                    |
| 8-gon (Octagon)    | ✔️                      | ✔️                           | ✔️                    |
| 9-gon (Enneagon)   | ✖️                      | ▲                           | ✔️                    |
| 10-gon (Decagon)   | ✔️                      | ✔️                           | ✔️                    |
| 11-gon            | ✖️                      | ✖️                           | ✔️                    |
| 12-gon            | ✔️                      | ✔️                           | ✔️                    |
| 13-gon            | ✖️                      | ✖️                           | ✔️                    |
| 15-gon            | ✔️                      | ✔️                           | ✔️                    |
| 17-gon            | ✔️                      | ✔️                           | ✔️                    |
| 18-gon            | ✖️                      | ▲                           | ✔️                    |
| 19-gon            | ✖️                      | ✖️                           | ✔️                    |
| 27-gon            | ✖️                      | ▲                           | ✔️                    |
+---------------------+------------------------+-----------------------------+----------------------+

Legend:
✔️ - Constructible
▲ - Requires Angle Trisection (Cube Roots)
✖️ - Not Constructible with this method

Anyone

Will Kraus