This is one of these things that are kind of hidden in after effects. Sometimes when you create a parametric shape (with the rectangle tool, rounded rectangle tool, ellipse tool, polygon tool,star tool) you want to be able to edit, delete or add vertex points. If you create the shape normally, you’re stuck with the shape. But if you hold down ALT on your keyboard when you draw the shape, you’ll be able to change the vertex points afterwards.

You will lose some shape layer attributes that are linked to certain shapes (like roundness of the rounded rectangle tool).

Changing Vertex Points of Parametric ShapesThe star in above GIF is how it looks normally, and the below one is drawn with holding down ALT. As you can see, you already see the vertex points in the below one.

Changing Vertex Points of Parametric ShapesYou can also use the scroll wheel on your mouse to add more points/edges to the star/polygon shape. And holding down shift will lock the rotation.

Honestly this is the kind of thing that bothers me about After Effects. We shouldn’t have to remember esoteric key commands to do basic functions like this. We should be able to right click on the layer, and under shapes and masks there should be a command “make editable.”

Adobe released Creative Cloud 12.2 update last December with option for creating shape layers based on Bezier paths and command for converting a parametric shape layer path to a Bezier path.

Here’s the relevant excerpt from the “After Effects CC (12.2): what’s new and changed in this December 2013 update” page:

Option for creating shape layers based on Bezier paths

When a shape tool (Rectangle, Rounded Rectangle, Polygon, Star, or Ellipse tool) is active, you can use the new Bezier Path option in the Tools panel to create a new shape based on a Bezier path, as opposed to the default of creating a new shape based on a parametric path.

Holding the Alt (Windows) or Option (Mac OS) key while drawing a shape causes the opposite behavior—i.e., if the Bezier Path option is enabled, holding the Alt or Option key causes the shape tool to create a parametric path; if the Bezier Path option is disabled, holding the Alt or Option key causes the shape tool to create a Bezier path.

Command for converting a parametric shape layer path to a Bezier path

You can convert a parametric path to a Bezier path after the parametric path has already been created by context-clicking (right-clicking or Control-clicking on Mac OS) the property group for the parametric path (e.g., Rectangle Path 1) and choosing the Convert To Bezier Path command from the context menu.

If the parametric path is animated (keyframed), the converted Bezier path is a static path based on the parametric path at the current time; keyframes are lost.