How to "flatten" the faces of a solid to level with its vertices? I have the following decahedron:

But as you can see below, its faces are not &quot;flat&quot; but rather curve towards the inside:

How can I make it so that all the faces become flat kites, without adding edges or vertices?
EDIT: To be clear, I want to end up with a shape similar to this:
A very unscientific way to do it would be to first create this shape:

Use the Array modifier in Object Offset mode, rotate the offset object 72° on the Z axis:

Rotate your mesh in Edit mode so that if fits perfectly with its instances:

Apply the modifier, duplicate, rotate the copy 180° on the Y axis, rotate 36° on the Z axis, merge the 2 meshes:

Bevel if you want more geometry: