For this you will need four pennies. Arrange the pennies so that the centers of all four are equidistant from each other.

Example:

(1) (2) (3) (4)

This will not work because penny 1 and penny 4 are farther apart than penny 1 and penny 2.

(In reply to

Pennies of Giza by Jyqm)

I believe both Jyqm and TZIDON grasped the concept of what in my mind is a way to solve this. However, Jyqm's pyramid would have 5 vertices for 4 pennies, while an equilateral tetrahedron would do the trick (a vertex for each penny, far from each other by the exact same distance).

I'm sure it was just a matter of speech, but a pyramid wouldn't fit due to it's rectangular or square base (and, therefore, at least two pennies would be separated by this polygon's diagonal).