For this you will need four pennies. Arrange the pennies so that the centers of all four are equidistant from each other.
(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 re(2): Pennies of Giza
by Vishal Gupta)
When we come to triangle-shaped pyramids, I see no problem at all, Vishal. What I pointed at was the definition of pyramid, as follows:
A solid figure with a polygonal base and triangular faces that meet at a common point.
And, as our best images of pyramids I imagine to be the ones of Egypt, here's the description of those:
A massive monument of ancient Egypt having a rectangular base and four triangular faces culminating in a single apex, built over or around a crypt or tomb.
So, as you see, the vocabule "pyramid" may mean a polyhydron with four vertices and faces, but not necessarily (and not commonly as well). As this word was potentially misleading to me, I thought it might have been the same to others and decided to give the polyhedron its rightful name to fit the problem's solving (in this stance, a tetrahedron). Like I said, all was probably a matter of speech, but in a hurry I might have mistaken Jyqm's idea.
Now that I think of it, it's not as important, other than giving the polyhedron Jyqm described its rightful name.