There are many countries which use a penny as its minor currency unit and these coins are not the same size. Furthermore, the citizens of the US refer to their cent as a penny - for some bizarre reason. Without any indication as to which country's currency the question is about, it is not possible to give an answer.
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Nominal thickness is 1.55mm
Quarter: 24.26mm Nickel: 21.21mm Penny: 19.05mm
There are several countries in which the minor currency unit is a penny - including the US where a cent is called a penny!The UK penny has a diameter of 20.3 mm.
A U.S. cent is 1.55mm thick.
There are no ridges on a US Penny or the US Nickel, the edges are smooth.