Aberystwyth University provided a block from Clarach beach to represent Wales in the Geological Survey of Austria display.
It is a charcoal-grey sandstone with white veins of calcite mineral dating back more than 419 million years to the Silurian period.
The 24 miniature footballs have been sectioned into their groups.
Wales' sandstone is joined by England's limestone, Slovakia's golden onyx and Russia's black dolerite.
Prof Alex Malman said: "If a country already has a rock football from previous years they use the same one for display again, but as Wales has not qualified for a while, they needed an initial one and it was great to see us up there.
"I have high hopes that I will be seeing it up there once again in four years' time."
A rock from a Ceredigion beach has been shaped into a football for a Euro 2016 exhibition in Vienna.