Aerogels, aerographenes included, are open cell solids by their very nature of manufacture. They are porous.
To make an aerogel a colloidal solution is made. Gelatinous, after meal deserts are a colloidal mixture made of a suspension of animal bone extract in sugar water. The usual aerogel is a silicate. Normally, through evaporation, your strawberry-tuna flavored Jello(R) will collapse, under the surface tension of the retreating water, into a very small, hard to consume solid.
Aerogels are created in a chamber of raised pressure and temperature. Either the fluid portion of the colloidal solution is raised to a regime of high pressure and temperature of superfluidity or another fluid is introduced under it's conditions of superfluidity. In this regime the fluid acts like both a fluid and a gas. Look it up. The fluid can be extracted from the mixture without the structure collapsing undergone the by long-abandoned plate of jello.
Here is a photograph of an aerographene supported by a few plant fibres.
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
Aerographenes have a density as low as 160 grams per cubic meter. By comparison, the density of air, at STP, is about 1225 grams per cubic meter. They are very porous, and in the photograph, surely full of air.
Evacuted aerographene, as I recall, will collapse like a sponge under atmospheric pressure, and not float. As far as I know, all the rigid, evacuated aerogels will shatter at STP.
Unfortunately, these fail to have the full, visceral appeal of an unadulterated solid floating in air, at STP. I guess we'll have to wait a little longer.