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People who make concrete counter tops use a lot of fibreglass fillers to get them fairly thin but if you wanted it truly light weight you’d probably need to make it out of a dense foam and coat it with something that looks like concrete.
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My bathroom is a couple mm of microcement over Schluter Kerdi-Board foam, it's fairly strong. I think it can hold a laptop no problem.
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Concrete counter top mixes usually use either much smaller, or no aggregate and use more sand. The mixes resemble mortar more than concrete and they are typically a little harder and less forgiving to work with.
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Even structural items can be made quite thin! There is a college design competition to make concrete canoes which can be 3/8" to 7/16" thick: https://www.concretecanoe.org/2008Triva/Florida2008DesignPap...
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oh wow that takes me back. I remember touring, i think it was Texas A&M, in HS and they showed off their "concrete canoe" to the group. This would have been in the late 1900s.. 1995 or around there.
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There have been ships made of concrete.

https://en.wikipedia.org/wiki/Concrete_ship

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You could mix concrete with other materiais too. I worked as a lab assistant in a engineering lab for some time. Putting styrofoam into the mix would result in lighter concrete within acceptable levels of resistance (for low level buildings). You might be onto something
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I've read that adding a little bit of graphene can make concrete much stronger, lighter and easy to shape, so would allow for thinner objects.
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There are a lot of additives to concrete - the industry is large and has put a lot of money into research over the decades. You can read many many books on the pros and cons of different options.
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> Maybe with clever use of fillers and thin walls you could have a version of this you could actually lift

You could likely also pour something like this out of aircrete, which would make it a lot lighter even at the same thickness

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