I have java:

$ java -version
java version "1.7.0_51"
Java(TM) SE Runtime Environment (build 1.7.0_51-b13)
Java HotSpot(TM) 64-Bit Server VM (build 24.51-b03, mixed mode)
$

Double clicking on the icon does nothing.

I downloaded SweetHome3D-4.3.jar and this works:
java -Xmx2048m -jar SweetHome3D-4.3.jar

So, I have a working solution. I just wished the icon will work too.

Thanks for the great product.