Re: "geometric shapes including hexagrams that have some kind of mystical meaning "
A mason is someone who constructs an edifice. Today's modern "stonemason' or bricklayer is an occupation derived from the earliest 'masons'. Freemasons consider that a Supreme Being is the Ultimate Designer Architect and Builder of the Universe, responsible for the original basic geometric designs used to create the Universe and everything in it. Freemasonry is a secretive fraternal order which sees its 'mission statement' as an organization dedicated to construct and build a 'brotherhood of man' on Earth.
The sphere, square, cross, parabola, pyramid, hexagram, pentangle, etc. - are all basic geometric patterns seen repeatedly, and are considered "sacred geometry" in the metaphysical studies of all major religions. They are not exclusive to Freemasonry. If you want to see some "sacred geometry" sit down at a well set dining table, look around, and see how many geometric shapes you can identify right in front of you about which you never previously gave much thought!