When I first started playing, my friend who taught me the game said that your t1 hex must connect to both your home world hex and the galactic core. Is this correct? Is it possible to explore the hex from the side, or by using wormhole generator/lyra shrine bonus, place the hex so that it does not connect to your home world hex or galactic core?
That is incorrect. The only limitation is that you need to form at least one full wormhole connection to at least one space that you COULD legally explore from (Disc or ship present). There is no requirement to max out connections or to connect to any specific hex if there are multiple legal avenues into the hex.
The presence of a wormhole generator does NOT change this requirement.
Edit says: Woops, apparently the wormhole generator allows you to form a "half connection" for this purpose.
Check out Page 9 of the rules for all the info.
- the hex can be placed only to the spot that you explored
- the hex must be oriented so that at least one of the
Wormholes on the hex connects with a Wormhole on
one of the hexes where you have a disc or a Ship
If you have the Wormhole Generator
Technology, you may place the hex
so that there is only a half Wormhole
connecting the placed hex and
the hex you Explored from.
Edit2: it is one of my standard tactics to not connect to the center. I tend to like to stay out of the free for all that that often devolves into.