You will need some Trigonometry skills for this honest method.
Sometimes I can anticipate the locations of unseen stars in a dark galaxy.
In most NP2 Triton games, the locations of empire starting HW home star can be figured out.
In most standard games, HW are a known "Starting Distance" apart.
close = 8.0 LY = 12.0 LY * 2/3
medium = 12.0 LY
far = 16.0 LY = 12.0 LY * 4/3
In a hex map, HW are at 60 degree angles from each other, usually forming equilateral triangles.
In a circular map, take 360 degrees and divide by the number of player empires, and this can help figure out the angles between HW.
In my 64 player (custom) "Three neighbors maps", HW locations are specifically placed, and form many equilateral triangles, and there is a lot of symmetry. Jay has change the HW distance to 9.92 LY = 12.4 LY * 4/5 .
In a custom map, the player who designed the galaxy map often has some kind of geometric theme in mind for HW, but otherwise anything goes.
If you are able to see a second HW from your own HW, then this can form a Vector with distance and angle, and be used as a Baseline for Triangulation calculations.
Hit shortcut key "V" to use the Chain Ruler. The Chain Ruler measures LY distances to one decimal place accuracy. I improve that by measuring distance between two stars 10 times to multiply that distance, which will reveal one more digit of accuracy. Read this tip.
Once I acquire the distances between three stars, I can use the Law of Cosines to calculate angles between them.
Once I know the distance & angle towards one star, I can use use Sine and Cosine functions to calculate X and Y coordinates for that star.
Often in inverse trigonometric functions, calculators will return Radians.