Dots structures codified

Here are patterns of white and black dots and list of numbers that somehow describe those patterns. What combinations correspond to numbers on the right side?

(black dots in the last line form a square; white dot in the middle of it)

Hint 1:

Hint 2:

Think which rules do you assume here but are not actually given

One possibility is the following:

Take the diagram, and connect any pair of dots that is exactly one unit apart. (The size of a unit is the smallest distance between two dots.) The first number is the number of dots.
The second number is the number of connections.
The third number is 1 if the midpoint of the white dots is the same as the midpoint of the black dots, 0 otherwise.

So to satisfy the given patterns...

for 4,6,0, we need to place four dots so that all four are the same distance apart from each other. The only way to do that with three is to make an equilateral triangle... so to add the fourth, we need to jump to 3D! The pattern for 4,6,0 is a regular tetrahedron (all black).

Similarly, the pattern for 8,12,1 is a cube, with two opposing vertices white.
And the pattern for 8,28,0... well, the number 28 is ridiculously big - it means that every vertex needs to be connected to every other. So the only way we can do this is by going into 7-dimensional space, and arranging the points in a 7-simplex! (And of course, all the vertices would be black again.)

• I am fairly sure my answers for the first two numbers are correct here, but don't believe that the third number is what was intended. It fits, though!
– Deusovi
Commented May 1, 2022 at 6:36
• Not sure about your BWB rule. Wouldn't that make the second pattern 331?
– fljx
Commented May 1, 2022 at 8:09
• I think the last(third) rule might be how many intersection points there are with whites. rot13(Lbh pbaarpg oynpx jvgu oynpx, juvgr jvgu juvgr naq frr ubj znal vagrefrpgvba cbvagf lbh trg jurer gur vagrefrpgvba cbvag vf RVGURE n juvgr qbg bayl BE na vagrefrpgvba bs gur yvar orgjrra gjb juvgr qbgf.) Commented May 1, 2022 at 11:58
• You correctly indentified rules for first and second numbers and the twist in the puzzle. But the rule for third number is wrong (there is contradicting example in the list) and example for 8/12/0 is mistaken. Otherwise good job! I'll accept this answer if you correct for mistakes or if there is no other correct answer in two days (since this answer is mostly correct) Commented May 2, 2022 at 9:14
• I think the third one is something like (nyy pbaarpgvbaf unir gb gbhpu n juvgr iregrk) Commented May 3, 2022 at 12:56