So in this puzzle the goal is to come up with an answer that consist of 9 letters. Without giving away anymore info (atleast for now) on how to approach this puzzle I'll let you try make sense of it first.
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The 'family of 7' clued in this puzzle is:
the family of 7 Tetris shapes - otherwise known as tetrominos!
How? First notice that the bottom-right corner shows:
a key, giving the initial letter of what each of the other non-blank squares represents. These are (row by row):
Primes (clued by the top cube of this pyramid, where top is a synonym for prime - though I spent far too long looking at pyramidal numbers!),
Roman numerals (the Roman empire is mapped),
Chemical elements with 1-letter symbols,
Vowels (the 5 crossed spaces correspond to the positions of the 5 vowels in the alphabet if counting from 1 to 26),
Hexadecimal numbers (clued by 'base 16'!).
If we shade the spaces in each box which correspond to these categories, we see the following:
These are the Tetris pieces! (Note that the vowel box uses Braille representation.) In other words, these are the 7 unique shapes (excluding reflection) that can be made from an arrangement of 4 squares.
This means the final 9-letter answer is:
TETROMINO i.e. a shape which can be made from an arrangement of 4 squares.