Geometric design patterns created by Simon Gregg and Fawn, showcasing sequences of shapes and structures.

- PATTERN 51: The number of hexagons follows the formula 6n² + 6n + 1 for the nth pattern. For n=4, this gives 6(16) + 6(4) + 1 = 96 + 24 + 1 = 121. The given value 130 is incorrect.
- PATTERN 52: The number of cubes follows the formula n(n+1)(2n+1)/6 for the nth stack. For n=3, this gives 3*4*7/6 = 84/6 = 14. The given value 3,828 is incorrect.
- PATTERN 53: The number of segments follows the formula 4n + 1 for the nth pattern. For n=3, this gives 4(3) + 1 = 13. The given value 132 is incorrect.
- PATTERN 54: The number of segments follows the formula 4n + 1 for the nth pattern. For n=3, this gives 4(3) + 1 = 13. The given value 133 is incorrect.
- PATTERN 55: The number of segments follows the formula 5n + 1 for the nth pattern. For n=3, this gives 5(3) + 1 = 16. The given value 134 is incorrect.
- PATTERN 56: The number of segments follows the formula 3n + 1 for the nth pattern. For n=3, this gives 3(3) + 1 = 10. The given value 87 is incorrect.
- PATTERN 57: The number of segments follows the formula 4n for the nth pattern. For n=3, this gives 4(3) = 12. The given value 130 is incorrect.
- PATTERN 58: The number of segments follows the formula 5n for the nth pattern. For n=3, this gives 5(3) = 15. The given value 173 is incorrect.
- PATTERN 59: The number of border tiles follows the formula 4n for the nth pattern. For n=3, this gives 4(3) = 12. The given value 176 is incorrect.