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Cake number C₆
C₆ = 42
Calculated
Maximum pieces of a cube (or cake) cut by 6 planes in general position
Six flat cuts through a cake, as many pieces as possible: 42. Named, exact, one term of a sequence. Not Catalan.
What it supports
C_n = n(n²+5)/6 + 1 = (n³ + 5n + 6)/6. Sequence 1, 2, 4, 8, 15, 26, 42, 64, … (OEIS A000125). C₆ = 42. Equivalently the first four entries of Pascal row 6: 1 + 6 + 15 + 20 = 42.
What it does not
Not “the” cake number. Not Catalan C₅. Different geometry: plane cuts, not polygon triangulations. Every integer appears somewhere in C_n. Keep because the object is independently named.
Calculation
C₆ = (216 + 30 + 6)/6 = 252/6 = 42. Pascal row 6: 1+6+15+20 = 42.
Maximum regions of a cube by n planes in general position.
ExactnessExact
Form42
Unitregions
Strengthhard