Solution: A regular octahedron has 8 equilateral triangular faces. The area of one face is $\frac{\sqrt{3}}{4} \times 4^2 = 4\sqrt{3}$. Total surface area: $8 \times 4\sqrt{3} = 32\sqrt{3}$ nm².

["Understanding the Surface Area of a Regular Octahedron", "When exploring geometric shapes, the regular octahedron stands out for its symmetrical beauty and unique structure. A regular octahedron consists of 8 identical equilateral triangular faces, each sharing edges equally with its neighbors. This elegant polyhedron is not only fascinating in geometry but also relevant in fields like chemistry, architecture, and design.", "### What Is a Regular Octahedron?", "A regular octahedron is a three-dimensional shape with 8 equilateral triangular faces, 6 vertices, and 12 equal-length edges. Each internal angle of an equilateral triangle measures 60°, giving the octahedron its smooth, balanced form. It is one of the five Platonic solids, renowned for their perfect symmetry and uniformity.", "### Calculating the Area of One Face", "Each face of the regular octahedron is an equilateral triangle. The formula for the area ( A ) of an equilateral triangle with side length ( s ) is:", "[\nA = \frac{\sqrt{3}}{4} s^2\n]", "In the case of a regular octahedron with side length ( s = 4 ), substituting into the formula gives:", "[\nA = \frac{\sqrt{3}}{4} \ imes 4^2 = \frac{\sqrt{3}}{4} \ imes 16 = 4\sqrt{3} \ ext{ nm}^2\n]", "So, each triangular face has an area of ( 4\sqrt{3} ) square nanometers (nm²).", "### Total Surface Area of the Octahedron", "Since a regular octahedron has 8 identical faces, the total surface area ( S ) is simply:", "[\nS = 8 \ imes 4\sqrt{3} = 32\sqrt{3} \ ext{ nm}^2\n]", "This computation reveals the octahedron’s total exposed area—a key metric in engineering, material science, and modeling.", "### Why Surface Area Matters", "Knowing the surface area of a regular octahedron supports practical applications such as determining surface coatings, heat exchange efficiency, and structural load distribution. In science, this geometry appears in molecular structures like certain fullerenes, while in art and design, it inspires visually compelling and structurally sound forms.", "### Summary", "A regular octahedron with side length 4 nm features 8 equilateral triangular faces. Each face has an area of ( 4\sqrt{3} ) nm², and the full total surface area reaches ( 32\sqrt{3} ) nm². Understanding this geometric property enhances both theoretical knowledge and practical design capabilities in multiple disciplines.", "---", "Keywords: regular octahedron, surface area formula, equilateral triangle area, octahedron geometry, 8-faced polyhedron, nanometer² surface area."]