1. What is the Total Surface Area of Hexakis Octahedron?

The Total Surface Area (TSA) of a Hexakis Octahedron is the total area of all its faces. It is a measure of the complete outer surface of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area (m²)
• \( V \) — Volume of Hexakis Octahedron (m³)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the total surface area based on the volume of the Hexakis Octahedron, using mathematical constants and relationships specific to this geometric shape.

3. Importance of TSA Calculation

Details: Calculating the total surface area is important in various fields including geometry, material science, and engineering where surface properties affect material behavior, heat transfer, and other physical characteristics.

4. Using the Calculator

Tips: Enter the volume of the Hexakis Octahedron in cubic meters. The volume must be a positive value greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Octahedron?
A: A Hexakis Octahedron is a Catalan solid that is the dual of the truncated cube. It has 48 faces, 72 edges, and 26 vertices.

Q2: Why is the formula so complex?
A: The complexity arises from the mathematical relationships between volume and surface area in this specific polyhedral shape, which involves irrational numbers and fractional exponents.

Q3: What are typical TSA values?
A: TSA values depend entirely on the volume. Larger volumes will produce larger surface areas, following the mathematical relationship defined by the formula.

Q4: Are there limitations to this formula?
A: This formula is specifically designed for perfect Hexakis Octahedrons. It may not be accurate for irregular or deformed shapes.

Q5: Can this calculator handle very large or small volumes?
A: The calculator should work for any positive volume value, though extremely large or small values may be limited by PHP's floating point precision.