Volume of Hexakis Octahedron Calculator

Volume of Hexakis Octahedron Formula:

\[ V = \frac{(le_{Long})^3 \times \sqrt{6 \times (986 + 607 \times \sqrt{2})}}{28} \]

Volume of Hexakis Octahedron:

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1. What is Volume of Hexakis Octahedron?

The Volume of Hexakis Octahedron is the quantity of three dimensional space enclosed by the entire surface of Hexakis Octahedron. It represents the total capacity or space occupied by this complex polyhedral shape.

2. How Does the Calculator Work?

The calculator uses the Hexakis Octahedron volume formula:

\[ V = \frac{(le_{Long})^3 \times \sqrt{6 \times (986 + 607 \times \sqrt{2})}}{28} \]

Where:

\( V \) — Volume of Hexakis Octahedron (m³)
\( le_{Long} \) — Long Edge of Hexakis Octahedron (m)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the volume based on the cube of the long edge length multiplied by a complex constant derived from the geometric properties of the Hexakis Octahedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. For complex polyhedra like the Hexakis Octahedron, volume calculation helps in material estimation, structural analysis, and spatial planning applications.

4. Using the Calculator

Tips: Enter the Long Edge of Hexakis Octahedron in meters. The value must be positive and greater than zero. The calculator will compute the volume using the precise mathematical formula.

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 cuboctahedron. It has 48 faces, 72 edges, and 26 vertices.

Q2: Why is the formula so complex?
A: The complexity arises from the irregular nature of the Hexakis Octahedron and the mathematical relationships between its edges, faces, and volume in three-dimensional space.

Q3: What units should I use for input?
A: The calculator expects meters as input, but you can use any consistent unit of length as the volume will scale accordingly (e.g., cm input gives cm³ output).

Q4: How accurate is this calculation?
A: The calculation is mathematically precise based on the formula, limited only by the precision of your input value and computational floating-point arithmetic.

Q5: Can this calculator handle very large or small values?
A: Yes, the calculator can handle a wide range of values, though extremely large or small numbers may be limited by PHP's floating-point precision.