Volume Of Hexakis Octahedron Given Truncated Cuboctahedron Edge Calculator

Volume of Hexakis Octahedron Formula:

\[ V = \frac{\sqrt{6(986+607\sqrt{2})}}{28} \times \frac{8}{343} \times (60+6\sqrt{2})^{\frac{3}{2}} \times l_{e(Truncated\ Cuboctahedron)}^3 \]

Volume of Hexakis Octahedron:

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1. What is the 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 is calculated based on the truncated cuboctahedron edge length using a specific mathematical formula.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{\sqrt{6(986+607\sqrt{2})}}{28} \times \frac{8}{343} \times (60+6\sqrt{2})^{\frac{3}{2}} \times l_{e(Truncated\ Cuboctahedron)}^3 \]

Where:

\( V \) — Volume of Hexakis Octahedron (m³)
\( l_{e(Truncated\ Cuboctahedron)} \) — Truncated Cuboctahedron Edge of Hexakis Octahedron (m)
\( \sqrt{} \) — Square root function

Explanation: The formula combines multiple mathematical operations including square roots, exponents, and multiplication to compute the volume based on the given edge length.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes like Hexakis Octahedron is crucial in various fields including mathematics, engineering, architecture, and material science for understanding spatial properties and capacity.

4. Using the Calculator

Tips: Enter the truncated cuboctahedron edge length in meters. The value must be positive and valid for accurate calculation.

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: What units should I use for input?
A: The calculator expects the edge length in meters (m), and returns volume in cubic meters (m³).

Q3: Can I use other units for calculation?
A: You can use other units, but you'll need to convert the result accordingly. The formula is dimensionally consistent.

Q4: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision for accurate representation.

Q5: Are there any limitations to this formula?
A: The formula is mathematically derived and accurate for all valid positive edge length values of Hexakis Octahedron.