Volume Of Hexakis Octahedron Given Surface To Volume Ratio Calculator

Formula Used:

\[ V = \frac{\sqrt{6(986+607\sqrt{2})}}{28} \times \left( \frac{12\sqrt{543+176\sqrt{2}}}{RA/V \times \sqrt{6(986+607\sqrt{2})}} \right)^3 \]

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 is a geometric measurement that represents the capacity of this particular polyhedral shape.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ V = \frac{\sqrt{6(986+607\sqrt{2})}}{28} \times \left( \frac{12\sqrt{543+176\sqrt{2}}}{RA/V \times \sqrt{6(986+607\sqrt{2})}} \right)^3 \]

Where:

\( V \) — Volume of Hexakis Octahedron (m³)
\( RA/V \) — Surface to Volume Ratio of Hexakis Octahedron (1/m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the volume of a Hexakis Octahedron based on its surface to volume ratio, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Volume Calculation

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

4. Using the Calculator

Tips: Enter the surface to volume ratio value in 1/m. The value must be positive and greater than zero. The calculator will compute the corresponding volume of the Hexakis Octahedron.

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: What units should I use for the surface to volume ratio?
A: The surface to volume ratio should be entered in reciprocal meters (1/m), and the resulting volume will be in cubic meters (m³).

Q3: Can this calculator handle very small or very large values?
A: The calculator can handle a wide range of values, but extremely small values may approach computational limits due to floating-point precision.

Q4: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the specific dimensions of the Hexakis Octahedron. There's no fixed "typical" value as it varies with the size and proportions of the polyhedron.

Q5: Is this formula applicable to all Hexakis Octahedra?
A: Yes, this formula is derived from the geometric properties of the Hexakis Octahedron and applies to all regular Hexakis Octahedra.