Volume Of Hexakis Octahedron Given Total Surface Area Calculator

Formula Used:

\[ V = \frac{\sqrt{6(986+607\sqrt{2})}}{28} \times \left( \frac{7 \times TSA}{3\sqrt{543+176\sqrt{2}}} \right)^{\frac{3}{2}} \]

Volume of Hexakis Octahedron:

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1. What is the Volume of Hexakis Octahedron?

The volume of a Hexakis Octahedron is the quantity of three dimensional space enclosed by the entire surface of the polyhedron. It represents the total capacity or space occupied by this geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{\sqrt{6(986+607\sqrt{2})}}{28} \times \left( \frac{7 \times TSA}{3\sqrt{543+176\sqrt{2}}} \right)^{\frac{3}{2}} \]

Where:

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

Explanation: This formula calculates the volume of a Hexakis Octahedron based on its total surface area, 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. It helps in understanding spatial relationships, material requirements, and structural properties.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding volume in cubic meters.

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 are the units for the input and output?
A: Input is in square meters (m²) for surface area, and output is in cubic meters (m³) for volume.

Q3: Can this formula be used for any polyhedron?
A: No, this specific formula applies only to Hexakis Octahedrons as it uses constants derived from its unique geometric properties.

Q4: What is the precision of the calculation?
A: The calculator provides results with 4 decimal places precision, which is typically sufficient for most applications.

Q5: Are there alternative methods to calculate the volume?
A: Yes, the volume can also be calculated using other parameters such as edge length or midradius, but this calculator specifically uses the total surface area.