Volume Of Hexakis Octahedron Given Insphere Radius Calculator

Formula Used:

\[ V = \frac{\sqrt{6(986+607\sqrt{2})}}{28} \times \left( \frac{2r_i}{\sqrt{\frac{402+195\sqrt{2}}{194}}} \right)^3 \]

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's a geometric property that describes the capacity of this particular polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{\sqrt{6(986+607\sqrt{2})}}{28} \times \left( \frac{2r_i}{\sqrt{\frac{402+195\sqrt{2}}{194}}} \right)^3 \]

Where:

\( V \) — Volume of Hexakis Octahedron (m³)
\( r_i \) — Insphere Radius of Hexakis Octahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the volume of a Hexakis Octahedron based on its insphere radius, 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 understanding spatial properties, material requirements, and structural characteristics.

4. Using the Calculator

Tips: Enter the insphere radius in meters. 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 cuboctahedron. It has 48 faces, 72 edges, and 26 vertices.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can be contained within the polyhedron, touching all its faces.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first or adjust the result accordingly.

Q4: How accurate is the calculation?
A: The calculation uses precise mathematical formulas and provides results accurate to six decimal places.

Q5: What are practical applications of this calculation?
A: This calculation is useful in crystallography, molecular modeling, architectural design, and any field dealing with complex polyhedral structures.