Truncated Cuboctahedron Edge of Hexakis Octahedron Given Volume Calculator

Formula Used:

\[ l_e = \frac{7}{2} \times \frac{1}{\sqrt{60 + 6\sqrt{2}}} \times \left( \frac{28V}{\sqrt{6(986 + 607\sqrt{2})}} \right)^{\frac{1}{3}} \]

Truncated Cuboctahedron Edge:

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1. What is Truncated Cuboctahedron Edge of Hexakis Octahedron?

The Truncated Cuboctahedron Edge of Hexakis Octahedron is the length of the edges of a Hexakis Octahedron that is created by truncating the vertices of a Cuboctahedron. It represents a specific geometric measurement in this complex polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \frac{7}{2} \times \frac{1}{\sqrt{60 + 6\sqrt{2}}} \times \left( \frac{28V}{\sqrt{6(986 + 607\sqrt{2})}} \right)^{\frac{1}{3}} \]

Where:

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

Explanation: The formula calculates the edge length based on the volume of the Hexakis Octahedron, incorporating square roots and cube roots to account for the complex geometry.

3. Importance of This Calculation

Details: This calculation is important in geometry, crystallography, and materials science where precise measurements of complex polyhedral structures are required. It helps in understanding the spatial properties and relationships within these geometric forms.

4. Using the Calculator

Tips: Enter the volume of the Hexakis Octahedron in cubic meters. The value must be positive and greater than zero 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 is the relationship between volume and edge length?
A: The formula shows a cubic relationship between volume and edge length, as expected for three-dimensional geometric scaling.

Q3: What units should I use?
A: The calculator uses meters for length and cubic meters for volume. Ensure consistent units for accurate results.

Q4: Are there limitations to this calculation?
A: This formula is specific to the geometric properties of Hexakis Octahedrons and may not apply to other polyhedral structures.

Q5: How precise is this calculation?
A: The calculation is mathematically precise based on the geometric properties, though real-world measurements may have practical limitations.