Truncated Cuboctahedron Edge of Hexakis Octahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ \text{Truncated Cuboctahedron Edge} = \frac{12 \cdot \sqrt{543 + 176\sqrt{2}}}{\sqrt{6 \cdot (986 + 607\sqrt{2})}} \cdot \frac{7}{2 \cdot \sqrt{60 + 6\sqrt{2}} \cdot \text{Surface to Volume Ratio}} \]

Truncated Cuboctahedron Edge:

Unit Converter ▲

Unit Converter ▼

From:	To:

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. This geometric measurement is important in advanced polyhedral studies and applications.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

Surface to Volume Ratio (RA/V) — The ratio of surface area to volume of the Hexakis Octahedron
\(\sqrt{}\) — Square root function
Constants derived from geometric properties of the polyhedron

Explanation: The formula calculates the edge length based on the surface to volume ratio, incorporating mathematical constants specific to the geometry of Hexakis Octahedron.

3. Importance of This Calculation

Details: This calculation is crucial for geometric modeling, architectural design, material science applications, and advanced mathematical studies involving polyhedral structures and their properties.

4. Using the Calculator

Tips: Enter the Surface to Volume Ratio value in the input field. The value must be a positive number greater than zero. The calculator will compute the corresponding Truncated Cuboctahedron Edge length.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for Surface to Volume Ratio?
A: The Surface to Volume Ratio should be entered in units of 1/meter (1/m), and the result will be in meters.

Q2: What is the typical range for Surface to Volume Ratio values?
A: The range varies depending on the specific Hexakis Octahedron dimensions, but typically ranges from very small values (for large volumes) to larger values (for small volumes).

Q3: Can this calculator handle very small or very large values?
A: Yes, the calculator can process a wide range of positive values, though extremely small values may approach computational limits.

Q4: What are the mathematical constants in the formula derived from?
A: The constants (543, 176, 986, 607, etc.) are derived from the specific geometric properties and relationships within the Hexakis Octahedron structure.

Q5: Is this calculation applicable to other polyhedral shapes?
A: No, this specific formula is designed specifically for the Truncated Cuboctahedron Edge of Hexakis Octahedron and its relationship to the surface to volume ratio.