Truncated Cuboctahedron Edge of Hexakis Octahedron given Total Surface Area Calculator

Formula Used:

\[ le(Truncated Cuboctahedron) = \sqrt{\frac{7 \times 49 \times TSA}{12 \times (60 + (6 \times \sqrt{2})) \times \sqrt{543 + (176 \times \sqrt{2})}}} \]

Truncated Cuboctahedron Edge of Hexakis Octahedron:

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1. What is the 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 polyhedral geometry.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ le(Truncated Cuboctahedron) = \sqrt{\frac{7 \times 49 \times TSA}{12 \times (60 + (6 \times \sqrt{2})) \times \sqrt{543 + (176 \times \sqrt{2})}}} \]

Where:

\( le(Truncated Cuboctahedron) \) — Truncated Cuboctahedron Edge length (m)
\( TSA \) — Total Surface Area of Hexakis Octahedron (m²)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the edge length based on the total surface area of the Hexakis Octahedron, incorporating mathematical constants and geometric relationships.

3. Importance of Truncated Cuboctahedron Edge Calculation

Details: Calculating the truncated cuboctahedron edge is important in geometric modeling, architectural design, and mathematical research involving polyhedral structures. It helps in understanding the properties and relationships between different geometric forms.

4. Using the Calculator

Tips: Enter the total surface area of the Hexakis Octahedron in square 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, featuring 48 faces that are irregular triangles.

Q2: What is the relationship between surface area and edge length?
A: The edge length can be derived from the total surface area through specific geometric formulas that account for the polyhedron's structure and symmetry.

Q3: What are typical values for Truncated Cuboctahedron Edge?
A: The edge length varies depending on the size of the polyhedron, typically ranging from millimeters to meters depending on the application.

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect geometric form and may not account for manufacturing tolerances or material properties in real-world applications.

Q5: Can this formula be used for other polyhedral calculations?
A: This specific formula is designed for Hexakis Octahedron geometry and may not be directly applicable to other polyhedral forms without modification.