Edge Length of Truncated Rhombohedron given Total Surface Area Calculator

Formula Used:

\[ l_e = \frac{3-\sqrt{5}}{2} \times \sqrt{\frac{2 \times TSA}{3 \times \sqrt{5+2\sqrt{5}} + 5\sqrt{3} - 2\sqrt{15}}} \]

Edge Length of Truncated Rhombohedron:

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1. What is the Edge Length of Truncated Rhombohedron?

The Edge Length of Truncated Rhombohedron is the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron. It is a fundamental geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \frac{3-\sqrt{5}}{2} \times \sqrt{\frac{2 \times TSA}{3 \times \sqrt{5+2\sqrt{5}} + 5\sqrt{3} - 2\sqrt{15}}} \]

Where:

\( l_e \) — Edge Length of Truncated Rhombohedron (m)
\( TSA \) — Total Surface Area of Truncated Rhombohedron (m²)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the edge length based on the total surface area of the truncated rhombohedron, incorporating various square root terms to account for the complex geometry.

3. Importance of Edge Length Calculation

Details: Accurate calculation of edge length is crucial for understanding the geometric properties of truncated rhombohedrons, which are used in crystallography, material science, and architectural design.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Rhombohedron?
A: A truncated rhombohedron is a polyhedron obtained by cutting the corners of a rhombohedron, resulting in a shape with both triangular and rhombohedral faces.

Q2: What units should be used for input?
A: The calculator uses square meters for surface area input, but consistent units should be maintained throughout calculations.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula is derived for truncated rhombohedrons and may not apply to other geometric shapes.

Q4: What is the precision of the calculation?
A: The calculator provides results with 10 decimal places precision, suitable for most engineering and mathematical applications.

Q5: Are there any limitations to this calculation?
A: The formula assumes a perfect geometric shape and may not account for manufacturing tolerances or material deformations in practical applications.