Rhombohedral Edge Length of Truncated Rhombohedron Given Total Surface Area Calculator

Formula Used:

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

Rhombohedral Edge Length:

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1. What is Rhombohedral Edge Length of Truncated Rhombohedron?

The Rhombohedral Edge Length of a Truncated Rhombohedron is the length of any edge of the original rhombohedron from which the truncated rhombohedron is formed. It's a fundamental measurement in understanding the geometry of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( l \) — Rhombohedral Edge Length (m)
\( TSA \) — Total Surface Area of the truncated rhombohedron (m²)

Explanation: This formula calculates the edge length of the original rhombohedron based on the total surface area of the truncated rhombohedron, incorporating various geometric constants.

3. Importance of Rhombohedral Edge Length Calculation

Details: Calculating the rhombohedral edge length is essential for understanding the geometric properties of truncated rhombohedrons, which have applications in crystallography, material science, and architectural design.

4. Using the Calculator

Tips: Enter the total surface area of the truncated rhombohedron in square meters. The value must be positive and greater than zero.

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 hexagonal and triangular faces.

Q2: What are the units for the input and output?
A: The input (total surface area) should be in square meters (m²), and the output (edge length) will be in meters (m).

Q3: Can this calculator handle very large or very small values?
A: Yes, the calculator can handle a wide range of values, but extremely large or small values may be limited by PHP's floating-point precision.

Q4: What if I get an error or unexpected result?
A: Ensure you've entered a valid positive number for the total surface area. Negative values or zero will not produce valid results.

Q5: Are there any limitations to this calculation?
A: This calculation assumes a perfect geometric form and may not account for real-world imperfections in physical objects.