Edge Length of Truncated Rhombohedron given Triangular Edge Length Calculator

Formula Used:

\[ l_e = \frac{3-\sqrt{5}}{2} \times \frac{l_{e(Triangle)}}{\sqrt{5-2\sqrt{5}}} \]

Edge Length of Truncated Rhombohedron:

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1. What is 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 measurement in this polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ l_e = \frac{3-\sqrt{5}}{2} \times \frac{l_{e(Triangle)}}{\sqrt{5-2\sqrt{5}}} \]

Where:

\( l_e \) — Edge Length of Truncated Rhombohedron (m)
\( l_{e(Triangle)} \) — Triangular Edge Length of Truncated Rhombohedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula establishes the precise mathematical relationship between the triangular edge length and the resulting edge length in a truncated rhombohedron geometry.

3. Importance of Edge Length Calculation

Details: Accurate edge length calculation is crucial for geometric modeling, architectural design, material science applications, and understanding the spatial properties of truncated rhombohedron structures.

4. Using the Calculator

Tips: Enter the triangular edge length in meters. The value must be positive and valid. The calculator will compute the corresponding edge length using the mathematical relationship.

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: Why is the golden ratio (√5) involved in this formula?
A: The golden ratio and its mathematical properties are fundamental to many geometric relationships, including those found in rhombohedral structures.

Q3: What are typical applications of this calculation?
A: This calculation is used in crystallography, architectural design, geometric modeling, and materials science where truncated rhombohedron shapes are encountered.

Q4: How accurate is this formula?
A: The formula is mathematically exact and provides precise results when correct input values are used.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can convert your measurements to meters before input for consistent results.