Edge Length of Truncated Rhombohedron given Circumsphere Radius Calculator

Formula Used:

\[ l_e = \frac{3-\sqrt{5}}{2} \times \frac{4 \times r_c}{\sqrt{14-2\sqrt{5}}} \]

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 of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \frac{3-\sqrt{5}}{2} \times \frac{4 \times r_c}{\sqrt{14-2\sqrt{5}}} \]

Where:

\( l_e \) — Edge Length of Truncated Rhombohedron (m)
\( r_c \) — Circumsphere Radius of Truncated Rhombohedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the edge length based on the circumsphere radius, using the mathematical relationship derived from the geometry of the truncated rhombohedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties of the truncated rhombohedron, including its surface area, volume, and other dimensional characteristics.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding edge length of the truncated rhombohedron.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the Circumsphere Radius?
A: The circumsphere radius is the radius of the sphere that contains the truncated rhombohedron such that all vertices lie on the sphere's surface.

Q3: What are typical values for Edge Length?
A: The edge length depends on the specific dimensions of the truncated rhombohedron and can vary based on the circumsphere radius.

Q4: Are there limitations to this formula?
A: This formula is specifically derived for truncated rhombohedrons and assumes perfect geometric proportions.

Q5: Can this calculator be used for other polyhedrons?
A: No, this calculator is specifically designed for truncated rhombohedrons. Other polyhedrons require different formulas.