Edge Length of Truncated Rhombohedron given Surface to Volume Ratio Calculator

Formula Used:

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

Edge Length (l_e):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Edge Length of Truncated Rhombohedron?

The edge length of a 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 complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

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

Where:

\( l_e \) — Edge length of truncated rhombohedron (m)
\( \frac{R_A}{V} \) — Surface to volume ratio (m⁻¹)
\( \sqrt{5}, \sqrt{3}, \sqrt{15} \) — Mathematical constants

Explanation: This complex formula relates the edge length to the surface-to-volume ratio through various mathematical constants and operations.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is crucial for understanding the geometric properties, volume, surface area, and other characteristics of truncated rhombohedrons in mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the surface to volume ratio in m⁻¹. The value must be positive and valid for accurate calculation of the edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated rhombohedron?
A: A truncated rhombohedron is a complex polyhedron formed by truncating the vertices of a rhombohedron, creating new triangular faces at the truncated vertices.

Q2: What units should I use for the surface to volume ratio?
A: The calculator uses meters for length units, so surface to volume ratio should be in m⁻¹ (inverse meters).

Q3: Can this calculator handle very small or very large values?
A: The calculator can handle a wide range of values, but extremely small or large values may affect computational precision.

Q4: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the specific geometry and size of the truncated rhombohedron, and can vary significantly.

Q5: Is this formula applicable to all truncated rhombohedrons?
A: This specific formula applies to truncated rhombohedrons with the particular geometric properties described by this mathematical relationship.