1. What is the Edge Length of Truncated Dodecahedron?

The Edge Length of a Truncated Dodecahedron is the length of any edge of this polyhedron. A truncated dodecahedron is an Archimedean solid created by truncating the vertices of a regular dodecahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( le \) — Edge Length of Truncated Dodecahedron (m)
• \( RA/V \) — Surface to Volume Ratio of Truncated Dodecahedron (1/m)
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the edge length based on the surface to volume ratio of a truncated dodecahedron, incorporating mathematical constants and square roots.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties of truncated dodecahedrons, which have applications in architecture, crystallography, and mathematical modeling.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated dodecahedron?
A: A truncated dodecahedron is an Archimedean solid with 20 regular triangular faces, 12 regular decagonal faces, 60 vertices, and 90 edges.

Q2: What are typical values for surface to volume ratio?
A: The surface to volume ratio varies depending on the size of the polyhedron, with smaller polyhedrons having higher ratios.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula is designed only for truncated dodecahedrons. Other polyhedrons have different geometric relationships.

Q4: What units should I use?
A: The calculator uses meters for length and 1/m for surface to volume ratio. Ensure consistent units for accurate results.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of truncated dodecahedrons, assuming precise input values.