1. What is the Edge Length of Truncated Dodecahedron?

The edge length of a truncated dodecahedron is the measurement of any of its edges. A truncated dodecahedron is an Archimedean solid created by truncating the vertices of a regular dodecahedron, resulting in 20 regular triangular faces and 12 regular decagonal faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge length of truncated dodecahedron (m)
• \( V \) — Volume of truncated dodecahedron (m³)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the edge length from the given volume using the mathematical relationship specific to truncated dodecahedrons.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for geometric analysis, architectural design, and understanding the properties of this particular polyhedron in three-dimensional space.

4. Using the Calculator

Tips: Enter the volume of the truncated dodecahedron in cubic meters. The volume must be a positive value greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated dodecahedron?
A: A truncated dodecahedron is an Archimedean solid with 32 faces - 20 equilateral triangles and 12 regular decagons.

Q2: How many edges does a truncated dodecahedron have?
A: A truncated dodecahedron has 90 edges of equal length.

Q3: What are the applications of truncated dodecahedrons?
A: They are used in architecture, molecular modeling, and as dice in certain tabletop games due to their geometric properties.

Q4: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to truncated dodecahedrons. Other polyhedrons have different volume-to-edge relationships.

Q5: What if I have the edge length and want to find the volume?
A: The formula can be rearranged to calculate volume from edge length: \( V = \frac{5 \times (99 + 47 \times \sqrt{5}) \times l_e^3}{12} \)