1. What is 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 dodecahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Circumsphere Radius \) — Radius of the sphere that contains the truncated dodecahedron
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the edge length based on the circumsphere radius using the mathematical relationship specific to truncated dodecahedrons.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for geometric analysis, 3D modeling, architectural design, and understanding the properties of this specific polyhedron in mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid 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: How is this formula derived?
A: The formula is derived from the geometric properties and trigonometric relationships within the truncated dodecahedron structure.

Q3: What are practical applications of this calculation?
A: This calculation is used in crystallography, architectural design, 3D computer graphics, and mathematical research involving polyhedra.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters before calculation.

Q5: What is the accuracy of this calculation?
A: The calculation provides results accurate to 6 decimal places, which is sufficient for most practical applications.