1. What is the Edge Length of Dodecahedron?

The edge length of a dodecahedron is the length of any of the edges of this regular polyhedron, which consists of 12 regular pentagonal faces, 20 vertices, and 30 edges. It is a fundamental geometric measurement for this three-dimensional shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Midsphere Radius — The radius of the sphere that is tangent to all edges of the dodecahedron
• √5 — Square root of 5 (approximately 2.23607)

Explanation: This formula establishes the mathematical relationship between the midsphere radius and the edge length of a regular dodecahedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from the midsphere radius is essential in geometry, 3D modeling, material science, and architectural design where dodecahedral structures are used.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a dodecahedron?
A: A dodecahedron is a regular polyhedron with 12 pentagonal faces, 20 vertices, and 30 edges. It is one of the five Platonic solids.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the dodecahedron, also known as the "edge-tangent sphere."

Q3: Can this formula be used for irregular dodecahedrons?
A: No, this formula applies only to regular dodecahedrons where all edges are equal and all faces are regular pentagons.

Q4: What are practical applications of dodecahedrons?
A: Dodecahedrons are used in various fields including crystallography, game design (dice), architecture, and molecular modeling.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect regular dodecahedrons, with accuracy limited only by the precision of the input values and computational rounding.