1. What is Face Diagonal of Dodecahedron?

The Face Diagonal of a Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron. It's an important geometric measurement in understanding the properties of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Insphere Radius — The radius of the sphere contained by the Dodecahedron
• √5 — Square root of 5 (approximately 2.23607)

Explanation: This formula relates the face diagonal length to the insphere radius through the mathematical constants and relationships specific to the dodecahedron's geometry.

3. Importance of Face Diagonal Calculation

Details: Calculating the face diagonal is crucial for understanding the spatial properties of dodecahedrons, which have applications in geometry, crystallography, and various engineering fields.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and non-zero. The calculator will compute the corresponding face diagonal length.

5. Frequently Asked Questions (FAQ)

Q1: What is a dodecahedron?
A: A dodecahedron is a three-dimensional shape with twelve flat faces, each being a regular pentagon.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can fit inside the dodecahedron, touching all faces.

Q3: Are there other ways to calculate face diagonal?
A: Yes, the face diagonal can also be calculated using edge length or circumsphere radius through different formulas.

Q4: What are practical applications of this calculation?
A: This calculation is used in geometry research, architectural design, and in understanding molecular structures in chemistry.

Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect regular dodecahedrons and provides precise calculations.