1. What is the Edge Length of Snub Dodecahedron?

The Edge Length of Snub Dodecahedron is the length of any edge of the Snub Dodecahedron, a polyhedron with 80 faces (12 pentagons and 20+48 triangles), 150 edges, and 60 vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Snub Dodecahedron (m)
• \( r_c \) — Circumsphere Radius of Snub Dodecahedron (m)

Explanation: This formula calculates the edge length of a snub dodecahedron based on its circumsphere radius using a specific mathematical relationship.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties of the snub dodecahedron, including its surface area, volume, and other dimensional characteristics.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be valid (radius > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is a Snub Dodecahedron?
A: A snub dodecahedron is an Archimedean solid with 80 faces, 150 edges, and 60 vertices, consisting of 12 pentagons and 68 triangles.

Q2: What is the Circumsphere Radius?
A: The circumsphere radius is the radius of the sphere that contains the snub dodecahedron such that all vertices lie on the sphere's surface.

Q3: Are there other ways to calculate edge length?
A: Yes, edge length can also be calculated from other parameters like surface area or volume, but the circumsphere radius provides a direct relationship.

Q4: What are typical applications of this calculation?
A: This calculation is used in geometry, 3D modeling, architectural design, and mathematical research involving polyhedra.

Q5: How accurate is this formula?
A: The formula provides precise mathematical results based on the geometric properties of the snub dodecahedron.