1. What is the Edge Length of Rhombic Dodecahedron?

The Edge Length of a Rhombic Dodecahedron is the length of any of the edges of this polyhedron or the distance between any pair of adjacent vertices. It is a fundamental geometric measurement used in crystallography and materials science.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Rhombic Dodecahedron (m)
• \( r_m \) — Midsphere Radius of Rhombic Dodecahedron (m)

Explanation: This formula calculates the edge length based on the midsphere radius, which is the radius of the sphere tangent to all edges of the polyhedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties, volume, surface area, and other characteristics of rhombic dodecahedrons, which are important in crystal structures and material packing.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombic Dodecahedron?
A: A rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It is a Catalan solid and the dual polyhedron of the cuboctahedron.

Q2: What is the Midsphere Radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: What are typical applications of Rhombic Dodecahedrons?
A: They are used in crystallography, particularly in the study of garnet crystals, and in materials science for packing problems.

Q4: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to rhombic dodecahedrons. Other polyhedrons have different relationships between edge length and midsphere radius.

Q5: What units should be used?
A: The calculator uses meters, but any consistent unit of length can be used as long as both input and output are in the same units.