1. What is Insphere Radius of Rhombic Dodecahedron?

The Insphere Radius of Rhombic Dodecahedron is the radius of the sphere that is contained by the Rhombic Dodecahedron in such a way that all the faces are just touching the sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius of Rhombic Dodecahedron (m)
• \( RA/V \) — Surface to Volume Ratio of Rhombic Dodecahedron (1/m)

Explanation: The formula calculates the insphere radius by taking the reciprocal of the surface to volume ratio and multiplying by 3.

3. Importance of Insphere Radius Calculation

Details: The insphere radius is important in geometry and materials science for understanding the packing efficiency and spatial properties of rhombic dodecahedron structures.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombic Dodecahedron?
A: A rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces, 24 edges, and 14 vertices.

Q2: What are typical values for surface to volume ratio?
A: The surface to volume ratio varies depending on the size and dimensions of the rhombic dodecahedron, but is always a positive value.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the rhombic dodecahedron. Other polyhedra have different relationships between insphere radius and surface to volume ratio.

Q4: What units should be used?
A: Consistent units must be used throughout. If surface to volume ratio is in 1/meter, the insphere radius will be in meters.

Q5: Are there limitations to this formula?
A: This formula assumes a perfect rhombic dodecahedron shape and may not apply to irregular or deformed structures.