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

Explanation: This formula establishes a direct proportional relationship between the insphere radius and midsphere radius of a rhombic dodecahedron, with a constant factor of √3/2.

3. Importance of Insphere Radius Calculation

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

4. Using the Calculator

Tips: Enter the midsphere radius value 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 polyhedron with 12 congruent rhombic faces, 14 vertices, and 24 edges. It's a Catalan solid and the dual polyhedron of the cuboctahedron.

Q2: What is the relationship between insphere and midsphere radii?
A: The insphere radius is exactly √3/2 times the midsphere radius for a rhombic dodecahedron.

Q3: Can this formula be used for other polyhedra?
A: No, this specific relationship is unique to the rhombic dodecahedron due to its particular geometric properties.

Q4: What are practical applications of this calculation?
A: This calculation is used in crystallography, materials science, and geometry research involving close-packing structures and space-filling polyhedra.

Q5: How accurate is this formula?
A: The formula is mathematically exact and provides precise results for any valid input value.