1. What is the Insphere Radius of Rhombic Dodecahedron?

The Insphere Radius of a Rhombic Dodecahedron is the radius of the largest sphere that can be inscribed within the polyhedron, touching all its faces. It represents the distance from the center of the polyhedron to the center of any face.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere radius (m)
• \( TSA \) — Total surface area of the rhombic dodecahedron (m²)
• \( \sqrt{6} \) — Square root of 6 (≈2.449)
• \( \sqrt{2} \) — Square root of 2 (≈1.414)

Explanation: This formula calculates the radius of the inscribed sphere based on the total surface area of the rhombic dodecahedron, using mathematical constants and geometric relationships.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry, materials science, and crystallography for understanding the packing efficiency and spatial relationships within polyhedral structures.

4. Using the Calculator

Tips: Enter the total surface area of the rhombic dodecahedron in square meters. The value must be positive and greater than zero.

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's a Catalan solid and the dual polyhedron of the cuboctahedron.

Q2: What are the applications of this calculation?
A: This calculation is used in crystallography, materials science, and geometry to understand atomic packing, material properties, and spatial relationships in polyhedral structures.

Q3: How accurate is this formula?
A: The formula is mathematically exact for perfect rhombic dodecahedrons and provides precise results when accurate measurements are input.

Q4: Can this calculator be used for other polyhedrons?
A: No, this specific formula applies only to rhombic dodecahedrons. Other polyhedrons have different formulas for calculating their insphere radii.

Q5: What units should I use for the surface area?
A: The calculator expects square meters, but you can use any consistent area unit as long as you interpret the result in the corresponding length unit.