1. What is the Insphere Radius of Rhombic Triacontahedron?

The Insphere Radius of a Rhombic Triacontahedron is the radius of the sphere that is contained within the polyhedron such that it touches all the faces of the Rhombic Triacontahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius of Rhombic Triacontahedron (m)
• \( r_m \) — Midsphere Radius of Rhombic Triacontahedron (m)
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the insphere radius from the given midsphere radius using geometric relationships specific to the Rhombic Triacontahedron.

3. Importance of Insphere Radius Calculation

Details: The insphere radius is important in geometry and materials science for understanding the packing properties and spatial relationships within the Rhombic Triacontahedron structure.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombic Triacontahedron?
A: A Rhombic Triacontahedron is a convex polyhedron with 30 rhombic faces. It is one of the Catalan solids and is the dual polyhedron of the icosidodecahedron.

Q2: What is the relationship between insphere and midsphere radii?
A: The insphere radius is always smaller than the midsphere radius in a Rhombic Triacontahedron, and their ratio is determined by the geometric properties of the shape.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Rhombic Triacontahedron due to its unique geometric properties.

Q4: What are practical applications of this calculation?
A: This calculation is used in crystallography, nanotechnology, and materials science where Rhombic Triacontahedron structures occur.

Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect Rhombic Triacontahedron and provides precise results when accurate inputs are provided.