1. What is the Insphere Radius of Deltoidal Hexecontahedron?

The Insphere Radius of a Deltoidal Hexecontahedron is the radius of the sphere that is contained within the polyhedron such that it is tangent to all the faces. It represents the largest sphere that can fit inside the Deltoidal Hexecontahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius (m)
• \( r_m \) — Midsphere Radius (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula establishes the mathematical relationship between the insphere radius and midsphere radius of a Deltoidal Hexecontahedron, incorporating the golden ratio through the square root of 5.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and materials science for understanding the spatial properties of polyhedra, determining packing efficiency, and analyzing the structural characteristics of Deltoidal Hexecontahedron-shaped objects.

4. Using the Calculator

Tips: Enter the midsphere radius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding insphere radius using the mathematical relationship between these two parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a polyhedron with 60 deltoid (kite-shaped) faces. It is one of the Catalan solids, dual to the rhombicosidodecahedron.

Q2: How is the insphere radius different from the midsphere radius?
A: The insphere radius is the radius of the sphere tangent to all faces, while the midsphere radius is the radius of the sphere tangent to all edges of the polyhedron.

Q3: What are typical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, architectural design, and any field dealing with complex polyhedral structures.

Q4: How accurate is this formula?
A: The formula is mathematically exact for a perfect Deltoidal Hexecontahedron. The accuracy of the result depends on the precision of the input value.

Q5: Can this calculator handle very large or very small values?
A: Yes, the calculator can process any positive numerical value, though extremely large or small values may be limited by PHP's floating-point precision.