1. What is Insphere Radius of Deltoidal Hexecontahedron?

The Insphere Radius of Deltoidal Hexecontahedron is the radius of the sphere that is contained by the Deltoidal Hexecontahedron in such a way that all the faces just touch the sphere. It represents the largest sphere that can fit inside this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius (m)
• \( l_e \) — Short Edge of Deltoidal Hexecontahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the radius of the inscribed sphere based on the length of the short edge of the deltoidal hexecontahedron.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and materials science for understanding the spatial properties and packing efficiency of this particular polyhedral shape.

4. Using the Calculator

Tips: Enter the short edge length in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a polyhedron with 60 deltoidal (kite-shaped) faces, 120 edges, and 62 vertices.

Q2: How is the insphere radius different from circumsphere radius?
A: The insphere radius is the radius of the largest sphere that fits inside the polyhedron, while the circumsphere radius is the radius of the smallest sphere that contains the polyhedron.

Q3: What are the practical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, and the study of geometric properties of complex polyhedra.

Q4: Are there any limitations to this formula?
A: This formula is specific to the Deltoidal Hexecontahedron and assumes perfect geometric proportions.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can convert from other units by providing the equivalent value in meters.