1. What is the Midsphere Radius of Deltoidal Hexecontahedron?

The Midsphere Radius of Deltoidal Hexecontahedron is the radius of the sphere for which all the edges of the Deltoidal Hexecontahedron become a tangent line on that sphere. It represents the sphere that is tangent to all edges of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the midsphere radius based on the length of the short edge of the deltoidal hexecontahedron, incorporating mathematical constants and geometric relationships.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometric modeling, 3D design, and mathematical analysis of polyhedra. It helps in understanding the spatial properties and relationships of the deltoidal hexecontahedron.

4. Using the Calculator

Tips: Enter the short edge length of the deltoidal hexecontahedron in meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a deltoidal hexecontahedron?
A: A deltoidal hexecontahedron is a polyhedron with 60 deltoidal (kite-shaped) faces. It is one of the Catalan solids.

Q2: What are the applications of this calculation?
A: This calculation is used in geometry research, 3D modeling, architectural design, and mathematical education.

Q3: What units should I use for input?
A: The calculator uses meters as the unit of measurement. Ensure consistent units for accurate results.

Q4: How accurate is this formula?
A: The formula is mathematically exact for the geometric properties of a perfect deltoidal hexecontahedron.

Q5: Can this calculator handle very small or large values?
A: Yes, as long as the input is a positive number, the calculator can handle a wide range of values.