Midsphere Radius of Deltoidal Hexecontahedron Calculator

Midsphere Radius of Deltoidal Hexecontahedron Formula:

\[ r_m = \frac{3}{20} \times (5 + 3\sqrt{5}) \times l_e \]

Midsphere Radius of Deltoidal Hexecontahedron:

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1. What is 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:

\[ r_m = \frac{3}{20} \times (5 + 3\sqrt{5}) \times l_e \]

Where:

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

Explanation: The formula calculates the midsphere radius based on the long edge length of the deltoidal hexecontahedron, incorporating the mathematical constant √5.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of deltoidal hexecontahedrons. It helps in determining the sphere that touches all edges of this complex polyhedron.

4. Using the Calculator

Tips: Enter the long edge length of the deltoidal hexecontahedron 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. It is one of the Catalan solids.

Q2: What are the applications of this calculation?
A: This calculation is used in geometry, crystallography, architectural design, and 3D modeling where deltoidal hexecontahedrons are involved.

Q3: How accurate is this formula?
A: The formula is mathematically exact for perfect deltoidal hexecontahedrons and provides precise results when correct measurements are used.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters before calculation.

Q5: What is the significance of √5 in this formula?
A: √5 is an irrational number that appears frequently in geometry calculations involving pentagonal symmetry, which is characteristic of deltoidal hexecontahedrons.