Midsphere Radius of Deltoidal Hexecontahedron given NonSymmetry Diagonal Calculator

Formula Used:

\[ r_m = \frac{3}{20} \times (5 + 3\sqrt{5}) \times \frac{11 \times d_{NonSymmetry}}{\sqrt{\frac{470 + 156\sqrt{5}}{5}}} \]

Midsphere Radius of Deltoidal Hexecontahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Midsphere Radius of Deltoidal Hexecontahedron?

The Midsphere Radius of a Deltoidal Hexecontahedron is the radius of the sphere that is tangent to all edges of the polyhedron. It represents the distance from the center of the polyhedron to the point where the sphere touches the midpoints of its edges.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_m = \frac{3}{20} \times (5 + 3\sqrt{5}) \times \frac{11 \times d_{NonSymmetry}}{\sqrt{\frac{470 + 156\sqrt{5}}{5}}} \]

Where:

\( r_m \) — Midsphere Radius of Deltoidal Hexecontahedron (m)
\( d_{NonSymmetry} \) — NonSymmetry Diagonal of Deltoidal Hexecontahedron (m)

Explanation: This formula calculates the midsphere radius based on the non-symmetry diagonal length, incorporating mathematical constants and geometric relationships specific to the deltoidal hexecontahedron.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and crystallography for understanding the spatial properties and symmetry of the deltoidal hexecontahedron, which has applications in material science and mathematical modeling.

4. Using the Calculator

Tips: Enter the NonSymmetry Diagonal length in meters. The value must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a Catalan solid with 60 deltoid faces, 120 edges, and 62 vertices. It is the dual polyhedron of the rhombicosidodecahedron.

Q2: What is the significance of the midsphere?
A: The midsphere (or intersphere) is important in polyhedral geometry as it touches all edges of the polyhedron, providing insight into the polyhedron's symmetry and spatial relationships.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact based on the given formula, assuming precise input values and proper implementation of the mathematical operations.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the deltoidal hexecontahedron. Other polyhedra have different formulas for calculating their midsphere radii.

Q5: What are practical applications of this calculation?
A: This calculation is used in mathematical research, computer graphics, crystallography, and the study of geometric properties of complex polyhedra.