Nonsymmetry Diagonal Of Deltoidal Hexecontahedron Given Midsphere Radius Calculator

Formula Used:

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

NonSymmetry Diagonal of Deltoidal Hexecontahedron:

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1. What is NonSymmetry Diagonal of Deltoidal Hexecontahedron?

The NonSymmetry Diagonal of Deltoidal Hexecontahedron is the length of the diagonal which divides the deltoid faces of Deltoidal Hexecontahedron into two isosceles triangles. It is an important geometric property of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( d_{Non\ Symmetry} \) — NonSymmetry Diagonal of Deltoidal Hexecontahedron (m)
\( r_m \) — Midsphere Radius of Deltoidal Hexecontahedron (m)
\( \sqrt{5} \) — Mathematical constant (approximately 2.23607)

Explanation: This formula calculates the non-symmetry diagonal length based on the midsphere radius of the deltoidal hexecontahedron, incorporating the golden ratio and other mathematical constants specific to this geometric shape.

3. Importance of NonSymmetry Diagonal Calculation

Details: Calculating the non-symmetry diagonal is crucial for understanding the geometric properties of deltoidal hexecontahedrons, which are used in various mathematical studies, architectural designs, and crystallography applications.

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 non-symmetry diagonal length.

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 Midsphere Radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Are there other types of diagonals in this polyhedron?
A: Yes, deltoidal hexecontahedrons have both symmetry and non-symmetry diagonals, each with different geometric properties and calculation methods.

Q4: What are typical values for midsphere radius?
A: The midsphere radius depends on the specific dimensions of the polyhedron, but it's typically proportional to the edge length of the shape.

Q5: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to deltoidal hexecontahedrons. Other polyhedrons have different geometric relationships and require different formulas.