Nonsymmetry Diagonal Of Deltoidal Hexecontahedron Given Short Edge Calculator

Formula Used:

\[ d_{Non\ Symmetry} = \frac{\sqrt{\frac{470+156\sqrt{5}}{5}}}{11} \times \frac{22 \times l_{Short}}{3(7-\sqrt{5})} \]

NonSymmetry Diagonal of Deltoidal Hexecontahedron:

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1. What is NonSymmetry Diagonal of Deltoidal Hexecontahedron?

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Non\ Symmetry} = \frac{\sqrt{\frac{470+156\sqrt{5}}{5}}}{11} \times \frac{22 \times l_{Short}}{3(7-\sqrt{5})} \]

Where:

\( d_{Non\ Symmetry} \) — NonSymmetry Diagonal of Deltoidal Hexecontahedron (m)
\( l_{Short} \) — Short Edge of Deltoidal Hexecontahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the non-symmetry diagonal length based on the short edge measurement of the deltoidal hexecontahedron.

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 and engineering applications, particularly in crystallography and structural design.

4. Using the Calculator

Tips: Enter the short 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 Catalan solid with 60 deltoid faces. It is the dual polyhedron of the rhombicosidodecahedron.

Q2: What are the applications of this calculation?
A: This calculation is used in geometry research, architectural design, crystallography, and in the study of polyhedral structures.

Q3: What units should be used for input?
A: The calculator uses meters as the default unit, but the formula works with any consistent unit system.

Q4: How accurate is the calculation?
A: The calculation provides results with high precision (up to 12 decimal places) based on the mathematical formula.

Q5: Can this calculator handle very large or very small values?
A: Yes, the calculator can handle a wide range of positive values, though extremely large values may be limited by PHP's floating-point precision.