Nonsymmetry Diagonal Of Deltoidal Hexecontahedron Given Volume Calculator

Formula Used:

\[ d_{Non\ Symmetry} = \frac{\sqrt{\frac{470 + 156\sqrt{5}}{5}}}{11} \times \left( \frac{11V}{45\sqrt{\frac{370 + 164\sqrt{5}}{25}}} \right)^{\frac{1}{3}} \]

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:

\[ d_{Non\ Symmetry} = \frac{\sqrt{\frac{470 + 156\sqrt{5}}{5}}}{11} \times \left( \frac{11V}{45\sqrt{\frac{370 + 164\sqrt{5}}{25}}} \right)^{\frac{1}{3}} \]

Where:

\( d_{Non\ Symmetry} \) — NonSymmetry Diagonal of Deltoidal Hexecontahedron (m)
\( V \) — Volume of Deltoidal Hexecontahedron (m³)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the non-symmetry diagonal length based on the volume of the deltoidal hexecontahedron, using mathematical constants derived from the geometric properties of this shape.

3. Importance of NonSymmetry Diagonal Calculation

Details: Calculating the non-symmetry diagonal is crucial for understanding the geometric properties of deltoidal hexecontahedron, for architectural applications, mathematical modeling, and 3D design where this specific polyhedron is used.

4. Using the Calculator

Tips: Enter the volume of deltoidal hexecontahedron in cubic meters. The value must be positive and valid. 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.

Q2: Why is this diagonal called "NonSymmetry"?
A: It's called non-symmetry diagonal because it divides the deltoid faces asymmetrically into two isosceles triangles.

Q3: What are the units for this calculation?
A: The volume should be in cubic meters (m³) and the resulting diagonal length will be in meters (m).

Q4: Can this formula be used for any polyhedron?
A: No, this specific formula applies only to the deltoidal hexecontahedron and its unique geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the derived formula for this specific geometric relationship.