Volume of Deltoidal Hexecontahedron given NonSymmetry Diagonal Calculator

Formula Used:

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

Volume of Deltoidal Hexecontahedron:

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1. What is the Volume of Deltoidal Hexecontahedron?

The Volume of Deltoidal Hexecontahedron is the quantity of three dimensional space enclosed by the entire surface of Deltoidal Hexecontahedron. It is a Catalan solid with 60 deltoid faces.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

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

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including mathematics, engineering, architecture, and 3D modeling. It helps in understanding spatial properties and material requirements.

4. Using the Calculator

Tips: Enter the NonSymmetry Diagonal length in meters. The value must be positive and non-zero. The calculator will compute the volume using the precise mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a Catalan solid with 60 deltoid (kite-shaped) faces, 120 edges, and 62 vertices.

Q2: What is the NonSymmetry Diagonal?
A: The NonSymmetry Diagonal is the diagonal that divides the deltoid faces of Deltoidal Hexecontahedron into two isosceles triangles.

Q3: What units should I use for the input?
A: The calculator uses meters as the unit for length input, and returns volume in cubic meters.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.

Q5: What is the typical range of values for the NonSymmetry Diagonal?
A: The NonSymmetry Diagonal can vary depending on the specific Deltoidal Hexecontahedron, but typically ranges from a few centimeters to several meters in practical applications.