Volume Of Deltoidal Hexecontahedron Given Symmetry Diagonal Calculator

Formula Used:

\[ V = \frac{45}{11} \times \sqrt{\frac{370 + 164 \times \sqrt{5}}{25}} \times \left( \frac{d_{Symmetry}}{3 \times \sqrt{\frac{5 - \sqrt{5}}{20}}} \right)^3 \]

Volume of Deltoidal Hexecontahedron:

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1. What is 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's a Catalan solid with 60 deltoid faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{45}{11} \times \sqrt{\frac{370 + 164 \times \sqrt{5}}{25}} \times \left( \frac{d_{Symmetry}}{3 \times \sqrt{\frac{5 - \sqrt{5}}{20}}} \right)^3 \]

Where:

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

Explanation: This formula calculates the volume based on the symmetry diagonal measurement, using mathematical constants and geometric relationships specific to the deltoidal hexecontahedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, and various scientific fields. For the deltoidal hexecontahedron, volume calculation helps in understanding its spatial properties and applications in crystallography and architecture.

4. Using the Calculator

Tips: Enter the symmetry diagonal measurement in meters. The value must be positive and greater than 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 symmetry diagonal?
A: The symmetry diagonal is the diagonal that cuts the deltoid faces of the Deltoidal Hexecontahedron into two equal halves.

Q3: What are the practical applications of this calculation?
A: This calculation is used in geometric modeling, crystallography, architectural design, and mathematical research involving polyhedra.

Q4: How accurate is this formula?
A: The formula is mathematically exact for a perfect deltoidal hexecontahedron, providing precise volume calculations.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first before calculation.