Volume Of Deltoidal Icositetrahedron Given Short Edge Calculator

Formula Used:

\[ V = \frac{2}{7} \times \sqrt{292 + (206 \times \sqrt{2})} \times \left( \frac{7 \times l_{short}}{4 + \sqrt{2}} \right)^3 \]

Volume of Deltoidal Icositetrahedron:

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1. What is the Volume of Deltoidal Icositetrahedron?

The volume of a Deltoidal Icositetrahedron is the quantity of three dimensional space enclosed by the entire surface of this polyhedron. It is calculated based on the length of its edges and specific geometric properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{2}{7} \times \sqrt{292 + (206 \times \sqrt{2})} \times \left( \frac{7 \times l_{short}}{4 + \sqrt{2}} \right)^3 \]

Where:

\( V \) — Volume of Deltoidal Icositetrahedron (m³)
\( l_{short} \) — Short Edge of Deltoidal Icositetrahedron (m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the volume based on the shortest edge length of the deltoidal faces, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including architecture, engineering, material science, and mathematical research. It helps in understanding spatial properties and material requirements.

4. Using the Calculator

Tips: Enter the short edge length of the deltoidal icositetrahedron in meters. The value must be positive and valid. The calculator will compute the volume using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 deltoidal (kite-shaped) faces, 26 vertices, and 48 edges.

Q2: Why is this specific formula used?
A: This formula is derived from the geometric properties and mathematical relationships specific to the Deltoidal Icositetrahedron, providing an accurate volume calculation based on the short edge length.

Q3: What units should I use for input?
A: The calculator uses meters as the default unit for length measurements. Ensure consistent units for accurate results.

Q4: Can this calculator handle very small or large values?
A: Yes, the calculator can handle a wide range of values, but extremely small values may approach precision limits of floating-point arithmetic.

Q5: Are there any limitations to this calculation?
A: The calculation assumes a perfect geometric shape and may not account for manufacturing tolerances or material variations in real-world objects.