Volume of Deltoidal Icositetrahedron Given Nonsymmetry Diagonal Calculator

Formula Used:

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

Volume of Deltoidal Icositetrahedron:

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1. What is the Volume of Deltoidal Icositetrahedron?

The Volume of Deltoidal Icositetrahedron is the quantity of three dimensional space enclosed by the entire surface of Deltoidal Icositetrahedron. It is a Catalan solid with 24 deltoid faces.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Deltoidal Icositetrahedron (m³)
\( d_{Non\ Symmetry} \) — NonSymmetry Diagonal of Deltoidal Icositetrahedron (m)

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

3. Importance of Volume Calculation

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

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A deltoidal icositetrahedron is a Catalan solid with 24 deltoid faces, 26 vertices, and 48 edges. It is the dual of the rhombicuboctahedron.

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

Q3: What are the units of measurement?
A: The calculator uses meters for input (NonSymmetry Diagonal) and cubic meters for output (Volume). Ensure consistent units for accurate results.

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

Q5: What if I get an error in calculation?
A: Make sure the input value is positive and non-zero. The calculator requires valid numerical input to perform the calculation.