Volume of Deltoidal Icositetrahedron given Midsphere Radius Calculator

Formula Used:

\[ V = \frac{2}{7} \times \sqrt{292 + (206 \times \sqrt{2})} \times \left( \frac{2 \times r_m}{1 + \sqrt{2}} \right)^3 \]

Volume of Deltoidal Icositetrahedron:

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1. What is 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:

\[ V = \frac{2}{7} \times \sqrt{292 + (206 \times \sqrt{2})} \times \left( \frac{2 \times r_m}{1 + \sqrt{2}} \right)^3 \]

Where:

\( V \) — Volume of Deltoidal Icositetrahedron (m³)
\( r_m \) — Midsphere Radius of Deltoidal Icositetrahedron (m)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the volume based on the midsphere radius, incorporating mathematical constants and geometric relationships specific to the deltoidal icositetrahedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including mathematics, engineering, architecture, and material science for understanding spatial properties and capacity.

4. Using the Calculator

Tips: Enter the midsphere radius 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 (kite-shaped) faces, 26 vertices, and 48 edges.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters before input.

Q4: How accurate is the calculation?
A: The calculation uses precise mathematical constants and provides results with 6 decimal places accuracy.

Q5: What are the practical applications of this calculation?
A: This calculation is useful in geometric modeling, architectural design, and understanding the properties of complex polyhedra.