Total Surface Area Of Deltoidal Icositetrahedron Given Short Edge Calculator

Formula Used:

\[ TSA = \frac{12}{7} \times \sqrt{61 + (38 \times \sqrt{2})} \times \left( \frac{7 \times le(Short)}{4 + \sqrt{2}} \right)^2 \]

Total Surface Area of Deltoidal Icositetrahedron:

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1. What is the Total Surface Area of Deltoidal Icositetrahedron?

The Total Surface Area of Deltoidal Icositetrahedron is the total area covered by all the faces of this polyhedron. It is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{12}{7} \times \sqrt{61 + (38 \times \sqrt{2})} \times \left( \frac{7 \times le(Short)}{4 + \sqrt{2}} \right)^2 \]

Where:

\( TSA \) — Total Surface Area of Deltoidal Icositetrahedron (m²)
\( le(Short) \) — Short Edge of Deltoidal Icositetrahedron (m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the total surface area based on the length of the short edge of the deltoidal faces, incorporating mathematical constants and operations.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for understanding the geometric properties of the deltoidal icositetrahedron, which has applications in crystallography, architecture, and mathematical modeling.

4. Using the Calculator

Tips: Enter the length of the short edge in meters. The value must be positive and greater than zero for accurate calculation.

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. It is the dual of the rhombicuboctahedron.

Q2: What units should be used for input?
A: The calculator uses meters as the unit for the short edge length, and returns the surface area in square meters.

Q3: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for more precise calculations.

Q4: What is the precision of the calculation?
A: The result is rounded to 6 decimal places for clarity while maintaining reasonable precision.

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