1. What is Total Surface Area of Deltoidal Icositetrahedron?

The Total Surface Area of a Deltoidal Icositetrahedron is the total area of all the faces of this polyhedron. It's a Catalan solid with 24 deltoid (kite-shaped) faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area (m²)
• \( r_m \) — Midsphere Radius (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the total surface area based on the midsphere radius of the deltoidal icositetrahedron, incorporating the mathematical constant √2.

3. Importance of Surface Area Calculation

Details: Calculating the surface area is important in geometry, material science, and engineering applications where the surface properties of this specific polyhedral shape need to be determined.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the total surface area in square meters.

5. Frequently Asked Questions (FAQ)

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

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

Q3: Are there other ways to calculate surface area?
A: Yes, surface area can also be calculated using edge length or other parameters, but this calculator specifically uses the midsphere radius.

Q4: What are practical applications of this calculation?
A: This calculation is useful in crystallography, architecture, and design where this specific polyhedral shape is employed.

Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect deltoidal icositetrahedron shape.