1. What is the Total Surface Area of Truncated Icosidodecahedron?

The Total Surface Area of a Truncated Icosidodecahedron is the total quantity of plane enclosed by the entire surface of this complex polyhedron. It represents the sum of the areas of all its faces.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( TSA \) — Total Surface Area (m²)
• \( le \) — Edge Length of the Truncated Icosidodecahedron (m)
• \( \sqrt{} \) — Square root function

Explanation: The formula calculates the total surface area based on the edge length of the polyhedron, incorporating mathematical constants and square root functions.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for understanding the geometric properties of truncated icosidodecahedrons, which is important in various fields including mathematics, architecture, and material science.

4. Using the Calculator

Tips: Enter the edge length in meters. The value must be positive and valid. The calculator will compute the total surface area using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Icosidodecahedron?
A: A truncated icosidodecahedron is an Archimedean solid with 62 faces: 30 squares, 20 regular hexagons, and 12 regular decagons.

Q2: What units should I use for edge length?
A: The edge length should be entered in meters, and the result will be in square meters.

Q3: Can I use decimal values for edge length?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.

Q4: What is the precision of the calculation?
A: The result is rounded to 6 decimal places for accuracy.

Q5: Are there any limitations to this calculation?
A: This calculation assumes a perfect geometric shape with all edges equal and all faces regular polygons.