1. What is the Total Surface Area of Triakis Icosahedron?

The Total Surface Area of a Triakis Icosahedron refers to the total area of all its faces. A Triakis Icosahedron is a polyhedron created by attaching a triangular pyramid to each face of a regular icosahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area (m²)
• \( l_{pyramid} \) — Pyramidal Edge Length (m)
• \( \sqrt{5} \) — Mathematical constant (approximately 2.23607)

Explanation: The formula calculates the total surface area based on the pyramidal edge length, incorporating geometric constants specific to the Triakis Icosahedron structure.

3. Importance of TSA Calculation

Details: Calculating the total surface area is important in geometry, material science, and engineering applications where surface properties need to be determined for objects with this specific polyhedral structure.

4. Using the Calculator

Tips: Enter the pyramidal edge length in meters. The value must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid created by attaching a triangular pyramid to each face of a regular icosahedron, resulting in a polyhedron with 60 faces.

Q2: What units should be used for input?
A: The pyramidal edge length should be entered in meters. The calculator will output 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 range of valid input values?
A: Any positive non-zero value is valid. Extremely large values may cause computational limitations.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical constants and functions, providing results accurate to six decimal places.