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

The Total Surface Area of a Triakis Octahedron is the total quantity of plane enclosed on the entire surface of this polyhedron. It's calculated based on the midsphere radius using a specific mathematical formula.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area of Triakis Octahedron (m²)
• \( r_m \) — Midsphere Radius of Triakis Octahedron (m)

Explanation: This formula calculates the total surface area based on the midsphere radius, incorporating geometric constants specific to the Triakis Octahedron structure.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is crucial for understanding the geometric properties of the Triakis Octahedron, material requirements for construction, and various engineering applications involving this specific polyhedral shape.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid for accurate calculation results.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that is the dual of the truncated cube. It has 24 isosceles triangular faces.

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: What units should I use for input?
A: Use meters for the midsphere radius. The calculator will output surface area in square meters.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places for precise calculations.

Q5: What are typical applications of this calculation?
A: This calculation is used in geometry, architecture, material science, and various engineering fields where polyhedral structures are employed.