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 the Triakis Octahedron. It represents the sum of the areas of all its faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area of Triakis Octahedron (m²)
• \( r_i \) — Insphere Radius of Triakis Octahedron (m)

Explanation: This formula calculates the total surface area based on the insphere radius of the Triakis Octahedron, using mathematical constants and square root functions.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is important in geometry and material science for determining properties like heat transfer, coating requirements, and structural characteristics of polyhedral shapes.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero for accurate calculation.

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 insphere radius?
A: The insphere radius is the radius of the sphere that is contained by the Triakis Octahedron such that all faces are tangent to the sphere.

Q3: Are there other ways to calculate surface area?
A: Yes, surface area can also be calculated using edge length or other geometric parameters of the Triakis Octahedron.

Q4: What are typical applications of this calculation?
A: This calculation is used in crystallography, architecture, and 3D modeling where precise surface area measurements are required.

Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect Triakis Octahedron shape and provides precise surface area calculations.