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

The Total Surface Area of a Truncated Cuboctahedron is the total quantity of plane enclosed by the entire surface of this polyhedron. It's an important geometric property used in various mathematical and engineering applications.

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 (≈1.414)
• \( \sqrt{3} \) — Square root of 3 (≈1.732)

Explanation: This formula calculates the total surface area based on the midsphere radius of the truncated cuboctahedron, incorporating mathematical constants and geometric relationships.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, structural analysis, and geometric modeling in mathematics and engineering fields.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Cuboctahedron?
A: A truncated cuboctahedron is an Archimedean solid with 26 faces: 12 squares, 8 regular hexagons, and 6 regular octagons.

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 are typical applications of this calculation?
A: This calculation is used in geometry, architecture, material science, and 3D modeling applications.

Q4: How accurate is this formula?
A: The formula is mathematically exact for perfect truncated cuboctahedrons and provides precise surface area calculations.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the base unit. For other units, convert your measurement to meters before calculation.