1. What is the Edge Length of Truncated Cuboctahedron?

The Edge Length of a Truncated Cuboctahedron is the length of any edge of this Archimedean solid. It is a fundamental geometric property used in various mathematical and engineering calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Truncated Cuboctahedron (m)
• \( r_m \) — Midsphere Radius of Truncated Cuboctahedron (m)

Explanation: This formula relates the edge length of a truncated cuboctahedron to its midsphere radius through a precise mathematical relationship involving square roots.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for determining various geometric properties of the truncated cuboctahedron, including surface area, volume, and other dimensional characteristics important in geometric modeling and architectural design.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding edge length of the truncated cuboctahedron.

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, crystallography, architectural design, and 3D modeling where precise polyhedral dimensions are required.

Q4: How accurate is this formula?
A: The formula is mathematically exact for perfect truncated cuboctahedrons and provides precise results when accurate inputs are provided.

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