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 uniform polyhedron with 12 square faces, 8 regular hexagonal faces, and 6 regular octagonal faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Truncated Cuboctahedron (m)
• \( V \) — Volume of Truncated Cuboctahedron (m³)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the edge length from the volume of a truncated cuboctahedron using its known volume-edge length relationship.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for geometric analysis, 3D modeling, architectural design, and understanding the properties of this complex polyhedron.

4. Using the Calculator

Tips: Enter the volume of the truncated cuboctahedron in cubic meters. The volume must be a positive value greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated cuboctahedron?
A: A truncated cuboctahedron is an Archimedean solid with 48 vertices, 72 edges, and 26 faces (12 squares, 8 hexagons, and 6 octagons).

Q2: What are the applications of this calculation?
A: This calculation is used in geometry, crystallography, architectural design, and 3D computer graphics modeling.

Q3: How accurate is this formula?
A: The formula is mathematically exact for perfect truncated cuboctahedrons and provides precise results when correct volume values are used.

Q4: Can this calculator handle different units?
A: The calculator uses cubic meters for volume input. Convert other volume units to cubic meters before calculation.

Q5: What is the significance of the constant in the formula?
A: The constant 2×(11+7√2) represents the volume scaling factor specific to the truncated cuboctahedron's geometry.