1. What is the Midsphere Radius of Truncated Cube?

The Midsphere Radius of a Truncated Cube is the radius of the sphere that is tangent to all the edges of the Truncated Cube. It represents the sphere that fits perfectly within the polyhedron, touching each edge at exactly one point.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere Radius of Truncated Cube (m)
• \( l_e \) — Edge Length of Truncated Cube (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.414214)

Explanation: The formula calculates the midsphere radius based on the edge length of the truncated cube, incorporating the mathematical constant √2.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of truncated cubes and their relationship with inscribed spheres.

4. Using the Calculator

Tips: Enter the edge length of the truncated cube in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Cube?
A: A truncated cube is an Archimedean solid created by truncating the corners of a cube, resulting in 14 faces: 8 regular triangles and 6 regular octagons.

Q2: How is the midsphere different from the insphere?
A: The midsphere is tangent to all edges, while the insphere is tangent to all faces of the polyhedron.

Q3: What are practical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, architectural design, and computer graphics where truncated cube geometries appear.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to truncated cubes. Other polyhedra have different formulas for calculating their midsphere radii.

Q5: What is the accuracy of this calculation?
A: The calculation is mathematically exact when using the precise value of √2. The calculator provides results with 6 decimal places for practical purposes.