Midsphere Radius Of Truncated Cuboctahedron Given Volume Calculator

Midsphere Radius of Truncated Cuboctahedron Formula:

\[ r_m = \frac{\sqrt{12 + 6\sqrt{2}}}{2} \times \left( \frac{V}{2(11 + 7\sqrt{2})} \right)^{1/3} \]

Midsphere Radius of Truncated Cuboctahedron (rₘ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Midsphere Radius of Truncated Cuboctahedron?

The midsphere radius of a truncated cuboctahedron is the radius of the sphere that is tangent to all edges of the polyhedron. It represents the sphere that fits perfectly between the inscribed and circumscribed spheres of the truncated cuboctahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_m = \frac{\sqrt{12 + 6\sqrt{2}}}{2} \times \left( \frac{V}{2(11 + 7\sqrt{2})} \right)^{1/3} \]

Where:

\( r_m \) — Midsphere radius of truncated cuboctahedron
\( V \) — Volume of truncated cuboctahedron
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula derives from the geometric properties of the truncated cuboctahedron, relating its midsphere radius to its volume through mathematical constants and relationships.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and materials science for understanding the spatial relationships within polyhedral structures and for applications in crystalography and molecular modeling.

4. Using the Calculator

Tips: Enter the volume of the truncated cuboctahedron in cubic meters. The value must be positive and non-zero 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), 72 edges, and 48 vertices.

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

Q3: What are typical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, architectural design, and geometric analysis of polyhedral structures.

Q4: Are there limitations to this formula?
A: This formula applies specifically to regular truncated cuboctahedrons and assumes perfect geometric proportions.

Q5: Can this formula be used for other polyhedra?
A: No, this formula is specific to truncated cuboctahedrons. Other polyhedra have different formulas for calculating their midsphere radii.