Midsphere Radius Of Rhombicuboctahedron Given Volume Calculator

Formula Used:

\[ r_m = \frac{\sqrt{4 + 2\sqrt{2}}}{2} \times \left( \frac{3V}{2(6 + 5\sqrt{2})} \right)^{\frac{1}{3}} \]

Midsphere Radius of Rhombicuboctahedron (rₘ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Midsphere Radius of Rhombicuboctahedron?

The Midsphere Radius of a Rhombicuboctahedron is the radius of the sphere that is tangent to all the edges of the Rhombicuboctahedron. It lies midway between the inscribed sphere and the circumscribed sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_m = \frac{\sqrt{4 + 2\sqrt{2}}}{2} \times \left( \frac{3V}{2(6 + 5\sqrt{2})} \right)^{\frac{1}{3}} \]

Where:

\( r_m \) — Midsphere Radius (m)
\( V \) — Volume of Rhombicuboctahedron (m³)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

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

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the Rhombicuboctahedron and its relationship with other geometric elements.

4. Using the Calculator

Tips: Enter the volume of the Rhombicuboctahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicuboctahedron?
A: A Rhombicuboctahedron is an Archimedean solid with 8 triangular and 18 square faces, 24 identical vertices, and 48 edges.

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.

Q3: What are typical applications of this calculation?
A: This calculation is used in mathematics education, architectural design, and 3D computer graphics involving polyhedral models.

Q4: What precision does this calculator provide?
A: The calculator provides results with up to 6 decimal places for precise geometric calculations.

Q5: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Rhombicuboctahedron as it incorporates its unique geometric constants.