Edge Length of Rhombicuboctahedron given Circumsphere Radius Calculator

Formula Used:

\[ Edge\ Length\ of\ Rhombicuboctahedron = \frac{2 \times Circumsphere\ Radius\ of\ Rhombicuboctahedron}{\sqrt{5 + (2 \times \sqrt{2})}} \]

Edge Length of Rhombicuboctahedron:

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1. What is the Edge Length of Rhombicuboctahedron?

The Edge Length of Rhombicuboctahedron is the length of any edge of the Rhombicuboctahedron, which is an Archimedean solid with 8 triangular and 18 square faces. It is a key parameter in geometric calculations involving this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Edge\ Length = \frac{2 \times Circumsphere\ Radius}{\sqrt{5 + (2 \times \sqrt{2})}} \]

Where:

\( Circumsphere\ Radius \) — Radius of the sphere that contains the Rhombicuboctahedron with all vertices lying on the sphere (in meters)

Explanation: This formula derives from the geometric relationship between the circumsphere radius and the edge length of a Rhombicuboctahedron, incorporating the mathematical constant √2.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for determining various properties of the Rhombicuboctahedron, including surface area, volume, and other geometric characteristics. It is fundamental in architectural design, crystallography, and mathematical modeling.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding edge length of the Rhombicuboctahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicuboctahedron?
A: A Rhombicuboctahedron is an Archimedean solid with 26 faces (8 triangles and 18 squares), 24 vertices, and 48 edges.

Q2: How is the circumsphere radius related to the edge length?
A: The circumsphere radius is proportional to the edge length through a constant factor derived from the geometry of the Rhombicuboctahedron.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Rhombicuboctahedron. Other polyhedra have different relationships between circumsphere radius and edge length.

Q4: What are typical units for these measurements?
A: The units can be any length unit (meters, centimeters, inches, etc.) as long as consistency is maintained. The calculator uses meters by default.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Rhombicuboctahedron, providing precise results when accurate inputs are given.