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The circumsphere radius of a tetrahedron is the radius of the sphere that passes through all four vertices of the tetrahedron. When given the insphere radius (the radius of the sphere tangent to all four faces), there is a specific mathematical relationship between these two measurements.
The calculator uses the formula:
Where:
Explanation: For a regular tetrahedron, the circumsphere radius is exactly three times the insphere radius. This relationship holds true for all regular tetrahedrons.
Details: Calculating the circumsphere radius is important in geometry, 3D modeling, crystallography, and molecular modeling where tetrahedral structures are common. It helps in understanding the spatial dimensions and relationships within tetrahedral arrangements.
Tips: Enter the insphere radius value in the input field. The value must be a positive number. The calculator will automatically compute the circumsphere radius using the formula R = 3r.
Q1: Does this formula work for all tetrahedrons?
A: This specific formula R = 3r applies only to regular tetrahedrons (where all edges are equal). For irregular tetrahedrons, the relationship is more complex.
Q2: What are the units of measurement?
A: The units depend on your input. If you enter the insphere radius in centimeters, the circumsphere radius will also be in centimeters.
Q3: Can I use this calculator for other polyhedrons?
A: No, this calculator is specifically designed for regular tetrahedrons. Other polyhedrons have different relationships between their insphere and circumsphere radii.
Q4: What if my tetrahedron is not regular?
A: For irregular tetrahedrons, you would need more information (such as edge lengths or face areas) to calculate the circumsphere radius accurately.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular tetrahedrons. The accuracy depends on the precision of your input value.