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The Midsphere Radius of a Truncated Cuboctahedron is the radius of the sphere that is tangent to all the edges of the polyhedron. It lies midway between the inscribed sphere and the circumscribed sphere.
The calculator uses the formula:
Where:
Explanation: This formula establishes the mathematical relationship between the midsphere radius and the circumsphere radius of a truncated cuboctahedron, incorporating square roots and constants derived from the geometry of the shape.
Details: Calculating the midsphere radius is important in geometric analysis and 3D modeling of polyhedra. It helps in understanding the spatial properties and symmetry of the truncated cuboctahedron, which has applications in architecture, crystallography, and mathematical research.
Tips: Enter the circumsphere radius in meters. The value must be positive and non-zero. The calculator will compute the corresponding midsphere radius using the established geometric relationship.
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.
Q2: How is the midsphere different from circumsphere?
A: The circumsphere passes through all vertices of the polyhedron, while the midsphere is tangent to all edges.
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the truncated cuboctahedron. Other polyhedra have different geometric relationships.
Q4: What are practical applications of this calculation?
A: This calculation is used in mathematical research, 3D modeling, architectural design, and in understanding crystal structures in materials science.
Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect truncated cuboctahedron. The accuracy of practical applications depends on the precision of the input values.