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The Midsphere Radius of Tetrakis Hexahedron is the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere. It represents the sphere that touches all the edges of the polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the midsphere radius based on the pyramidal edge length of the Tetrakis Hexahedron, using the mathematical constant √2.
Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the Tetrakis Hexahedron. It helps in determining the sphere that is tangent to all edges of the polyhedron.
Tips: Enter the pyramidal edge length in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with square pyramids on each face. It has 24 faces, 36 edges, and 14 vertices.
Q2: How is the midsphere different from the insphere?
A: The midsphere is tangent to all edges of the polyhedron, while the insphere is tangent to all faces. They are different spheres with different radii.
Q3: What are the applications of this calculation?
A: This calculation is used in geometry, crystallography, architecture, and 3D modeling where precise spatial relationships of polyhedra are required.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different formulas for calculating their midsphere radii.
Q5: What units should be used for the input?
A: The calculator uses meters as the default unit, but any consistent unit system can be used as long as the input and output use the same units.