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The Midsphere Radius of Hexakis Octahedron is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron 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: The formula provides a direct relationship between the medium edge length and the midsphere radius of the Hexakis Octahedron, with a constant factor of 7/6.
Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the Hexakis Octahedron. It helps in determining the sphere that would perfectly contain all the edges of the polyhedron as tangents.
Tips: Enter the medium edge length of the Hexakis Octahedron in meters. The value must be positive and greater than zero. The calculator will compute the corresponding midsphere radius.
Q1: What is a Hexakis Octahedron?
A: A Hexakis Octahedron is a Catalan solid that is the dual of the truncated cube. It has 48 faces, 72 edges, and 26 vertices.
Q2: What is the significance of the midsphere?
A: The midsphere (or intersphere) is a sphere that is tangent to all the edges of a polyhedron, providing important geometric properties.
Q3: Are there other ways to calculate the midsphere radius?
A: Yes, the midsphere radius can also be calculated using other parameters of the Hexakis Octahedron, but this formula provides the most direct calculation from the medium edge length.
Q4: What units should I use for input?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as long as you maintain consistency throughout your calculations.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Hexakis Octahedron, so it's as accurate as your input value.