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The Midsphere Radius of Triakis Octahedron is the radius of the sphere for which all the edges of the Triakis Octahedron become a tangent line on that sphere. It's an important geometric property in polyhedral studies.
The calculator uses the formula:
Where:
Explanation: This formula establishes the mathematical relationship between the midsphere radius and insphere radius of a Triakis Octahedron, incorporating the geometric constant \( \sqrt{2} \).
Details: Calculating the midsphere radius is crucial for understanding the geometric properties of Triakis Octahedron, including its symmetry, packing efficiency, and spatial relationships in three-dimensional space.
Tips: Enter the insphere radius value in meters. The value must be a positive number greater than zero for accurate calculation.
Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that is the dual of the truncated cube. It has 24 isosceles triangular faces.
Q2: How is midsphere radius different from insphere radius?
A: The insphere radius touches all faces of the polyhedron, while the midsphere radius is tangent to all edges of the polyhedron.
Q3: What are the practical applications of this calculation?
A: This calculation is used in crystallography, material science, and architectural design where geometric properties of polyhedra are important.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to Triakis Octahedron. Other polyhedra have different mathematical relationships between their midsphere and insphere radii.
Q5: What is the significance of the constant √2 in the formula?
A: The constant √2 appears due to the octahedral symmetry and the specific geometric proportions of the Triakis Octahedron.