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The Insphere Radius of Triakis Octahedron is the radius of the sphere that is contained by the Triakis Octahedron in such a way that all the faces are touching the sphere. It represents the largest sphere that can fit inside the polyhedron while touching all its faces.
The calculator uses the formula:
Where:
Explanation: This formula calculates the radius of the inscribed sphere based on the octahedral edge length of the Triakis Octahedron, using the mathematical constant √2.
Details: Calculating the insphere radius is important in geometry and materials science for understanding the packing properties, volume relationships, and spatial characteristics of polyhedral structures.
Tips: Enter the octahedral edge length in meters. The value must be positive and greater than zero.
Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that can be obtained by placing a square pyramid on each face of a regular octahedron.
Q2: How is the insphere radius different from the circumsphere radius?
A: The insphere radius is the radius of the sphere inscribed inside the polyhedron (touching all faces), while the circumsphere radius is the radius of the sphere that circumscribes the polyhedron (passing through all vertices).
Q3: What are the units for the insphere radius?
A: The insphere radius is measured in the same units as the input edge length (typically meters).
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Octahedron. Different polyhedra have different formulas for calculating their insphere radii.
Q5: What is the significance of the mathematical constant √2 in this formula?
A: The √2 constant appears in the formula due to the geometric properties and symmetry of the Triakis Octahedron, particularly its relationship to the regular octahedron.