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The Long Edge of Hexakis Octahedron given Insphere Radius is a geometric calculation that determines the length of the longest edge of a Hexakis Octahedron based on the radius of its inscribed sphere.
The calculator uses the formula:
Where:
Explanation: This formula establishes the mathematical relationship between the insphere radius and the long edge length of a Hexakis Octahedron, incorporating specific geometric constants.
Details: Calculating the long edge from the insphere radius is essential in geometric modeling, architectural design, and mathematical analysis of polyhedral structures, particularly in understanding the dimensional relationships within complex geometric shapes.
Tips: Enter the insphere radius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding long edge length of the Hexakis Octahedron.
Q1: What is a Hexakis Octahedron?
A: A Hexakis Octahedron is a Catalan solid that is the dual of the truncated cuboctahedron, featuring 48 faces, 72 edges, and 26 vertices.
Q2: Why is this specific formula used?
A: This formula is derived from the geometric properties and mathematical relationships specific to the Hexakis Octahedron, ensuring accurate calculation of edge lengths from the insphere radius.
Q3: What are typical values for insphere radius?
A: The insphere radius varies depending on the size of the Hexakis Octahedron, but it must always be a positive value greater than zero.
Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters before calculation, or convert the result afterward.
Q5: How precise are the calculations?
A: The calculator provides results with up to 10 decimal places, ensuring high precision for mathematical and engineering applications.