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The Medium Edge of Hexakis Octahedron is the length of the medium edge of any of the congruent triangular faces of the Hexakis Octahedron. It is a geometric property that helps in understanding the dimensions and proportions of this polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula establishes a mathematical relationship between the short edge and medium edge of a Hexakis Octahedron, incorporating the irrational number \(\sqrt{2}\) which is common in geometric calculations.
Details: Calculating the medium edge is important for geometric analysis, 3D modeling, and understanding the spatial properties of Hexakis Octahedrons in various applications including crystallography, architecture, and mathematical research.
Tips: Enter the short edge length in meters. The value must be positive and non-zero. The calculator will compute the corresponding medium edge length.
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 congruent triangular faces, 72 edges, and 26 vertices.
Q2: Why does the formula contain \(\sqrt{2}\)?
A: The \(\sqrt{2}\) appears due to the geometric relationships and trigonometric properties inherent in the structure of the Hexakis Octahedron.
Q3: Can this formula be used for any Hexakis Octahedron?
A: Yes, this formula applies to all regular Hexakis Octahedrons where the faces are congruent triangles.
Q4: What are typical values for the short edge?
A: The short edge length can vary significantly depending on the specific Hexakis Octahedron, but it must always be a positive real number.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Hexakis Octahedron. The accuracy of the result depends on the precision of the input value.