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The Short Edge of Hexakis Icosahedron is the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron. It is an important geometric measurement in this complex polyhedron structure.
The calculator uses the mathematical formula:
Where:
Explanation: This formula establishes the precise mathematical relationship between the medium edge and short edge lengths in a Hexakis Icosahedron, incorporating the golden ratio properties through the √5 term.
Details: Accurate calculation of the short edge is crucial for geometric modeling, architectural design, and mathematical analysis of polyhedral structures. It helps in understanding the proportions and symmetry of the Hexakis Icosahedron.
Tips: Enter the medium edge length in meters. The value must be positive and greater than zero. The calculator will compute the corresponding short edge length using the mathematical relationship.
Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid that is the dual of the truncated icosahedron. It has 120 faces, 180 edges, and 62 vertices.
Q2: Why are there different edge lengths in a Hexakis Icosahedron?
A: The Hexakis Icosahedron has three distinct edge lengths (short, medium, and long) due to its complex geometric structure and symmetry properties.
Q3: What are typical applications of this calculation?
A: This calculation is used in geometric modeling, crystal structure analysis, architectural design, and mathematical research involving polyhedra.
Q4: How accurate is this formula?
A: The formula is mathematically exact and provides precise results based on the geometric properties of the Hexakis Icosahedron.
Q5: Can this calculator handle very large or very small values?
A: Yes, the calculator can process a wide range of values, though extremely large or small numbers may be limited by floating-point precision.