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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 a geometric property of this specific polyhedron shape.
The calculator uses the formula:
Where:
Explanation: This formula provides the mathematical relationship between the long edge and short edge of a Hexakis Icosahedron, using the constant (5/44)*(7-√5) which is approximately 0.541356.
Details: Calculating the short edge is important in geometric modeling, 3D design, and mathematical studies of polyhedra. It helps in understanding the proportions and symmetry of the Hexakis Icosahedron shape.
Tips: Enter the long edge measurement in meters. The value must be positive and greater than zero. The calculator will compute the corresponding short edge length.
Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron. It has 120 faces, 180 edges, and 62 vertices.
Q2: Why is there a specific formula for the short edge?
A: The formula exists because the Hexakis Icosahedron has precise geometric proportions where the short and long edges maintain a constant ratio based on mathematical constants.
Q3: What units should I use for the input?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as the formula is dimensionally consistent.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise value of √5. The calculator provides results with 6 decimal places for practical accuracy.
Q5: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Hexakis Icosahedron. Other polyhedra have different geometric relationships between their edges.