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The Truncated Edge of Hexakis Icosahedron is the length of the edges of a Hexakis Icosahedron that is created by truncating the vertices of an Icosidodecahedron. It represents a specific geometric measurement in this complex polyhedral structure.
The calculator uses the mathematical formula:
Where:
Explanation: This formula calculates the truncated edge length based on the known short edge length, using geometric relationships derived from the properties of the Hexakis Icosahedron.
Details: Calculating the truncated edge is important for understanding the geometric properties of Hexakis Icosahedrons, which have applications in mathematics, architecture, and molecular modeling. Accurate edge measurements are crucial for proper scaling and construction of these complex polyhedra.
Tips: Enter the short edge length in meters. The value must be positive and greater than zero. The calculator will compute the corresponding truncated edge length using the mathematical formula.
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: How is this polyhedron created?
A: The Hexakis Icosahedron is created by truncating the vertices of an Icosidodecahedron, resulting in a complex polyhedral structure with multiple edge lengths.
Q3: What are the practical applications of this calculation?
A: This calculation is used in geometric modeling, architectural design, and in understanding molecular structures that exhibit similar geometric properties.
Q4: Are there limitations to this formula?
A: The formula assumes a perfect geometric construction and may need adjustment for physical implementations where material thickness or construction tolerances apply.
Q5: Can this calculator be used for other polyhedra?
A: No, this specific formula applies only to the relationship between the short edge and truncated edge of a Hexakis Icosahedron.