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The edge length of an icosidodecahedron is the length of any edge of this Archimedean solid, which has 20 triangular faces and 12 pentagonal faces. It is a key geometric parameter for various calculations involving this polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the edge length based on the known area of the pentagonal faces, using the mathematical relationship derived from the geometry of regular pentagons and the icosidodecahedron structure.
Details: Calculating the edge length is essential for determining other geometric properties of the icosidodecahedron, such as surface area, volume, and for applications in architecture, crystallography, and mathematical modeling.
Tips: Enter the pentagonal face area in square meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is an icosidodecahedron?
A: An icosidodecahedron is an Archimedean solid with 32 faces (20 triangles and 12 pentagons), 60 edges, and 30 vertices.
Q2: Why is this formula specific to pentagonal face area?
A: The formula derives from the geometric relationship between the edge length and the area of the regular pentagonal faces in an icosidodecahedron.
Q3: Can I use triangular face area instead?
A: No, this specific formula requires the pentagonal face area. A different formula would be needed for triangular face area input.
Q4: What are typical units for these measurements?
A: While meters are used here, any consistent unit system can be applied (cm, mm, etc.), as long as area and length units match.
Q5: Is this calculation accurate for all icosidodecahedrons?
A: Yes, this formula applies to all regular icosidodecahedrons where all edges are equal length and all faces are regular polygons.