1. What is the Edge Length of Icosidodecahedron given Triangular Face Height?

The edge length of an icosidodecahedron can be calculated from the height of its triangular faces using the mathematical relationship between these geometric properties of this Archimedean solid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Icosidodecahedron (m)
• \( h_{Triangle} \) — Triangular Face Height of Icosidodecahedron (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula derives from the geometric relationship between the edge length and the height of the triangular faces in an icosidodecahedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for determining various geometric properties of the icosidodecahedron, including surface area, volume, and other dimensional characteristics.

4. Using the Calculator

Tips: Enter the triangular face height in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an Icosidodecahedron?
A: An icosidodecahedron is an Archimedean solid with 32 faces (20 triangles and 12 pentagons), 30 vertices, and 60 edges.

Q2: Why is this formula specific to triangular face height?
A: This formula specifically relates the edge length to the height of the triangular faces, which is a distinct geometric property of the icosidodecahedron.

Q3: Can this formula be used for other polyhedra?
A: No, this formula is specific to the icosidodecahedron due to its unique geometric properties and face configuration.

Q4: What are the practical applications of this calculation?
A: This calculation is useful in geometry, architecture, 3D modeling, and mathematical research involving polyhedral structures.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, provided the input values are accurate and the formula is correctly applied.