1. What is Edge Length of Truncated Icosidodecahedron?

The edge length of a truncated icosidodecahedron is the length of any edge of this Archimedean solid. It is a uniform polyhedron with 62 faces (30 squares, 20 regular hexagons, and 12 regular decagons).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Midsphere\ Radius \) — Radius of the midsphere that is tangent to all edges of the polyhedron (m)

Explanation: This formula derives from the geometric properties of the truncated icosidodecahedron and provides the relationship between the midsphere radius and the edge length.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometry, volume, surface area, and other properties of the truncated icosidodecahedron in mathematical and architectural applications.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated icosidodecahedron?
A: It is an Archimedean solid with 62 faces, 120 vertices, and 180 edges, formed by truncating both the icosidodecahedron's vertices and edges.

Q2: Why is the midsphere radius important?
A: The midsphere (or intersphere) is tangent to all edges of the polyhedron, making it a key parameter in understanding the polyhedron's geometry.

Q3: What are typical values for edge length?
A: The edge length depends on the size of the polyhedron. For a standard truncated icosidodecahedron, it relates directly to the midsphere radius through this formula.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the truncated icosidodecahedron due to its unique geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the properties of the truncated icosidodecahedron, assuming precise input values.