1. What is the Midsphere Radius of Icosidodecahedron?

The midsphere radius of an icosidodecahedron is the radius of the sphere that is tangent to all the edges of the icosidodecahedron. An icosidodecahedron is an Archimedean solid with 32 faces (20 triangles and 12 pentagons), 60 edges, and 30 vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere radius of icosidodecahedron (m)
• \( TSA \) — Total surface area of icosidodecahedron (m²)

Explanation: The formula calculates the midsphere radius based on the total surface area of the icosidodecahedron, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the icosidodecahedron and its relationship with inscribed spheres.

4. Using the Calculator

Tips: Enter the total surface area of the icosidodecahedron in square meters. The value must be positive and greater than zero.

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), 60 edges, and 30 vertices.

Q2: What is the midsphere of a polyhedron?
A: The midsphere (or intersphere) is a sphere that is tangent to all the edges of a polyhedron.

Q3: What units should I use for the total surface area?
A: The calculator uses square meters (m²), but you can use any consistent unit of area as long as you interpret the result in the same unit system.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula is only valid for the icosidodecahedron. Other polyhedra have different formulas for calculating their midsphere radii.

Q5: What is the precision of the calculation?
A: The calculator provides results with up to 10 decimal places for accuracy in geometric calculations.