1. What is Midsphere Radius of Icosidodecahedron?

The Midsphere Radius of an Icosidodecahedron is the radius of the sphere that is tangent to all edges of the Icosidodecahedron. It represents the sphere that touches the midpoint of each edge of this Archimedean solid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere Radius (m)
• \( RA/V \) — Surface to Volume Ratio (1/m)

Explanation: This formula calculates the midsphere radius based on the surface to volume ratio of the icosidodecahedron, incorporating various square root terms that are characteristic of this polyhedron's geometry.

3. Importance of Midsphere Radius Calculation

Details: The midsphere radius is important in geometry and materials science for understanding the spatial properties of the icosidodecahedron, including its packing efficiency and symmetry properties.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. 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: How is the midsphere different from the insphere?
A: The midsphere touches the edges of the polyhedron, while the insphere is tangent to the faces.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the size of the icosidodecahedron, with smaller polyhedra having higher ratios.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula is derived specifically for the icosidodecahedron geometry.

Q5: What precision should I expect from this calculation?
A: The calculator provides results with 10 decimal places precision, suitable for most geometric applications.