1. What is the Midsphere Radius of Hexakis Icosahedron?

The Midsphere Radius of a Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere. It represents the sphere that touches all edges of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere Radius of Hexakis Icosahedron (m)
• \( l_{long} \) — Long Edge of Hexakis Icosahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the midsphere radius based on the long edge length of the Hexakis Icosahedron, incorporating the mathematical constant √5.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties and proportions of the Hexakis Icosahedron shape.

4. Using the Calculator

Tips: Enter the long edge length of the Hexakis Icosahedron in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron, featuring 120 faces, 180 edges, and 62 vertices.

Q2: How is the midsphere different from the insphere?
A: The midsphere touches all edges of the polyhedron, while the insphere touches all faces from the inside.

Q3: What are practical applications of this calculation?
A: This calculation is used in geometry research, architectural design, and 3D computer graphics modeling.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Hexakis Icosahedron. Other polyhedra have different formulas for their midsphere radii.

Q5: What units should be used for input?
A: The calculator uses meters as the default unit, but any consistent unit of length can be used as long as the input and output use the same unit.