1. What is the Medium Edge of Hexakis Icosahedron?

The Medium Edge of Hexakis Icosahedron is the length of the edge that connects two non-adjacent and non-opposite vertices of the Hexakis Icosahedron. It is an important geometric measurement in this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Long Edge - The longest edge that connects two opposite vertices of the Hexakis Icosahedron (in meters)
• √5 - Square root of 5 (approximately 2.23607)

Explanation: This formula establishes a precise mathematical relationship between the medium and long edges of a Hexakis Icosahedron, using the golden ratio constant √5.

3. Importance of Medium Edge Calculation

Details: Calculating the medium edge is crucial for understanding the geometric properties of Hexakis Icosahedrons, which have applications in crystallography, architecture, and mathematical modeling of complex structures.

4. Using the Calculator

Tips: Enter the long edge measurement in meters. The value must be positive and greater than zero. The calculator will compute the corresponding medium edge length.

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. It has 120 faces, 180 edges, and 62 vertices.

Q2: How many different edge lengths does a Hexakis Icosahedron have?
A: A Hexakis Icosahedron has three distinct edge lengths: short, medium, and long edges.

Q3: What are typical applications of Hexakis Icosahedrons?
A: They are used in geometric modeling, architectural design, and as the shape of some viruses and fullerene molecules.

Q4: Is the formula exact or approximate?
A: The formula is mathematically exact, though calculations may involve rounding of irrational numbers like √5.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can use any consistent unit system as long as you maintain the same units for input and output.