1. What is the Short Edge of Hexakis Icosahedron?

The Short Edge of Hexakis Icosahedron is the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron. It is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( le(Short) \) — Short Edge of Hexakis Icosahedron (m)
• \( V \) — Volume of Hexakis Icosahedron (m³)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the short edge length based on the volume of the Hexakis Icosahedron, incorporating mathematical constants and cube root operations.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is essential for understanding the geometric properties of the Hexakis Icosahedron, which has applications in architecture, materials science, and mathematical modeling.

4. Using the Calculator

Tips: Enter the volume of the Hexakis Icosahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.

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

Q2: Why is the formula so complex?
A: The complexity arises from the mathematical relationships between volume and edge length in this specific polyhedron, involving irrational numbers and cube roots.

Q3: What units should I use?
A: The calculator uses meters for length and cubic meters for volume. Ensure consistent units for accurate results.

Q4: Can this calculator handle very large or small volumes?
A: Yes, but extremely large or small values may be limited by PHP's floating-point precision.

Q5: Are there other ways to calculate the short edge?
A: Yes, the short edge can also be calculated from other parameters like surface area or midradius, but the volume-based formula is commonly used.