1. What is the Volume of Hexakis Icosahedron?

The Volume of Hexakis Icosahedron is the quantity of three dimensional space enclosed by the entire surface of Hexakis Icosahedron. It represents the total capacity or space occupied by this geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Hexakis Icosahedron (m³)
• \( l_{long} \) — Long Edge of Hexakis Icosahedron (m)

Explanation: The formula calculates the volume based on the cube of the long edge length multiplied by a constant factor derived from the geometric properties of the Hexakis Icosahedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in various fields including mathematics, engineering, architecture, and 3D modeling. It helps in understanding spatial relationships and material requirements.

4. Using the Calculator

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

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: Why is the formula so complex?
A: The formula incorporates mathematical constants and relationships specific to the geometry of the Hexakis Icosahedron, ensuring accurate volume calculation.

Q3: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for Hexakis Icosahedron. Other polyhedra have different volume formulas.

Q4: What units should I use?
A: The calculator uses meters for input and cubic meters for output. You can convert from other units as needed.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the input value. The result is rounded to 6 decimal places for readability.