Volume Of Hexakis Icosahedron Given Midsphere Radius Calculator

Formula Used:

\[ V = \frac{25}{88} \times \left( \frac{8 \times r_m}{5 + 3 \times \sqrt{5}} \right)^3 \times \sqrt{6 \times (185 + 82 \times \sqrt{5})} \]

Volume of Hexakis Icosahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{25}{88} \times \left( \frac{8 \times r_m}{5 + 3 \times \sqrt{5}} \right)^3 \times \sqrt{6 \times (185 + 82 \times \sqrt{5})} \]

Where:

\( V \) — Volume of Hexakis Icosahedron (m³)
\( r_m \) — Midsphere Radius of Hexakis Icosahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the volume of a Hexakis Icosahedron based on its midsphere radius, incorporating mathematical constants and geometric relationships.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for various applications including material science, architectural design, and mathematical modeling of complex polyhedra.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid for accurate results.

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: What is the midsphere radius?
A: The midsphere radius is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.

Q3: What are typical values for midsphere radius?
A: The midsphere radius depends on the specific dimensions of the Hexakis Icosahedron and can vary based on the scale of the polyhedron.

Q4: Are there limitations to this formula?
A: This formula is specifically designed for perfect Hexakis Icosahedrons and assumes ideal geometric conditions.

Q5: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for Hexakis Icosahedrons. Other polyhedra require different formulas for volume calculation.