Medium Edge of Hexakis Icosahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ l_{Medium} = \frac{3}{22} \cdot (4+\sqrt{5}) \cdot \frac{\frac{6}{5} \cdot \sqrt{10 \cdot (417+107\sqrt{5})}}{RA/V \cdot \sqrt{6 \cdot (185+82\sqrt{5})}} \]

Medium Edge of Hexakis Icosahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is 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 parameter in this complex polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Medium} = \frac{3}{22} \cdot (4+\sqrt{5}) \cdot \frac{\frac{6}{5} \cdot \sqrt{10 \cdot (417+107\sqrt{5})}}{RA/V \cdot \sqrt{6 \cdot (185+82\sqrt{5})}} \]

Where:

\( l_{Medium} \) — Medium Edge of Hexakis Icosahedron (m)
\( RA/V \) — Surface to Volume Ratio (1/m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the medium edge length based on the surface to volume ratio of the Hexakis Icosahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Medium Edge Calculation

Details: Calculating the medium edge is crucial for understanding the geometric properties of Hexakis Icosahedron, including its symmetry, surface area, volume, and other dimensional characteristics in mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and valid. The calculator will compute the corresponding medium edge length of the Hexakis Icosahedron.

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 is surface to volume ratio defined?
A: Surface to volume ratio is the ratio of the total surface area to the total volume of a three-dimensional object, measured in 1/m.

Q3: What are the practical applications of this calculation?
A: This calculation is used in geometry, crystallography, architecture, and materials science where polyhedral structures are studied or utilized.

Q4: Are there different types of edges in Hexakis Icosahedron?
A: Yes, Hexakis Icosahedron has short, medium, and long edges, each with different lengths and geometric relationships.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula, though real-world measurements may have practical limitations.