Medium Edge of Hexakis Icosahedron given Midsphere Radius Calculator

Formula Used:

\[ l_{Medium} = \frac{3}{22} \times (4 + \sqrt{5}) \times \frac{8 \times r_m}{5 + (3 \times \sqrt{5})} \]

Medium Edge of Hexakis Icosahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 property of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Medium} = \frac{3}{22} \times (4 + \sqrt{5}) \times \frac{8 \times r_m}{5 + (3 \times \sqrt{5})} \]

Where:

\( l_{Medium} \) — Medium Edge of Hexakis Icosahedron (m)
\( r_m \) — Midsphere Radius of Hexakis Icosahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the medium edge length based on the given midsphere radius, using the mathematical relationship between these geometric properties of the Hexakis Icosahedron.

3. Importance of Medium Edge Calculation

Details: Calculating the medium edge is crucial for understanding the geometric properties of Hexakis Icosahedron, which has applications in various fields including crystallography, architecture, and mathematical modeling of complex structures.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. 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 the midsphere radius defined?
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 medium edge lengths?
A: The medium edge length depends on the specific dimensions of the Hexakis Icosahedron. For standard configurations, it typically ranges from a few centimeters to several meters in practical applications.

Q4: Are there limitations to this formula?
A: This formula is specifically derived for the Hexakis Icosahedron and assumes a perfect geometric shape. It may not apply to distorted or irregular variations.

Q5: What units should I use?
A: The calculator uses meters as the default unit, but you can use any consistent unit system as long as you maintain consistency between input and output values.