Midsphere Radius of Truncated Icosahedron Calculator

Midsphere Radius of Truncated Icosahedron Formula:

\[ r_m = \frac{3(1 + \sqrt{5})}{4} \times l_e \]

Midsphere Radius of Truncated Icosahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Midsphere Radius of Truncated Icosahedron?

The Midsphere Radius of a Truncated Icosahedron is the radius of the sphere that is tangent to all edges of the Truncated Icosahedron. This geometric property is important in understanding the spatial relationships and symmetry of this particular polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_m = \frac{3(1 + \sqrt{5})}{4} \times l_e \]

Where:

\( r_m \) — Midsphere Radius of Truncated Icosahedron (m)
\( l_e \) — Edge Length of Truncated Icosahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the midsphere radius based on the edge length of the truncated icosahedron, incorporating the mathematical constant related to the golden ratio.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is crucial for geometric analysis, 3D modeling, and understanding the spatial properties of truncated icosahedrons in various applications including architecture, chemistry, and mathematics.

4. Using the Calculator

Tips: Enter the edge length of the truncated icosahedron in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated icosahedron?
A: A truncated icosahedron is an Archimedean solid with 32 faces (12 pentagons and 20 hexagons), 90 edges, and 60 vertices. It's best known as the shape of a soccer ball.

Q2: Why is the golden ratio (√5) involved in this formula?
A: The truncated icosahedron has properties related to the golden ratio, which is why √5 appears in the mathematical relationship between its edge length and midsphere radius.

Q3: What are practical applications of this calculation?
A: This calculation is used in molecular modeling (fullerenes), architectural design, geometric art, and sports equipment design (soccer balls).

Q4: How accurate is this formula?
A: The formula is mathematically exact for perfect truncated icosahedrons and provides precise results when accurate edge length measurements are used.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first or adjust the result accordingly.