1. What is the Icosahedral Edge Length of Triakis Icosahedron?

The Icosahedral Edge Length of Triakis Icosahedron is the length of the line connecting any two adjacent vertices of icosahedron of Triakis Icosahedron. It is an important geometric measurement in polyhedral studies.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Pyramidal Edge Length — Length of the line connecting any two adjacent vertices of pyramid of Triakis Icosahedron (in meters)
• \(\sqrt{5}\) — Square root of 5 (approximately 2.23607)

Explanation: This formula establishes the mathematical relationship between the pyramidal edge length and the icosahedral edge length in a Triakis Icosahedron.

3. Importance of Icosahedral Edge Length Calculation

Details: Accurate calculation of icosahedral edge length is crucial for geometric modeling, architectural design, and understanding the properties of polyhedral structures in mathematics and engineering applications.

4. Using the Calculator

Tips: Enter the pyramidal edge length in meters. The value must be positive and valid. The calculator will compute the corresponding icosahedral edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron. It has 60 isosceles triangular faces.

Q2: Why is the square root of 5 used in the formula?
A: The square root of 5 appears naturally in the geometry of regular icosahedrons and related polyhedra due to their mathematical properties.

Q3: What are the units of measurement?
A: The calculator uses meters as the unit of measurement, but the formula works with any consistent unit system.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Icosahedron and its geometric properties.

Q5: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most practical applications.