1. What is Pyramidal Edge Length of Triakis Icosahedron?

The Pyramidal Edge Length of Triakis Icosahedron is the length of the line connecting any two adjacent vertices of pyramid of Triakis Icosahedron. It's a crucial geometric measurement for understanding the structure and properties of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( l_e \) — Pyramidal Edge Length (m)
• \( V \) — Volume of Triakis Icosahedron (m³)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives from the geometric relationships within the Triakis Icosahedron, relating the pyramid edge length to the overall volume of the polyhedron.

3. Importance of Pyramidal Edge Length Calculation

Details: Calculating the pyramidal edge length is essential for geometric analysis, structural design applications, and understanding the spatial properties of the Triakis Icosahedron in mathematical and engineering contexts.

4. Using the Calculator

Tips: Enter the volume of the Triakis Icosahedron in cubic meters. The value must be positive and non-zero. The calculator will compute the corresponding pyramidal 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, featuring 60 isosceles triangular faces.

Q2: How is this formula derived?
A: The formula is derived from the geometric relationships between the volume and edge lengths of the Triakis Icosahedron using solid geometry principles.

Q3: What are typical values for pyramidal edge length?
A: The pyramidal edge length varies based on the volume, but typically ranges from a few centimeters to several meters depending on the scale of the polyhedron.

Q4: Can this calculator handle very large volumes?
A: Yes, the calculator can handle large volume values, though extremely large values may be limited by computational precision.

Q5: What precision does the calculator provide?
A: The calculator provides results with 6 decimal places precision for accurate geometric calculations.