1. What is Pyramidal Edge Length of Triakis Octahedron?

The Pyramidal Edge Length of a Triakis Octahedron refers to the length of the edges that form the pyramidal components attached to each face of the base octahedron in this Catalan solid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_{pyramid} \) — Pyramidal Edge Length (m)
• \( TSA \) — Total Surface Area (m²)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the pyramidal edge length based on the total surface area of the Triakis Octahedron, using geometric relationships specific to this polyhedron.

3. Importance of Pyramidal Edge Length Calculation

Details: Calculating the pyramidal edge length is essential for understanding the geometric properties of Triakis Octahedron, including its symmetry, volume, and other dimensional characteristics.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that can be formed by attaching square pyramids to each face of a regular octahedron.

Q2: How is this different from a regular octahedron?
A: While a regular octahedron has 8 triangular faces, a Triakis Octahedron has 24 isosceles triangular faces due to the added pyramids.

Q3: What are the practical applications of this calculation?
A: This calculation is used in geometry, crystallography, architecture, and 3D modeling where precise dimensional relationships are required.

Q4: Are there limitations to this formula?
A: This formula assumes a perfect Triakis Octahedron shape and may not apply to distorted or irregular variations of the polyhedron.

Q5: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Octahedron due to its unique geometric properties and symmetry.