1. What is Volume of Triakis Octahedron?

The Volume of Triakis Octahedron is the quantity of three-dimensional space enclosed by the entire surface of the Triakis Octahedron. It is a Catalan solid that can be derived from the octahedron by adding a square pyramid to each face.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Triakis Octahedron (m³)
• \( r_i \) — Insphere Radius of Triakis Octahedron (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the volume of a Triakis Octahedron based on its insphere radius, using mathematical constants and geometric relationships.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including mathematics, engineering, architecture, and 3D modeling. It helps in understanding spatial properties and material requirements.

4. Using the Calculator

Tips: Enter the insphere radius in 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 results from adding a square pyramid to each face of a regular octahedron. It has 24 isosceles triangular faces.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can be contained within the Triakis Octahedron, touching all its faces.

Q3: What are the units of measurement?
A: The calculator uses meters for length and cubic meters for volume. Ensure consistent units for accurate results.

Q4: Can this calculator handle different units?
A: The calculator is designed for meters. If using other units, convert to meters first or adjust the result accordingly.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the given formula. The result is rounded to 6 decimal places for practical use.