1. What is Volume of Triakis Icosahedron?

The Volume of Triakis Icosahedron is the quantity of three dimensional space enclosed by the entire surface of Triakis Icosahedron. It is a Catalan solid that can be derived from the icosahedron by adding pyramids to each face.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Triakis Icosahedron (m³)
• \( r_i \) — Insphere Radius (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the volume based on the insphere radius, incorporating mathematical constants and geometric relationships specific to the Triakis Icosahedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, and various scientific fields. It helps in understanding spatial properties, material requirements, and structural characteristics of three-dimensional objects.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero. The calculator will compute the volume using the precise mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that can be obtained by adding a triangular pyramid to each face of a regular icosahedron.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the sphere that is tangent to all faces of the polyhedron, contained within it.

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

Q4: How accurate is the calculation?
A: The calculation uses precise mathematical constants and formulas, providing high accuracy for valid inputs.

Q5: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Triakis Icosahedron using its unique volume formula.