1. What is Insphere Radius of Triakis Tetrahedron?

The Insphere Radius of a Triakis Tetrahedron is defined as the straight line connecting the incenter and any point on the insphere of the Triakis Tetrahedron. It represents the radius of the largest sphere that can fit inside the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius of Triakis Tetrahedron (m)
• \( TSA \) — Total Surface Area of Triakis Tetrahedron (m²)

Explanation: This formula calculates the insphere radius based on the total surface area of the Triakis Tetrahedron, using mathematical constants and square root functions.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and 3D modeling for understanding the spatial properties of polyhedra, determining packing efficiency, and analyzing geometric relationships within complex shapes.

4. Using the Calculator

Tips: Enter the total surface area of the Triakis Tetrahedron in square meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that can be constructed by attaching triangular pyramids to each face of a regular tetrahedron.

Q2: What are the units for the insphere radius?
A: The insphere radius is measured in meters (m), consistent with the input surface area units.

Q3: Can this calculator handle different units?
A: The calculator uses consistent units. Make sure to convert all measurements to square meters for surface area input.

Q4: What is the range of valid input values?
A: The total surface area must be a positive number greater than zero.

Q5: How accurate is the calculation?
A: The calculation provides results with 10 decimal places precision, suitable for most geometric applications.