Insphere Radius of Triakis Tetrahedron given Volume Calculator

Formula Used:

\[ r_i = \frac{3}{4} \times \sqrt{\frac{2}{11}} \times \left( \frac{20 \times V}{3 \times \sqrt{2}} \right)^{\frac{1}{3}} \]

Insphere Radius of Triakis Tetrahedron (rᵢ):

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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 be inscribed within the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \frac{3}{4} \times \sqrt{\frac{2}{11}} \times \left( \frac{20 \times V}{3 \times \sqrt{2}} \right)^{\frac{1}{3}} \]

Where:

\( r_i \) — Insphere Radius of Triakis Tetrahedron (m)
\( V \) — Volume of Triakis Tetrahedron (m³)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the insphere radius based on the volume of the Triakis Tetrahedron, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and materials science for understanding the internal packing properties of polyhedra and their spatial relationships.

4. Using the Calculator

Tips: Enter the volume of the Triakis Tetrahedron in cubic 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 applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, and geometric analysis of polyhedral structures.

Q3: What units should be used for volume?
A: Volume should be entered in cubic meters (m³) for consistent results with the formula.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Tetrahedron due to its unique geometric properties.

Q5: What if I have the edge length instead of volume?
A: You would need to first calculate the volume from the edge length before using this calculator.