Insphere Radius of Triakis Tetrahedron given Height Calculator

Formula Used:

\[ r_i = \frac{5}{4} \times \sqrt{\frac{2}{11}} \times \frac{1}{\sqrt{6}} \times h \]

Insphere Radius of Triakis Tetrahedron:

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1. What is Insphere Radius of Triakis Tetrahedron?

The Insphere Radius of 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:

\[ r_i = \frac{5}{4} \times \sqrt{\frac{2}{11}} \times \frac{1}{\sqrt{6}} \times h \]

Where:

\( r_i \) — Insphere Radius of Triakis Tetrahedron (m)
\( h \) — Height of Triakis Tetrahedron (m)

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

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and 3D modeling as it helps determine the size of the largest inscribed sphere within the polyhedron, which has applications in material science, packaging, and spatial analysis.

4. Using the Calculator

Tips: Enter the height of the Triakis Tetrahedron in meters. The value must be positive and greater than zero for accurate calculation.

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 a triangular pyramid to each face of a regular tetrahedron.

Q2: What units should I use for the height?
A: The calculator uses meters as the default unit, but you can use any consistent unit as long as you maintain consistency throughout your calculations.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is designed specifically for the Triakis Tetrahedron and may not apply to other polyhedral shapes.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula, provided the input values are accurate.

Q5: What are practical applications of this calculation?
A: This calculation is useful in fields such as crystallography, architectural design, and 3D modeling where precise geometric measurements are required.