Insphere Radius of Triakis Tetrahedron Calculator

Formula Used:

\[ r_i = \frac{3}{4} \times l_e(Tetrahedron) \times \sqrt{\frac{2}{11}} \]

Insphere Radius:

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1. What is Insphere Radius of Triakis Tetrahedron?

The Insphere Radius of Triakis Tetrahedron is defined as straight line connecting incenter and any point on insphere of Triakis Tetrahedron. It represents the radius of the largest sphere that can be inscribed within the Triakis Tetrahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \frac{3}{4} \times l_e(Tetrahedron) \times \sqrt{\frac{2}{11}} \]

Where:

\( r_i \) — Insphere Radius of Triakis Tetrahedron (m)
\( l_e(Tetrahedron) \) — Tetrahedral Edge Length of Triakis Tetrahedron (m)

Explanation: This formula calculates the radius of the inscribed sphere based on the tetrahedral edge length of the Triakis Tetrahedron.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and 3D modeling as it helps determine the maximum size of a sphere that can fit inside the Triakis Tetrahedron without intersecting its faces.

4. Using the Calculator

Tips: Enter the tetrahedral edge length in meters. The value must be positive and greater than zero.

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: How is this formula derived?
A: The formula is derived from geometric properties and relationships between the insphere radius and the tetrahedral edge length of the Triakis Tetrahedron.

Q3: What are the units of measurement?
A: Both the insphere radius and tetrahedral edge length are measured in meters (m), though any consistent unit system can be used.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.

Q5: What is the significance of the square root term in the formula?
A: The square root term \( \sqrt{\frac{2}{11}} \) is a constant factor that relates the tetrahedral edge length to the insphere radius in the geometric configuration of the Triakis Tetrahedron.