Midsphere Radius of Triakis Tetrahedron given Pyramidal Edge Length Calculator

Formula Used:

\[ r_m = \frac{\sqrt{2}}{4} \times \frac{5 \times l_e(Pyramid)}{3} \]

Midsphere Radius:

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1. What is Midsphere Radius of Triakis Tetrahedron?

The Midsphere Radius of a Triakis Tetrahedron is defined as a straight line connecting the center and any point on the midsphere of the Triakis Tetrahedron. It represents the radius of the sphere that is tangent to all edges of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_m = \frac{\sqrt{2}}{4} \times \frac{5 \times l_e(Pyramid)}{3} \]

Where:

\( r_m \) — Midsphere Radius (m)
\( l_e(Pyramid) \) — Pyramidal Edge Length (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the midsphere radius based on the pyramidal edge length of the Triakis Tetrahedron, using the mathematical constant √2 and specific coefficients.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the Triakis Tetrahedron, determining its size relationships, and for various applications in crystallography and molecular modeling.

4. Using the Calculator

Tips: Enter the pyramidal edge length in meters. The value must be positive and greater than zero. The calculator will compute the corresponding midsphere radius.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that can be seen as a tetrahedron with triangular pyramids added to each face.

Q2: How is midsphere radius different from insphere radius?
A: The midsphere is tangent to all edges of the polyhedron, while the insphere is tangent to all faces. They represent different geometric properties.

Q3: What are typical values for pyramidal edge length?
A: The pyramidal edge length depends on the specific Triakis Tetrahedron being measured and can vary widely based on the application.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Tetrahedron. Other polyhedra have different formulas for calculating their midsphere radii.

Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most geometric and engineering applications.