Pyramidal Edge Length of Triakis Tetrahedron given Midsphere Radius Calculator

Formula Used:

\[ l_{pyramid} = \frac{12}{5\sqrt{2}} \times r_m \]

Pyramidal Edge Length of Triakis Tetrahedron:

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1. What is Pyramidal Edge Length of Triakis Tetrahedron?

The Pyramidal Edge Length of Triakis Tetrahedron is the length of the line connecting any two adjacent vertices of pyramid of Triakis Tetrahedron. It is an important geometric parameter in the study of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{pyramid} = \frac{12}{5\sqrt{2}} \times r_m \]

Where:

\( l_{pyramid} \) — Pyramidal Edge Length of Triakis Tetrahedron (m)
\( r_m \) — Midsphere Radius of Triakis Tetrahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula establishes a direct proportional relationship between the pyramidal edge length and the midsphere radius of the Triakis Tetrahedron.

3. Importance of Pyramidal Edge Length Calculation

Details: Calculating the pyramidal edge length is crucial for understanding the geometric properties of Triakis Tetrahedron, including its surface area, volume, and other dimensional relationships. It's particularly important in crystallography, materials science, and geometric modeling.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding pyramidal edge length using the established mathematical relationship.

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 is the midsphere radius?
A: The midsphere radius is the radius of a sphere that is tangent to all edges of the polyhedron.

Q3: 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.

Q4: What are the practical applications of this calculation?
A: This calculation is used in various fields including crystallography, architectural design, and 3D modeling where precise geometric relationships are required.

Q5: How accurate is this formula?
A: The formula is mathematically exact and provides precise results when accurate input values are provided.