Pyramidal Edge Length Of Triakis Octahedron Given Midsphere Radius Calculator

Formula Used:

\[ l_{pyramid} = (2 - \sqrt{2}) \times 2 \times r_m \]

Pyramidal Edge Length of Triakis Octahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Pyramidal Edge Length of Triakis Octahedron?

The Pyramidal Edge Length of Triakis Octahedron is the length of the line connecting any two adjacent vertices of pyramid of Triakis Octahedron. It is a key geometric parameter in understanding the structure of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{pyramid} = (2 - \sqrt{2}) \times 2 \times r_m \]

Where:

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

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

3. Importance of Pyramidal Edge Length Calculation

Details: Calculating the pyramidal edge length is essential for geometric analysis, 3D modeling, and understanding the structural properties of Triakis Octahedron in various mathematical and engineering applications.

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.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that can be seen as an octahedron with a pyramid added to each face, creating a polyhedron with 24 isosceles triangular faces.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Why is √2 used in the formula?
A: The square root of 2 appears naturally in geometric calculations involving right angles and is fundamental to the geometry of the Triakis Octahedron.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Octahedron and its relationship between pyramidal edge length and midsphere radius.

Q5: What are practical applications of this calculation?
A: This calculation is used in crystallography, architecture, 3D computer graphics, and mathematical modeling where precise geometric relationships are required.