Edge Length Of Peaks Of Stellated Octahedron Given Circumsphere Radius Calculator

Formula Used:

\[ l_{Peaks} = \frac{1}{2} \times \frac{4 \times r_c}{\sqrt{6}} \]

Edge Length of Peaks of Stellated Octahedron:

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1. What is Edge Length of Peaks of Stellated Octahedron?

The Edge Length of Peaks of Stellated Octahedron refers to the length of any of the edges of the tetrahedral shaped peaks attached on the faces of octahedron to form the Stellated Octahedron. It is a crucial geometric measurement in understanding the structure of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Peaks} = \frac{1}{2} \times \frac{4 \times r_c}{\sqrt{6}} \]

Where:

\( l_{Peaks} \) — Edge Length of Peaks of Stellated Octahedron (m)
\( r_c \) — Circumsphere Radius of Stellated Octahedron (m)
\( \sqrt{6} \) — Square root of 6 (approximately 2.44949)

Explanation: This formula calculates the edge length of the tetrahedral peaks based on the circumsphere radius that contains the entire stellated octahedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length of peaks is essential for understanding the geometric properties, volume calculations, and structural analysis of stellated octahedrons in mathematical modeling and architectural design.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding edge length of the tetrahedral peaks.

5. Frequently Asked Questions (FAQ)

Q1: What is a Stellated Octahedron?
A: A stellated octahedron is a polyhedron formed by attaching tetrahedral peaks to each face of a regular octahedron, creating a star-like shape.

Q2: What is the circumsphere radius?
A: The circumsphere radius is the radius of the sphere that contains the entire stellated octahedron with all vertices lying on the sphere's surface.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to the stellated octahedron and its geometric properties.

Q4: What are practical applications of this calculation?
A: This calculation is used in geometric modeling, architectural design, crystal structure analysis, and mathematical education.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise when using the exact formula, though practical measurements may have some margin of error.