Edge Length Of Peaks Of Stellated Octahedron Given Total Surface Area Calculator

Formula Used:

\[ Edge\ Length\ of\ Peaks\ of\ Stellated\ Octahedron = \frac{1}{2} \times \sqrt{\frac{2 \times Total\ Surface\ Area\ of\ Stellated\ Octahedron}{3 \times \sqrt{3}}} \]

Edge Length of Peaks of Stellated Octahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 an important geometric measurement in understanding the structure of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ Edge\ Length = \frac{1}{2} \times \sqrt{\frac{2 \times TSA}{3 \times \sqrt{3}}} \]

Where:

\( TSA \) — Total Surface Area of Stellated Octahedron (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the edge length of the tetrahedral peaks based on the total surface area of the stellated octahedron, using geometric relationships and mathematical constants.

3. Importance of Edge Length Calculation

Details: Calculating the edge length of peaks is crucial for understanding the geometric properties of stellated octahedrons, which have applications in crystallography, molecular modeling, and architectural design. It helps in determining the precise dimensions and proportions of this complex polyhedral structure.

4. Using the Calculator

Tips: Enter the total surface area of the stellated octahedron in square meters. The value must be positive and non-zero. The calculator will automatically compute the edge length of the peaks.

5. Frequently Asked Questions (FAQ)

Q1: What is a stellated octahedron?
A: A stellated octahedron is a polyhedron formed by attaching tetrahedral pyramids to each face of a regular octahedron, creating a star-like shape with 14 faces (8 triangular and 6 square).

Q2: How is this different from a regular octahedron?
A: While a regular octahedron has 8 triangular faces, a stellated octahedron has additional tetrahedral peaks attached to each face, creating a more complex structure with both triangular and square faces.

Q3: What are practical applications of this calculation?
A: This calculation is useful in crystallography for understanding crystal structures, in architectural design for creating complex geometric forms, and in mathematical education for studying polyhedral geometry.

Q4: Are there limitations to this formula?
A: This formula assumes a perfect geometric stellated octahedron with regular tetrahedral peaks. It may not be accurate for irregular or distorted shapes.

Q5: Can this formula be used for other polyhedrons?
A: No, this specific formula is designed specifically for calculating the edge length of peaks in a stellated octahedron based on its total surface area.