1. What is the Edge Length of Octahedron Formula?

The formula calculates the edge length of a regular octahedron given its total surface area. An octahedron is a polyhedron with eight faces, all of which are equilateral triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge length of the octahedron (m)
• \( TSA \) — Total surface area of the octahedron (m²)

Explanation: The formula derives from the relationship between the edge length and total surface area of a regular octahedron, which consists of eight equilateral triangles.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from surface area is essential in geometry, 3D modeling, and material science for determining the dimensions of octahedral structures and understanding their spatial properties.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular octahedron?
A: A regular octahedron is a polyhedron with eight equilateral triangular faces, twelve edges, and six vertices.

Q2: Why is there a √3 in the denominator?
A: The √3 comes from the area formula of an equilateral triangle (Area = (√3/4) × side²), which is used to calculate the total surface area.

Q3: Can this formula be used for irregular octahedrons?
A: No, this formula applies only to regular octahedrons where all edges are equal and all faces are congruent equilateral triangles.

Q4: What are the units for the result?
A: The edge length result will be in meters, matching the input unit of surface area (m²).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular octahedrons, assuming precise input values.