1. What is the Height of Gyrobifastigium?

The Height of Gyrobifastigium is the vertical distance between the lowest and highest points of this Johnson solid. It is an important geometric measurement that helps characterize the three-dimensional structure of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Gyrobifastigium (m)
• \( l_e \) — Edge Length of Gyrobifastigium (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula establishes a direct proportional relationship between the edge length and the height of the gyrobifastigium, with the square root of 3 serving as the constant of proportionality.

3. Importance of Height Calculation

Details: Calculating the height of a gyrobifastigium is essential for understanding its spatial dimensions, volume calculations, and for applications in architecture, crystallography, and mathematical modeling of polyhedral structures.

4. Using the Calculator

Tips: Enter the edge length of the gyrobifastigium in meters. The value must be positive and non-zero. The calculator will automatically compute the corresponding height.

5. Frequently Asked Questions (FAQ)

Q1: What is a Gyrobifastigium?
A: A gyrobifastigium is a Johnson solid constructed by attaching two triangular prisms along their square faces with a 90-degree rotation.

Q2: Why is the square root of 3 used in the formula?
A: The square root of 3 appears due to the geometric relationships and trigonometric properties inherent in the structure of the gyrobifastigium.

Q3: Can this formula be used for any polyhedron?
A: No, this specific formula applies only to the gyrobifastigium. Different polyhedra have different geometric relationships between their edge lengths and heights.

Q4: What are the units of measurement?
A: The calculator uses meters for both input and output, but the formula works with any consistent unit system (cm, mm, inches, etc.).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values. The result's practical accuracy depends on the precision of the edge length measurement.