Height of Gyrobifastigium given Total Surface Area Calculator

Formula Used:

\[ h = \sqrt{3} \times \sqrt{\frac{TSA}{4 + \sqrt{3}}} \]

Height of Gyrobifastigium (h):

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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's an important geometric measurement that helps characterize the three-dimensional properties of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \sqrt{3} \times \sqrt{\frac{TSA}{4 + \sqrt{3}}} \]

Where:

\( h \) — Height of Gyrobifastigium (m)
\( TSA \) — Total Surface Area of Gyrobifastigium (m²)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( 4 + \sqrt{3} \) — Constant value (approximately 5.732)

Explanation: This formula calculates the height based on the total surface area using the mathematical relationship specific to the Gyrobifastigium geometry.

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 complex polyhedra.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding height of the Gyrobifastigium.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the formula structured this way?
A: The formula derives from the geometric properties and surface area relationships specific to the Gyrobifastigium's unique structure.

Q3: What units should I use?
A: Use consistent units - typically meters for length and square meters for area. The calculator will return height in the same length unit.

Q4: Can this formula be used for other polyhedra?
A: No, this formula is specific to the Gyrobifastigium due to its unique geometric properties.

Q5: What if I get an unexpected result?
A: Double-check your input value for total surface area. Ensure it's a positive number that makes geometric sense for a Gyrobifastigium.