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Height of Gyrobifastigium Given Surface to Volume Ratio Calculator

Formula Used:

\[ h = \frac{4 + \sqrt{3}}{RA/V/2} \]

1/m

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1. What is Height of Gyrobifastigium?

The height of a Gyrobifastigium is the vertical distance between its lowest and highest points. It is an important geometric measurement that helps characterize this specific polyhedral shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{4 + \sqrt{3}}{RA/V/2} \]

Where:

Explanation: This formula calculates the height of a Gyrobifastigium based on its surface to volume ratio, incorporating the mathematical constant √3.

3. Importance of Height Calculation

Details: Calculating the height of a Gyrobifastigium is essential for understanding its geometric properties, volume calculations, and spatial relationships in three-dimensional geometry applications.

4. Using the Calculator

Tips: Enter the surface to volume ratio value in 1/meter. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Gyrobifastigium?
A: A Gyrobifastigium is a Johnson solid formed by attaching two triangular prisms base-to-base with a 90-degree rotation.

Q2: Why does the formula include √3?
A: The √3 constant appears due to the triangular face geometry and specific angle relationships within the Gyrobifastigium structure.

Q3: What are typical height values for Gyrobifastigium?
A: Height values vary depending on the surface to volume ratio, but typically range based on the specific dimensions of the polyhedron.

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

Q5: What units should I use for input and output?
A: Input should be in 1/meter for surface to volume ratio, and output will be in meters for height.

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