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The height of a Gyrobifastigium is the vertical distance between its lowest and highest points. It's a key dimensional parameter of this Johnson solid, which consists of two triangular prisms attached base-to-base with a 90-degree rotation.
The calculator uses the formula:
Where:
Explanation: This formula derives from the geometric properties of the Gyrobifastigium, relating its height to its volume through a cubic relationship.
Details: Calculating the height is essential for architectural applications, 3D modeling, and understanding the spatial dimensions of this unique polyhedron. It helps in determining the overall proportions and structural characteristics of the shape.
Tips: Enter the volume of the Gyrobifastigium in cubic meters. The value must be positive and non-zero. The calculator will compute the corresponding height based on the mathematical relationship between volume and height.
Q1: What is a Gyrobifastigium?
A: A Gyrobifastigium is a Johnson solid (J26) formed by two triangular prisms attached base-to-base with a 90-degree rotation between them.
Q2: Why is there a square root of 3 in the formula?
A: The √3 factor comes from the triangular face geometry of the Gyrobifastigium, which has equilateral triangle cross-sections.
Q3: Can this formula be used for any volume value?
A: Yes, the formula works for any positive volume value, as it represents the mathematical relationship between volume and height for this specific shape.
Q4: What are the units of measurement?
A: The calculator uses meters for height and cubic meters for volume. Ensure consistent units when inputting values.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect Gyrobifastigium shape. Real-world applications may require considering manufacturing tolerances and material properties.