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The height of an elongated dodecahedron is the vertical distance from the highest point to the lowest point of this polyhedron. It is an important geometric measurement used in various mathematical and engineering applications.
The calculator uses the formula:
Where:
Explanation: The formula calculates the height based on the surface to volume ratio of the elongated dodecahedron, incorporating the mathematical constant \( \sqrt{5} \).
Details: Calculating the height of an elongated dodecahedron is important in geometry, architecture, and material science for understanding the spatial properties and proportions of this specific polyhedral shape.
Tips: Enter the surface to volume ratio in 1/m. The value must be positive and greater than zero for accurate calculation.
Q1: What is an elongated dodecahedron?
A: An elongated dodecahedron is a polyhedron with 12 faces that has been stretched along one axis, creating a longer dimension in one direction.
Q2: Why is the square root of 5 used in the formula?
A: The square root of 5 appears naturally in the geometry of dodecahedrons and is related to the golden ratio, which is fundamental to their proportions.
Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the specific dimensions of the elongated dodecahedron, but generally ranges from 0.1 to 10 1/m for most practical applications.
Q4: Can this formula be used for regular dodecahedrons?
A: No, this specific formula applies only to elongated dodecahedrons. Regular dodecahedrons have different geometric properties and formulas.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input surface to volume ratio, assuming the shape is a perfect elongated dodecahedron.