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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 that helps define the overall dimensions and proportions of this specific polyhedral shape.
The calculator uses the mathematical formula:
Where:
Explanation: This formula establishes the precise mathematical relationship between the width and height of a regular elongated dodecahedron, derived from its geometric properties and symmetry.
Details: The formula \( h = \frac{w}{\sqrt{3}} \) is derived from the geometric properties of the elongated dodecahedron. The square root of 3 appears due to the triangular faces and the specific angles formed between different edges and faces of this polyhedron.
Tips: Enter the width of the elongated dodecahedron in meters. The value must be positive and greater than zero. The calculator will automatically compute the corresponding height based on the mathematical relationship.
Q1: What is an elongated dodecahedron?
A: An elongated dodecahedron is a polyhedron formed by elongating a regular dodecahedron along one of its axes, creating a shape with 12 pentagonal faces and additional rectangular faces.
Q2: Why is the square root of 3 used in this formula?
A: The square root of 3 appears naturally in geometry, particularly in relationships involving equilateral triangles and 30-60-90 triangles, which are fundamental to the structure of the elongated dodecahedron.
Q3: Can this formula be used for irregular elongated dodecahedrons?
A: No, this specific formula applies only to regular elongated dodecahedrons where all edges and angles maintain consistent relationships.
Q4: What are the practical applications of this calculation?
A: This calculation is useful in geometry, architecture, 3D modeling, and any field that requires precise dimensional relationships in polyhedral structures.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal geometric shapes. In practical applications, the accuracy depends on the precision of the input measurement and manufacturing tolerances.