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The edge length of a Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of this polyhedron. It is a fundamental geometric measurement that helps define the size and proportions of this complex three-dimensional shape.
The calculator uses the mathematical formula:
Where:
Explanation: This formula derives from the geometric properties of the Small Stellated Dodecahedron, relating its volume to its edge length through mathematical constants and relationships specific to this polyhedron.
Details: Calculating the edge length from volume is essential for geometric modeling, architectural design, and understanding the spatial properties of this complex polyhedron. It helps in material estimation, structural analysis, and mathematical studies of polyhedral geometry.
Tips: Enter the volume of the Small Stellated Dodecahedron in cubic meters. The volume must be a positive value greater than zero. The calculator will compute the corresponding edge length.
Q1: What is a Small Stellated Dodecahedron?
A: It's a Kepler-Poinsot polyhedron formed by extending the faces of a regular dodecahedron until they intersect, creating a star-shaped polyhedron with 12 pentagram faces.
Q2: Why is the formula so complex?
A: The complexity arises from the mathematical relationships between volume and edge length in this specific polyhedron, involving the golden ratio and other geometric constants.
Q3: Can this calculator handle different units?
A: The calculator uses meters for length and cubic meters for volume. For other units, convert your measurements to these standard units first.
Q4: What is the typical range of edge lengths?
A: The edge length can vary significantly depending on the volume, but it follows a cubic relationship with volume (edge ∝ ∛volume).
Q5: Are there practical applications of this calculation?
A: Yes, in architecture, jewelry design, mathematical education, and anywhere this specific geometric shape is used or studied.