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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 used in understanding the structure and properties of this complex shape.
The calculator uses the mathematical formula:
Where:
Explanation: This formula derives the edge length from the total surface area using geometric relationships specific to the Small Stellated Dodecahedron.
Details: Calculating the edge length is essential for geometric analysis, architectural applications, and understanding the spatial properties of this complex polyhedron. It helps in determining other geometric parameters and structural integrity.
Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding edge length.
Q1: What is a Small Stellated Dodecahedron?
A: It's a Kepler-Poinsot polyhedron that represents one of the four regular star polyhedra, formed by extending the faces of a regular dodecahedron.
Q2: Why is the formula structured this way?
A: The formula incorporates the mathematical constant φ (phi) and geometric relationships specific to pentagonal symmetry and stellated forms.
Q3: What are typical values for edge length?
A: Edge length values depend on the scale of the polyhedron. For mathematical models, they typically range from centimeters to meters depending on application.
Q4: Can this calculator handle different units?
A: The calculator uses square meters for surface area and meters for edge length. Convert other units to these before calculation.
Q5: What are practical applications of this calculation?
A: Applications include architectural design, mathematical modeling, crystal structure analysis, and educational purposes in geometry.