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The Pentagram Chord of Small Stellated Dodecahedron is the distance between any pair of non-adjacent peak vertices of the pentagram corresponding to the Small Stellated Dodecahedron. It represents a key geometric measurement in this complex polyhedron.
The calculator uses the formula:
Where:
Explanation: The formula calculates the pentagram chord based on the edge length of the small stellated dodecahedron, incorporating the mathematical constant φ (phi) through the expression (2 + √5).
Details: Calculating the pentagram chord is essential for understanding the geometric properties and proportions of the small stellated dodecahedron, which has significance in mathematical geometry, crystallography, and architectural design.
Tips: Enter the edge length of the small stellated dodecahedron in meters. The value must be positive and greater than zero.
Q1: What is a small stellated dodecahedron?
A: The small stellated dodecahedron is 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 (2 + √5) used?
A: The expression (2 + √5) is derived from the golden ratio φ, where φ = (1 + √5)/2, and is fundamental to the geometry of pentagrams and dodecahedrons.
Q3: What are the practical applications of this calculation?
A: This calculation is used in mathematical research, geometric modeling, architectural design, and in understanding the properties of crystalline structures.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the small stellated dodecahedron and its pentagram chords.
Q5: How accurate is the calculation?
A: The calculation is mathematically exact when using the precise value of √5, though practical measurements may have some degree of error.