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The Pentagram Chord of Great Stellated Dodecahedron is the distance between any pair of non-adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron. It represents a key geometric measurement in this complex polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the pentagram chord length based on the total surface area of the Great Stellated Dodecahedron, incorporating the mathematical constant φ (phi) through the (2+√5) term.
Details: Calculating the pentagram chord is essential for understanding the geometric properties of the Great Stellated Dodecahedron, which has applications in mathematical research, architectural design, and artistic patterns based on sacred geometry.
Tips: Enter the total surface area of the Great Stellated Dodecahedron in square meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a Great Stellated Dodecahedron?
A: The Great Stellated Dodecahedron is one of the Kepler-Poinsot polyhedra, formed by extending the faces of a regular dodecahedron until they intersect to form star-shaped faces.
Q2: How is this different from a regular dodecahedron?
A: While both are based on the dodecahedron, the Great Stellated Dodecahedron has star-shaped faces and more complex geometry with intersecting planes.
Q3: What practical applications does this calculation have?
A: This calculation is primarily used in mathematical research, but also finds applications in architectural design, crystalography studies, and creating complex geometric art.
Q4: Are there limitations to this formula?
A: The formula assumes a perfect Great Stellated Dodecahedron with mathematically precise proportions and may not account for physical imperfections in real-world objects.
Q5: Can this formula be used for other polyhedra?
A: No, this specific formula is derived specifically for the Great Stellated Dodecahedron and its unique geometric properties.