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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: The formula calculates the pentagram chord based on the edge length of the great stellated dodecahedron, incorporating the mathematical constant related to the golden ratio.
Details: Accurate calculation of the pentagram chord is essential for geometric analysis, architectural design, and mathematical modeling involving the great stellated dodecahedron and its related structures.
Tips: Enter the edge length of the great stellated dodecahedron in meters. The value must be positive and valid.
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.
Q2: What does the pentagram chord represent?
A: The pentagram chord represents the distance between non-adjacent vertices of the pentagram shape that appears on the faces of the great stellated dodecahedron.
Q3: Why is the square root of 5 involved in the formula?
A: The square root of 5 appears due to the mathematical properties of the golden ratio, which is fundamental to the geometry of pentagrams and dodecahedrons.
Q4: 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 complex polyhedra.
Q5: Can this formula be used for other polyhedra?
A: This specific formula is unique to the great stellated dodecahedron. Other polyhedra have their own distinct geometric relationships and formulas.