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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 is a key geometric measurement in understanding the structure of this complex polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula relates the pentagram chord length to the circumradius of the Small Stellated Dodecahedron through a precise mathematical relationship involving the golden ratio and square roots.
Details: Calculating the pentagram chord is essential for understanding the geometric properties of the Small Stellated Dodecahedron, including its symmetry, proportions, and relationships between different elements of its structure.
Tips: Enter the circumradius of the Small Stellated Dodecahedron in meters. The value must be positive and greater than zero. The calculator will compute the corresponding pentagram chord length.
Q1: What is a Small Stellated Dodecahedron?
A: The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron that consists of 12 pentagram faces with five pentagrams meeting at each vertex.
Q2: How is the circumradius defined for this polyhedron?
A: The circumradius is the radius of the sphere that contains the Small Stellated Dodecahedron such that all vertices lie on the sphere's surface.
Q3: What is the significance of the golden ratio in this formula?
A: The golden ratio (φ = (1+√5)/2 ≈ 1.618) appears implicitly in the formula through the √5 terms, reflecting the fundamental role of this mathematical constant in pentagonal symmetry.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Small Stellated Dodecahedron due to its unique geometric properties and symmetry.
Q5: What precision should I expect from the calculation?
A: The calculator provides results with 12 decimal places of precision, which is sufficient for most geometric and mathematical applications involving this polyhedron.