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The Ridge Length of Small Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Small Stellated Dodecahedron. It is an important geometric measurement in this polyhedral structure.
The calculator uses the formula:
Where:
Explanation: This formula calculates the ridge length based on the pentagram chord measurement, using the golden ratio properties inherent in the dodecahedron's geometry.
Details: Accurate ridge length calculation is crucial for geometric modeling, architectural design, and mathematical analysis of polyhedral structures. It helps in understanding the spatial relationships and proportions within the Small Stellated Dodecahedron.
Tips: Enter the pentagram chord value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding ridge length using the mathematical relationship between these two measurements.
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. It is created by extending the faces of a regular dodecahedron until they intersect.
Q2: How is the pentagram chord defined?
A: The pentagram chord is the distance between any pair of non-adjacent peak vertices of the pentagram corresponding to the Small Stellated Dodecahedron.
Q3: What is the significance of the golden ratio in this formula?
A: The golden ratio (φ = (1+√5)/2) appears frequently in the geometry of regular polyhedra, particularly in dodecahedra and icosahedra, due to their five-fold symmetry.
Q4: Can this calculator be used for other polyhedral structures?
A: No, this specific formula applies only to the Small Stellated Dodecahedron and its geometric properties.
Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most geometric and architectural applications.