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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 complex polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula relates the ridge length to the pyramidal height using the golden ratio and geometric properties of the dodecahedron.
Details: Calculating the ridge length is essential for understanding the geometric properties and spatial relationships within the Small Stellated Dodecahedron, which has applications in mathematical modeling, crystallography, and architectural design.
Tips: Enter the pyramidal height in meters. The value must be positive and greater than zero. The calculator will compute the corresponding ridge length.
Q1: What is a Small Stellated Dodecahedron?
A: It's a Kepler-Poinsot polyhedron that consists of 12 pentagram faces with the Schläfli symbol {5/2,5}. It's one of four regular star polyhedra.
Q2: How is this different from a regular dodecahedron?
A: While both have 12 faces, the Small Stellated Dodecahedron has star-shaped pentagram faces rather than regular pentagons, creating a more complex structure with protruding points.
Q3: What practical applications does this calculation have?
A: This geometric calculation is used in mathematical research, architectural design of complex structures, and in understanding crystal formations in materials science.
Q4: Why does the formula include the golden ratio?
A: The golden ratio (φ = (1+√5)/2) appears naturally in pentagonal symmetry, which is fundamental to dodecahedral structures.
Q5: Can this calculator handle very large or very small values?
A: The calculator can handle a wide range of positive values, though extremely large values might be limited by computational precision.