Formula Used:
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The circumsphere radius of a snub dodecahedron is the radius of the sphere that contains the polyhedron such that all vertices lie on the sphere's surface. It's a fundamental geometric property of this Archimedean solid.
The calculator uses the complex mathematical formula:
Where:
Details: Calculating the circumsphere radius is essential for understanding the spatial dimensions and geometric properties of the snub dodecahedron, which has applications in crystallography, architecture, and mathematical modeling.
Tips: Enter the surface to volume ratio value in m⁻¹. The value must be positive and non-zero. The calculator will compute the corresponding circumsphere radius.
Q1: What is a snub dodecahedron?
A: A snub dodecahedron is an Archimedean solid with 92 faces (12 pentagons and 80 triangles), 150 edges, and 60 vertices.
Q2: Why is the golden ratio used in the formula?
A: The golden ratio appears naturally in the geometry of regular pentagons and dodecahedrons, making it fundamental to calculations involving these shapes.
Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the size of the polyhedron. Smaller polyhedra have higher ratios, while larger ones have lower ratios.
Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for the snub dodecahedron. Other polyhedra have different geometric relationships.
Q5: How accurate is the calculation?
A: The calculation uses precise mathematical constants and should be highly accurate, though rounding may occur in the final result display.