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The Circumsphere Radius of Snub Dodecahedron is the radius of the sphere that contains the Snub Dodecahedron in such a way that all the vertices are lying on the sphere. It is an important geometric property of this polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the circumsphere radius based on the given midsphere radius using a specific mathematical relationship unique to the snub dodecahedron.
Details: Calculating the circumsphere radius is crucial for understanding the spatial properties of the snub dodecahedron, its relationship with other geometric elements, and its applications in various mathematical and engineering contexts.
Tips: Enter the midsphere radius value in meters. The value must be positive and valid for accurate calculation.
Q1: What is a Snub Dodecahedron?
A: A snub dodecahedron is an Archimedean solid with 92 faces (80 triangles and 12 pentagons), 150 edges, and 60 vertices.
Q2: What is the difference between circumsphere and midsphere?
A: The circumsphere passes through all vertices of the polyhedron, while the midsphere is tangent to all edges of the polyhedron.
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the snub dodecahedron only. Other polyhedra have different mathematical relationships between their circumsphere and midsphere radii.
Q4: What are practical applications of this calculation?
A: This calculation is used in geometry research, computer graphics, architectural design, and materials science where precise spatial relationships of polyhedra are important.
Q5: How accurate is this formula?
A: The formula is mathematically exact for the snub dodecahedron, providing precise results when accurate input values are provided.