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The Circumsphere Radius of a Great Dodecahedron is the radius of the sphere that contains the polyhedron in such a way that all its vertices lie on the sphere's surface. It represents the distance from the center of the polyhedron to any of its vertices.
The calculator uses the formula:
Where:
Explanation: This formula calculates the circumsphere radius based on the total surface area of the Great Dodecahedron, incorporating mathematical constants related to its geometric properties.
Details: Calculating the circumsphere radius is essential for understanding the spatial dimensions of the Great Dodecahedron, its relationship with enclosing spheres, and for various applications in geometry, architecture, and 3D modeling.
Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the circumsphere radius based on the provided surface area.
Q1: What is a Great Dodecahedron?
A: A Great Dodecahedron is a Kepler-Poinsot polyhedron with 12 pentagonal faces that intersect each other.
Q2: How is circumsphere radius different from insphere radius?
A: Circumsphere radius touches all vertices, while insphere radius touches all faces from inside the polyhedron.
Q3: What units should I use for the calculation?
A: Use consistent units (preferably meters for length and square meters for area) for accurate results.
Q4: Can this formula be used for regular dodecahedrons?
A: No, this formula is specifically for the Great Dodecahedron, which has different geometric properties than regular dodecahedrons.
Q5: What if I have the edge length instead of surface area?
A: Different formulas exist for calculating circumsphere radius from edge length. This calculator specifically uses the surface area-based formula.