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The Insphere Radius of Rhombic Dodecahedron is the radius of the sphere that is contained by the Rhombic Dodecahedron in such a way that all the faces are just touching the sphere. It represents the largest sphere that can fit inside the polyhedron.
The calculator uses the formula:
Where:
Mathematical Basis: The formula derives from the geometric properties of the rhombic dodecahedron, where the insphere radius is directly proportional to the edge length with a constant factor of √6/3.
Functions Used: sqrt - A square root function that takes a non-negative number as input and returns the square root of the given input number.
Instructions: Enter the edge length of the rhombic dodecahedron in meters. The value must be positive. The calculator will compute the insphere radius using the established geometric relationship.
Q1: What is a Rhombic Dodecahedron?
A: A rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It occurs in nature as the shape of garnet crystals and has applications in geometry and crystallography.
Q2: Why is the constant √6/3 used in the formula?
A: This constant arises from the specific geometric proportions of the rhombic dodecahedron and represents the mathematical relationship between the edge length and the insphere radius.
Q3: Can this formula be used for any polyhedron?
A: No, this specific formula applies only to the rhombic dodecahedron. Different polyhedra have different relationships between edge length and insphere radius.
Q4: What are practical applications of this calculation?
A: This calculation is useful in crystallography, materials science, and geometric modeling where understanding the internal dimensions of rhombic dodecahedral structures is important.
Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect rhombic dodecahedra and provides precise results when accurate edge length measurements are provided.