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The edge length of a rhombic dodecahedron can be calculated from its insphere radius using the mathematical relationship between these geometric properties of the polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula establishes the proportional relationship between the edge length and the insphere radius of a rhombic dodecahedron, with the constant factor derived from the geometric properties of this specific polyhedron.
Details: Calculating the edge length from the insphere radius is important in geometric modeling, crystallography, and materials science where rhombic dodecahedra appear naturally or are used in structural designs.
Tips: Enter the insphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding edge length of the rhombic dodecahedron.
Q1: What is a rhombic dodecahedron?
A: A rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces, 14 vertices, and 24 edges. It occurs naturally in some crystal structures.
Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can be contained within the polyhedron, touching all faces tangentially.
Q3: Are there other ways to calculate edge length?
A: Yes, edge length can also be calculated from other parameters such as volume, surface area, or midsphere radius using different formulas.
Q4: What units should I use?
A: The calculator uses meters, but the formula works with any consistent unit system (cm, mm, inches, etc.) as long as both input and output use the same units.
Q5: Is this formula specific to rhombic dodecahedra?
A: Yes, this particular formula applies only to rhombic dodecahedra and reflects the unique geometric relationships of this specific polyhedron.