Home
Back
Total Surface Area Formula:
| From: | To: |
The Total Surface Area of a Rhombic Dodecahedron is the total quantity of plane enclosed on the entire surface of this polyhedron. A Rhombic Dodecahedron is a convex polyhedron with 12 congruent rhombic faces, 14 vertices, and 24 edges.
The calculator uses the formula:
Where:
Explanation: The formula calculates the total surface area by multiplying 8 times the square root of 2 times the square of the edge length.
Details: Calculating the surface area of geometric solids is crucial in various fields including architecture, materials science, and engineering. For Rhombic Dodecahedrons, this calculation helps in determining material requirements, heat transfer properties, and structural analysis.
Tips: Enter the edge length in meters. The value must be positive and valid. The calculator will compute the total surface area using the mathematical formula.
Q1: What is a Rhombic Dodecahedron?
A: A Rhombic Dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It is the dual polyhedron of the cuboctahedron and occurs in nature as a crystal form.
Q2: Why is the formula 8√2 × le²?
A: This formula is derived from the geometric properties of the Rhombic Dodecahedron. Each of the 12 rhombic faces has an area of (√3/2) × le², and when summed up and simplified, it results in 8√2 × le².
Q3: What units should I use for edge length?
A: The edge length should be in meters (m) for the surface area to be in square meters (m²). You can convert from other units as needed.
Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for edge length with up to 4 decimal places precision.
Q5: What are some real-world applications of Rhombic Dodecahedrons?
A: Rhombic Dodecahedrons are used in crystallography, packaging design, architectural structures, and as dice in some board games due to their symmetrical properties.