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The Surface to Volume Ratio of Tetrakis Hexahedron is the numerical ratio of the total surface area to the volume of this specific polyhedron. It's an important geometric property that relates the external surface area to the internal volume of the shape.
The calculator uses the mathematical formula:
Where:
Explanation: This formula calculates the surface to volume ratio based on the total surface area of the Tetrakis Hexahedron, incorporating mathematical constants specific to this geometric shape.
Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and engineering. It helps understand properties like heat transfer, reaction rates, and structural efficiency in geometric shapes.
Tips: Enter the total surface area of the Tetrakis Hexahedron in square meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that is the dual of the truncated octahedron. It has 24 faces, 36 edges, and 14 vertices.
Q2: Why is the square root of 5 used in the formula?
A: The square root of 5 appears naturally in the geometric relationships and proportions of the Tetrakis Hexahedron, making it an essential mathematical constant in calculations involving this shape.
Q3: What are typical values for surface to volume ratio?
A: The ratio varies significantly based on the size of the Tetrakis Hexahedron. Smaller objects generally have higher surface to volume ratios than larger ones of the same shape.
Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for the Tetrakis Hexahedron. Other polyhedra have different mathematical relationships for their surface to volume ratios.
Q5: What units should I use for input?
A: The calculator expects the total surface area in square meters, and it returns the surface to volume ratio in reciprocal meters (1/m).