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The Volume of Tetrakis Hexahedron is the quantity of three-dimensional space enclosed by the entire surface of the Tetrakis Hexahedron. It is a Catalan solid that is dual to the truncated octahedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the volume of a Tetrakis Hexahedron based on its total surface area, using the mathematical relationship between surface area and volume for this specific polyhedron.
Details: Calculating the volume of geometric solids is fundamental in various fields including mathematics, engineering, architecture, and material science. It helps in determining capacity, material requirements, and structural properties.
Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding volume in cubic meters.
Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with a square pyramid on each face. 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 in the formula due to the geometric properties and mathematical relationships inherent in the Tetrakis Hexahedron's structure.
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the Tetrakis Hexahedron only. Other polyhedra have different volume formulas based on their unique geometric properties.
Q4: What are the practical applications of this calculation?
A: This calculation is useful in crystallography, architectural design, game development (for 3D modeling), and any field that requires working with this specific polyhedral shape.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect Tetrakis Hexahedron. The accuracy in practical applications depends on the precision of the input surface area measurement.