Volume of Tetrakis Hexahedron Given Height Calculator

Tetrakis Hexahedron Volume Formula:

\[ V = \frac{3}{2} \times \left( \frac{2 \times h}{3} \right)^3 \]

Volume of Tetrakis Hexahedron:

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1. What is the Tetrakis Hexahedron Volume Formula?

The Tetrakis Hexahedron is a Catalan solid that can be derived from a cube by adding a square pyramid on each face. The volume formula calculates the three-dimensional space enclosed by the entire surface of the Tetrakis Hexahedron based on its height.

2. How Does the Calculator Work?

The calculator uses the Tetrakis Hexahedron volume formula:

\[ V = \frac{3}{2} \times \left( \frac{2 \times h}{3} \right)^3 \]

Where:

\( V \) — Volume of Tetrakis Hexahedron (m³)
\( h \) — Height of Tetrakis Hexahedron (m)

Explanation: The formula calculates the volume based on the height measurement of the Tetrakis Hexahedron, which is the vertical distance from any vertex to the opposite face.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including architecture, engineering, material science, and 3D modeling. Accurate volume calculations help in determining capacity, material requirements, and spatial relationships.

4. Using the Calculator

Tips: Enter the height of the Tetrakis Hexahedron in meters. The value must be positive and greater than zero. The calculator will compute the volume in cubic meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid with 24 isosceles triangular faces, 14 vertices, and 36 edges. It's the dual polyhedron of the truncated octahedron.

Q2: How is height defined for a Tetrakis Hexahedron?
A: The height is defined as the vertical distance from any vertex of the Tetrakis Hexahedron to the face which is directly opposite to that vertex.

Q3: 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 requiring precise volume calculations of complex geometric shapes.

Q4: Can this formula be used for irregular shapes?
A: No, this specific formula only applies to regular Tetrakis Hexahedrons where all triangular faces are congruent isosceles triangles.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect Tetrakis Hexahedrons. The accuracy in practical applications depends on the precision of the height measurement.