Home
Back
Height of Tetrakis Hexahedron Formula:
| From: | To: |
The Height of Tetrakis Hexahedron is the vertical distance from any vertex of the Tetrakis Hexahedron to the face which is directly opposite to that vertex. It is an important geometric measurement in this polyhedral structure.
The calculator uses the formula:
Where:
Explanation: This formula calculates the height based on the surface to volume ratio of the Tetrakis Hexahedron, using the mathematical constant √5.
Details: Calculating the height of a Tetrakis Hexahedron is important in geometry, crystallography, and architectural design where this polyhedral form is used. It helps in understanding the spatial dimensions and proportions of the structure.
Tips: Enter the surface to volume ratio in 1/m. 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, 14 vertices, and 36 edges.
Q2: Why is √5 used in the formula?
A: The square root of 5 appears naturally in the geometry of the Tetrakis Hexahedron due to its specific proportions and angles between faces.
Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the size of the Tetrakis Hexahedron. Smaller structures have higher ratios, while larger ones have lower ratios.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different geometric relationships.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for an ideal Tetrakis Hexahedron. Real-world applications may require adjustments for material thickness or manufacturing tolerances.